Shrimp closed-loop supply chain network design

Behzad Mosallanezhad; Mostafa Hajiaghaei-Keshteli; Chefi Triki

doi:10.1007/s00500-021-05698-1

Shrimp closed-loop supply chain network design

Mosallanezhad, Behzad; Hajiaghaei-Keshteli, Mostafa; Triki, Chefi 2021-03-21 00:00:00 Recent developments in food industries have attracted both academic and industrial practitioners. Shrimp as a well-known, rich, and sought-after seafood, is generally obtained from either marine environments or aquaculture. Central prominence of Shrimp Supply Chain (SSC) is brought about by numerous factors such as high demand, market price, and diverse ﬁsheries or aquaculture locations. In this respect, this paper considers SSC as a set of distribution centers, wholesalers, shrimp processing factories, markets, shrimp waste powder factory, and shrimp waste powder market. Subsequently, a mathematical model is proposed for the SSC, whose aim is to minimize the total cost through the supply chain. The SSC model is NP-hard and is not able to solve large-size problems. Therefore, three well-known metaheuristics accompanied by two hybrid ones are exerted. Moreover, a real-world application with 15 test problems are established to validate the model. Finally, the results conﬁrm that the SSC model and the solution methods are effective and useful to achieve cost savings. Keywords Closed-loop supply chain Supply chain design Metaheuristics Seafood Shrimp 1 Introduction management activities. Signiﬁcantly, it includes coordina- tion and collaboration with channel partners as well, which Over the past two decades, a great deal of attention is can be suppliers, intermediaries, third-party service provi- devoted to varied types and approaches in Supply Chains to ders, and customers. In essence, supply chain management reach a more suitable solution to create competitive integrates supply and demand management within and advantages for companies, governments, and parties. across companies’’ (Hanne and Dornberger 2017). According to the literature, the supply chain is stated as In today’s world, one of the leading sectors in developed series of facilities that provide the ﬁnal products (Haji- and developing countries is food industries. Food produc- aghaei-Keshteli and Sajadifar 2010; Hajiaghaei-Keshteli tion and distribution have become enough efﬁcient in et al 2011). Moreover, the Council of Supply Chain various aspects to satisfy the growing demands (Sharma Management Professionals (CSCMP) deﬁnes the Supply et al. 2018). The Food Supply Chain (FSC) is resemblance Chain Management (SCM) as: ‘‘SCM encompasses the to any other supply chain, since it made up of several planning and management of all activities involved in stages (production, handling and storage, processing and sourcing and procurement, conversion, and all logistic packaging, distribution, and consumption). Final goods move along the FSC from the producers to reach con- sumers through pre- and post-production actions, and under quality and time-conscious work (Govindan et al. 2017; & Cheﬁ Triki [email protected] Wunderlich and Martinez 2018). However, it can be sep- arated in many ways, since poorly timed distribution in Tecnologico de Monterrey, Escuela de Ingenierıa y Ciencias, FSC makes perishable products unusable. It holds, thus, a Puebla, Mexico prominent situation in the global marketplace and has Division of Engineering Management and Decision Sciences, impacts on society and also the economy of countries College of Sciences and Engineering, Hamad Bin Khalifa (Govindan et al. 2017). University, Doha, Qatar Seafood Supply Chain (SFSC) can be classiﬁed as a Department of Engineering Innovation, University of special FSC, that needs momentous consideration. Health Salento, Lecce, Italy 123 7400 B. Mosallanezhad et al. beneﬁts of seafood are hidden to no one. Indeed, scientists chain over the time (Fathollahi-Fard et al. 2017). Nowa- and organizations believe that seafood teems with sub- days, the economic and environmental concerns arising stantial nutritional values and assures food security due to from the growing demand for shrimp has led to a wide- the fact that over a third of global population beneﬁt from spread discussion regarding the performance within the its protein sources. Furthermore, it is predicted that ﬁsh- shrimp supply (Lin and Wu 2016). Shrimp, like any other eries and aquaculture are taken into account as prominent ﬁsh product, is perishable food. Hence, several important protein sources by 2050 as the population increases (Tab- factors have an indispensable inﬂuence on shrimp supply bakh and Freeland-Graves 2016; Schiller et al. 2018). network. Quality of product in distribution, speed, and Among seafoods, shrimps are a main source of protein efﬁciency in the design of supply network, and ﬁnally time and have low hazardous saturated fat and energy, making delivery and maintenance of cold chain result in the them a healthful preference as well as a desirable food commercial success of the supply chain network (Buritica around the world. In many developing countries, shrimps et al. 2017). Consequently, designing and optimizing the are served as a traditional meal and as a luxurious food in SSC network can help governments, investors, and active developed countries (Alam 2016). Over the past years, food parties to satisfy market demands, and to overcome and agricultural organization (FAO) statistics show that obstacles in the supply chain, and in general can boost the consumption of shrimp in developed countries like performance of the whole chain. China, the United States, and the United Kingdom is This study designs a mathematical modeling and opti- sharply increased, whereas in developing countries such as mization structure that focus on the SSC network. To the Iran, this amount is less than a kilogram per capita per year best of our knowledge, there is no prior study involving (See: Fig. 1). mathematical modeling for SSC network design. The main Iran has a prodigious potential of shrimp production in goal of the SSC model is to minimize the total cost. its both freshwater and marine resources, which drives Moreover, since the SSC model is characterized by the from 1800 km long coastline of the Persian Gulf and the hard complexity in solving large-scale problems, three Gulf of Oman and also appropriate condition for the ﬁshery recognized metaheuristic algorithms and two hybrid on this coastline. More than 2000 shrimp species are heuristics are conducted to address this issue and to analyze identiﬁed worldwide, ﬁve of which are caught and aqua- the model. Furthermore, to achieve better performance of cultured in Iran (See: Fig. 2) (Harlioglu and Farhadi 2016; these algorithms, the corresponding parameters are tuned Schiller et al. 2018). by using the Taguchi method. Statistics indicate that 82% of the total global pro- The remainder of this paper is structured as follows. duction of shrimp belongs to the Asian countries such as Section 2 entails the related literature review on FSC and SFSC. Our SSC mathematical model is proposed and for- China, Thailand, Vietnam, Indonesia, Malaysia, India, and Bangladesh. Moreover, Ecuador, Peru, Mexico, mulated in Sect. 3. The solution methods and computa- Honduras, Guatemala, Brazil, Nicaragua, Venezuela, and tional results are reported in Sect. 4 and Sect. 5, Belize have a 16% portion and the rest is owned by respectively. Finally, conclusions and suggestions for Saudi Arabia, Madagascar, and Australia (Alam 2016). future works are addressed in Sect. 6. As FAO ﬁshery statistics show, in 2016, the total global production of shrimp is approximately 8,671,358 tons with 59.74% of aquaculture production and 40.26% of 2 Literature marine capture. Shrimp is a crucial component of the coastal ﬁsheries resources in Iran, and FAO statistics This section is dedicated to the literature review on FSC illustrate that shrimp production between 2003 and 2016 and recent pertinent works on SFSC. has distinctly been grown and shrimp aquaculture has exceeded marine harvests. For example shrimp culture 2.1 Food supply chain (FSC) production approaches, in 2014, 22,500 tons (See: Figs. 3, 4). Mostly, food can be divided into two main categories: Supply Chain Network Design (SCND) facilitates perishable food (e.g. fruits, vegetables, ﬁshery, aquaculture making strategic decisions and plays a crucial role in the products, meats, etc.) and non-perishable (e.g. canned, supply chain performance. Moreover, its competitive ben- pickled, dehydrate, dried products). Recently, several eﬁts affect the operational and tactical levels of the supply studies investigated perishable food supply chain for fresh fruits (Cheraghalipour et al. 2018; Soto-Silva et al. 2016), agricultural (Borodin et al. 2016), and dairy (Sel et al. 2015) come along with different components of the supply chain such as inventory, resources location-allocation, http://www.fao.org/ﬁshery/statistics/collections/en. 123 Shrimp closed-loop supply chain network design 7401 Fig. 1 Developed Countries shrimp supply quantity versus Iran (kg/capita/year) (FAO Fishery Stats) Fig. 2 Shrimps species in Iran [FAO Aquatic Species Information (http://www.fao.org/ﬁshery/collection/cultured-species/en) planning and scheduling, production, and distribution One of the ﬁrst studies on perishable food supply chain (Musavi and Bozorgi-Amiri 2017; Govindan et al. 2014; was conducted by Stoecker et al. (1985). They used linear Attanasio et al. 2007; Kaasgari et al. 2017; Dai et al. 2018; integer programming for maximizing the proﬁt and for Triki 2016; Wu et al. 2018). planning the farm’s crop, livestock, and labor decisions. Miller et al. (1997) provided a simple and a fuzziﬁed linear 123 7402 B. Mosallanezhad et al. Fig. 3 World shrimp production statistics (capture and aquaculture) (FAO Fishery Stats) Fig. 4 Iran shrimp production statistics (capture and aquaculture) (FAO Fishery Stats) programs to produce scheduling of fresh tomato packing- With the aim of maximizing revenues under production house, then, they compared the costs obtained by each and distribution decisions, an operational model was sug- model. Ten Bergeet al. (2000) proposed an explorative gested by Ahumada and Villalobos (2011). Tan and model at the whole farm level that effectively integrates C¸o¨mden (2012) proposed a planning model to handle the component knowledge at a crop or animal level. Then, case random supply of annual fruits and vegetables from farms studies in dairy farming, ﬂower bulb industry, and arable and random demands of the retailers, which are results of farming were provided. A mathematical model was pre- the uncertainty of harvest time, and uncertainty of weekly sented by Caixeta-Filho (2006) who developed a linear demand, respectively. A simulation model for perishable optimization model with chemical, biologic, and logistic fruit and vegetables supply chain was presented by constraints for quality of harvested Brazilian’s oranges. Teimoury et al. (2013) to investigate behaviors and rela- Ferrer et al. (2008) recommended a mixed-integer linear tionships of supply chain and supply, demand and price programming model containing harvest scheduling, labor interactions. Agustina et al. (2014) studied a mixed-integer allocation, and routing decisions on wine grape harvesting linear model of vehicle scheduling and routing at a cross- operations by considering both operational costs and grape docking center for perishable food supply chains to mini- quality. Arnaout and Maatouk (2010) focused on a vine- mize earliness, tardiness, inventory holding, and trans- yard harvesting problem in developing countries to portation cost. A planning model for apples orchards was improve wine quality and reduce the operational costs. proposed by Gonza´lez-Araya et al. (2015) to minimize Additionally, they utilized heuristics for better assigning of labor costs, equipment use, loss of fruit quality, and also harvesting days to different grape blocks and validated the satisfying packing plants demand. The implementation of proposed model by solving several numerical examples. this model on three orchards in Chile showed a 16% Their results showed that their model is prominently able to decrease in the labor costs and loss of income. reduce harvesting costs. Rocco and Morabito (2016) suggested a production and logistics planning linear model for the Brazilian tomato 123 Shrimp closed-loop supply chain network design 7403 processing industry, which includes tactical planning have incredible capabilities for producing especial seafood decisions like the size of tomato area, selection of tomato like shrimps. There is an extraordinary domestic and types, transporting harvests, and so on. Three optimization oversea market demand for shrimp which can ensure a models for purchasing, transporting, and storing fresh proper income. So, designing a SSC can be a good start and produce were studied by Soto-Silva et al. (2017) to ensure a preliminary preparation to accomplish this mission. The an annual supply of fresh apple. An average of 8% savings accurate analysis reported in Table 1 determines the gaps in the real costs of purchasing, storing, and transporting that highlight the signiﬁcance of this paper. The main arisen from conducting a real case study in apple dehy- contributions of this study can be summarized as follows: dration in the Maule region of Chile has been achieved. • This study presented a seven-level MILP supply chain Cheraghalipour et al. (2018) provided a citrus closed-loop network for shrimp product including marine ﬁshery supply chain model to minimize costs and maximize and aquaculture product resources, distributors, whole- responsiveness to customers’ demand. One of the most salers, factories, markets (customers), shrimp waste recent food supply chain model was introduced by Ma powder factories and poultry and livestock food market. et al. (2019). They focused on the three-echelon supply • For the ﬁrst time, the proposed network considered chain for seasonal fresh products consisting of one sup- potential factories which use the collected waste of plier, third-party logistics service providers, and one shrimp products as input for their process. retailer. • In this study, the cost minimization of the network is considered while satisfying the demand of shrimp 2.2 Recent related works on seafood supply products and in the same time supplying the demands of chain (SFSC) poultry and livestock food market. • The above review has shown that all previous related During the last few decades, only a limited number of works have focused either on marine or aquaculture researchers and academics have studied SFSC in miscel- products; however our proposed model took both the laneous ways. In a preliminary study of SFSC problems, products into account with interesting industrial sights. Forsberg (1996) pointed out a multi-period linear pro- • The literature review has emphasized that most of the gramming approach to the production-planning of ﬁsh supply chain and logistics studies were based on NP- farms. In addition, Forsberg (1999) developed a multi-pe- hard models (Jo et al. 2007; Zheng et al. 2013; Deng riod linear programming model for ﬁsh growth that opti- et al. 2017). Hence, metaheuristic algorithms are the mizes the harvest. Sanders et al. (2003) suggested a compulsory and the best way to solve large-scale production model of white sturgeon caviar and meat for networks (Rocco and Morabito 2020; Wang et al. various management conditions. Using the network-ﬂow 2013). Therefore, this research not only takes advan- approach, Yu et al. (2009) implemented a nonlinear tages of classic and modern metaheuristics but also mathematical model of partial harvesting. Cisternas et al. develops two hybrid metaheuristics to solve the (2013) designed an integer programming model to improve suggested NP-hard problem. resource usage, planning, and economic evaluation of grow-out centers. The results obtained from implementing This paper addresses a new model to help the managers this model in one of the Chile’s largest salmon farmers of shrimp production industries in designing an optimal showed a 18% reduction in net maintenance cost together supply chain network for shrimp products. It also under- with several qualitative beneﬁts. Bravo et al. (2013) takes wastes generated in two main levels of network i.e. wholesalers and shrimp factories. The decisions to be taken employed mixed integer programming to propose two models for the production planning in salmon farming within this study consist of: suffering from a range of biological, economic, and health- • How many and which distribution points, wholesalers, related constraints. Bakhrankova et al. (2014) developed a shrimp factories, and shrimp waste powder factories stochastic production-planning model to overcome raw should be selected and established? material supply and product market price uncertainties. • How much shrimp products and shrimp waste powder As can be noticed from the recent literature, SFSC has should be transported within the network? been considered in different manners and for various • How do shrimp production and shrimp waste powder products. Real-world issues and case-based methods is the optimally ﬂow in the network? main factor to design an industrial problem for SSC net- works. In our case, we formulated the SSC network We believe that the mangers can extensively beneﬁt from the suggested mathematical model and its results to according to both the nature and characteristics of the product and due to its importance in Iran and even in make strategic decisions regarding the quality of shrimp today’s food world industry. Developing countries like Iran ﬂow in the supply network while minimizing the total cost. 123 7404 B. Mosallanezhad et al. Table 1 Comparison of previous studies with the current study Author(s) Year Type of Modeling Objective product Yu and 2005 Shrimp Linear Scheduling (the harvesting and restocking time) for maximizing total proﬁt throughout the Leung planning horizon, with biological and economic constraints Yu et al 2006 Shrimp Linear Production scheduling for maximizing the net revenue under different constraints Kumar et al 2006 Fish Multi- Minimization of service costs, late deliveries, and unfulﬁlled demands objective Pathumnakul 2009 Shrimp Mixed Minimization of overall inventory costs of the chain et al Integer Linear Jensen et al 2010 Fish Linear Maximization of ﬁsh supply chain proﬁt Blanchard 2013 Shrimp Non-Linear Determination of the optimal harvesting times and corresponding optimal harvesting et al fractions for Maximization of the total revenue Abedi and 2016 Fish Mixed Optimal purchase, production and distribution of ﬁsh farm for maximization of the total Zhu Integer proﬁt of the supply chain Linear Lin and Wu 2016 White Theoretical Optimal price and inventory level to maximize proﬁt Shrimp Models Tabrizi et al 2018 Warm- Non-Linear Maximization of the total proﬁt Water Fish This study 2020 Shrimp Mixed Minimization of the supply chain costs Integer Linear Additionally, since numerous countries do not have yet the livestock food in addition to the required nutrients for technology to convert shrimp waste to poultry and live- shrimp farming. stock food, this study can give guidelines to the mangers and governors on how to invest their resources to set up a 3.2 Assumptions shrimp waste powder factories in highly potential areas. The following real assumptions are set in the proposed SSC network: 3 Proposed model • The SSC model is a single-period, single-product mixed integer linear programming model. 3.1 Problem description • The locations of the ﬁsheries, aquacultures, and customers are considered ﬁxed. On the other hand, The present SSC network embodies producers (shrimp the distribution centers, wholesalers, factories, and ﬁshers and farmers), distribution centers, wholesalers, markets are assumed as potential locations. processing centers (factories), shrimp waste powder fac- • Market demands must be satisﬁed. tories, poultry and livestock food market, and customers. • It is supposed that there is shrimp waste and also there As can be observed in Fig. 5, captured or aquacultured is demand for the shrimp powder. shrimps are shipped in this network from the producing • Shrimp products are transported and preserved in cold locations (ﬁshery locations and aquacultures) to the dis- containers. tribution centers. The distribution centers, depending on their capacities, send shrimps to the wholesaler and fac- tories. Furthermore, factories, after peeling, packing or 3.3 Model notations canning, and freezing should transport ﬁnished goods to the ﬁnal customers. Finally, shrimp wastes collected from both The indices, parameters, and decision variables for the wholesalers and factories are shipped to shrimp waste mathematical model are presented as follows: powder factories. These factories make poultry and 123 Shrimp closed-loop supply chain network design 7405 V Quantity of product transported from factory l to Indices lm customer m i = 1,2,…,I The production location (shrimp ﬁsher) R Quantity of waste shrimp transported from kn i’ = 1,2,…,I’ The production location (shrimp farm) wholesaler k to shrimp waste powder factory n j = 1,2,…,J The potential point of the distribution center G Quantity of waste shrimp transported from factory l ln k = 1,2,…,K The potential location for the wholesaler to shrimp waste powder factory n l = 1,2,…,L The potential location for the factory B Quantity of shrimp waste powder transported from np m = 1,2,…,M The customer index factory n to market p n = 1,2,…,N The potential site for shrimp waste powder factory Ih Quantity of stored shrimp by distribution center j p = 1,2,…,P The poultry and livestock food market Dis Equal to 1 if distribution center j is opened at the elected location, 0 otherwise Parameters Wh Equal to 1 if wholesaler k is opened at the elected f Fixed cost of opening factory l k location, 0 otherwise f Fixed cost of opening shrimp waste powder factory n Fr Equal to 1 if factory l is opened at the elected Cx Transport cost per unit of product from shrimp ij location, 0 otherwise ﬁshers i to distribution center j Wp Equal to 1 if shrimp waste powder factory n is Cy 0 Transport cost per unit of product from shrimp i j opened at the elected location, 0 otherwise farmers i’ to distribution center j Cu Transport cost per unit of product from distribution jk center j to wholesaler k Ca Transport cost per unit of product from distribution jl center j to factories l 3.4 Shrimp supply chain mathematical model Cb Transport cost per unit of product from wholesaler km k to customer m Cd Transport cost per unit of product from factory l to The schematic view of the SSC network is illustrated in lm customer m Fig. 6. The proposed mixed integer linear programming Cf Transport cost per unit of shrimp waste from kn model of the SSC problem is formulated as follows: wholesaler k to shrimp waste powder factory n • Objective Function Cf Transport cost per unit of shrimp waste from factory ln The objective function of the SSC is to minimize the l to shrimp waste powder factory n total cost including ﬁxed opening costs and trans- Cl Transport cost per unit of shrimp waste powder from np portation costs by means of Eq. (1). factory n to market p k Production capacity of shrimp ﬁsher i "# " 0 L N I J X X XX k 0 Production capacity of shrimp farmer i’ MinZ ¼ f Fr þ f Wp þ Cx X l l n ij ij kd Holding capacity at distribution center j l¼1 n¼1 i¼1 j¼1 kf Production capacity of factory l I J J K XX XX kw Holding capacity at wholesaler k þ Cy 0 X þ Cu U k i j 0 jk jk i j i ¼1 j¼1 j¼1 k¼1 ks Production capacity of shrimp waste powder factory J L n XX þ Ca S jl jl a Shrimp waste rate by wholesaler k j¼1 l¼1 b Shrimp production rate by factory l K M L M XX XX n Shrimp waste powder production rate by factory n þ Cb W þ Cd V km km lm lm k¼1 m¼1 l¼1 m¼1 Db Shrimp product demand by customer m K N XX Dp Shrimp waste powder demand by poultry and þ Cf R kn kn livestock food market p k¼1 n¼1 Decision L N N P XX XX variables þ Cf G þ Cl B ln np np ln n¼1 n¼1 p¼1 l¼1 X Quantity of product transported from shrimp ﬁsher i ij to distribution center j ð1Þ X 0 Quantity of product transported from shrimp farmer i j i to distribution center j U Quantity of product transported from distribution • Constraint jk center j to wholesaler k S Quantity of product transported from distribution jl center j to factory l Dis 1 ð2Þ W Quantity of product transported from wholesaler k to km j¼1 customer m 123 7406 B. Mosallanezhad et al. Fig. 5 The Proposed SSC Network Fig. 6 The graphic view of SSC network K L I I X X X X U þ S X þ X 8j 2 J ð6Þ jk jl ij i j k¼1 l¼1 i¼1 I¼1 X k 8i 2 I ð3Þ ij i j¼1 Wh 1 ð7Þ k¼1 J X 0 0 0 0 Fr 1 ð8Þ X k 8i 2 I ð4Þ l 0 0 i j i l¼1 j¼1 I I X X X U kw Wh 8k 2 K ð9Þ jk k k X þ X 0 kd Dis 8j 2 J ð5Þ ij j j i j j¼1 i¼1 I¼1 123 Shrimp closed-loop supply chain network design 7407 Constraint (9) indicates the quantity of products to be S kf Fr 8l 2 L ð10Þ jl l l transported from the distribution centers to the factories j¼1 should respect the holding capacity of each factory, if it is K L opened. Likewise, constraint (10) applies to the wholesaler. X X W þ V Db 8m 2 M ð11Þ km lm m Constraint (11) ensures that the quantity of product trans- k¼1 l¼1 ported from wholesaler and factories to each customer is J M X X less or equal to the demand at customers side. Constraint ðÞ 1 a U ¼ W 8k 2 K ð12Þ k jk km (12) ensures that products transported from distribution j¼1 m¼1 centers to wholesalers minus wasted shrimp product are J M equal to the amount of product transported from whole- X X b S ¼ V 8l 2 L ð13Þ jl lm salers to customers. Constraint (13) ensures that shrimp j¼1 m¼1 production by factories is equal to the quantity of product N transported from factories to customers. Constraint (14) Wp 1 ð14Þ n determines that at least one shrimp waste powder factory n¼1 should be activated. Constraint (15) ensures the respect of K L X X the shrimp waste powder factories capacities. Constraint R þ G ks Wp 8n 2 N ð15Þ kn ln n n (16) ensures that wasted shrimp product transported from k¼1 l¼1 distribution centers to wholesalers is equal to waste prod- J N X X ucts transported from wholesalers to shrimp waste powder a U ¼ R 8k 2 K ð16Þ k jk kn factories. Constraint (17) ensures the ﬂow balance of the j¼1 n¼1 waste shrimps between factories and shrimp waste powder J N X X factories. Constraint (18) establishes the equality between ðÞ 1 b S ¼ G 8l 2 L ð17Þ jl ln the produced shrimp waste powder and the quantity of j¼1 n¼1 product transported to poultry and livestock food market. K L P Constraint (19) guarantees the demand satisfaction of the X X X R þ G n ¼ B 8n 2 N ð18Þ kn ln np n poultry and livestock food market. Finally, constraints (20) k¼1 l¼1 p¼1 represent the 0/1 restriction on the binary variables and constraints (21) enforce the non-negativity of the continu- B Dp 8p 2 P ð19Þ np p ous decision variables. n¼1 The above model results to be a mixed-integer linear Dis ; M ; Fr ; Wp 2fg 0; 1 8j 2 J; k 2 K; l 2 L; n 2 N model whose size increases quickly with the number of j k l n shrimp ﬁshers, farms, distribution centers, wholesalers, ð20Þ shrimp factory, customers, shrimp waste powder factories X ; X 0 ; U ; S ; W ; V ; R ; G ; B 0 ij jk jl km lm kn ln np i j and poultry and livestock food markets. Consequently, we 0 0 8i 2 I; i 2 I ; j 2 J; k 2 K; l 2 L; m 2 M; n 2 N; p 2 Pt will suggest in the sequel metaheuristic algorithms to solve 2 T real-world instances of SSC problems in a reasonable time. ð21Þ Constraint (2) states that at least one distribution center 4 Solution approach should be opened. Constraint (3) state that the quantity of products transported from shrimp ﬁshers to distribution As mentioned earlier, real-world supply chain network centers should be less than or equal to the production problems are complex and result to be NP-hard for large- capacity of each producer. Similarly, constraint (4) applies scale instances (Jo et al. 2007; Zheng et al. 2013; Deng to the shrimp farmers case. Constraint (5) indicates that the et al. 2017). Using exact methods to solve these problems quantity of products transported from the producers to the would be time-consuming and inefﬁcient especially for distribution centers should be less than or equal to the large-size problems (Rocco and Morabito 2020; Wang holding capacity of each distribution center, if it is opened. et al. 2013). In this study, the Genetic Algorithm (GA), Constraint (6) implies that the quantity of products trans- Simulated Annealing (SA) and Keshtel Algorithm (KA) are ported from the distribution centers to the wholesalers and employed to solve the problems. Moreover, two hybridized factories should not exceed the quantity of products algorithms including Hybrid of Genetic Algorithm with transported from the producers to distribution centers. Simulating Annealing (HGASA) and Hybrid of Keshtel Constraints (7) and (8) determine that at least one whole- Algorithm with Simulating Annealing (HKASA) are uti- saler and one factory should be opened, respectively. lized to ﬁnd the sub-optimal solution. In the sequel, the 123 7408 B. Mosallanezhad et al. encoding and decoding approaches used in the meta- complex problems, and avoidance of local optimum are the heuristic algorithms are explained. most outstanding advantages of these methods (Van Engeland et al. 2018; Diarrassouba et al. 2019; and 4.1 Encoding and decoding Fathollahi-Fard et al. 2020). For example, in order to solve the order acceptance and supply chain scheduling problem, Among the numerous approaches for encoding solutions in Sarvestani et al. (2019) applied GA and Variable Neigh- metaheuristics, we use the recent priority-based method borhood Search (VNS). Youseﬁ et al. (2018) used GA to (Cheraghalipour et al. 2018). Here, the proposed chromo- tackle the ﬁxed-charge transportation problem. Govindan some for the SSC network and application of the priority- et al. (2015) designed a sustainable supply chain problem based method for satisfying all the constraints is enlight- for order allocation and sustainability including stochastic ened using a small-size example. Assume that the numbers demand and used a multi-objective metaheuristic approach of shrimp ﬁshers, shrimp farms, distribution locations, to solve the given problem. This study utilizes the beneﬁts wholesaler, factories, customers, and shrimp waste powder of metaheuristic algorithms and develops three meta- factories, and poultry and livestock food markets are 2, 3, heuristic algorithms including GA, SA, KA as well as two 3, 2, 2, 3, 2, and 2, respectively. The proposed chromosome hybrid metaheuristics i.e. HGASA and HKASA to solve is a matrix with one row and (i ? i’ ? 2 9 j ? 3 9 k ? the SSC network design. In the following sections, the 3 9 l ? m ? 2 9 n ? p) columns that can be divided mentioned algorithms are discussed and the pseudo code of column-wise into ﬁve segments. The representation of each algorithm is rendered. proposed chromosome is presented in Fig. 7. Each segment in the proposed chromosome is designed according to the 4.2.1 Genetic algorithm (GA) network illustrated in Fig. 6. After generating the chromosome, whose all members Genetic algorithm (GA) is an outstanding evolutionary are random numbers in the interval of (0,1), all values are algorithm, contributing to solve successfully many appli- transformed into a priority-based matrix. As shown in cations in different ﬁelds. Holland (1992), inspired by the Fig. 8, Segment 1 states the amount of transported products genetic science and natural evolution, developed GA for from shrimp ﬁshers and shrimp farmers (i ? i’) to the the ﬁrst time. GA brings two main operators, including distribution centers (j). As reported in Fig. 9, in Segment 2, crossover and mutation, into play to execute intensiﬁcation products are allocated to wholesalers and shrimp factories and diversiﬁcation in the search process of the algorithm. (k ? l) from the distribution centers (j). According to Additionally, for the proportional selection within the Figs. 10 and 11, in segment 3, the allocation of products algorithm, we apply the probabilistic selection (Talbi from wholesalers and shrimp factories (k ? l) to customers 2009). Our pseudo-code of GA is illustrated in Fig. 13. is conducted and segment 4 obtains the allocation of wasted products from wholesalers and shrimp factories 4.2.2 Simulated annealing (SA) (k ? l) to shrimp waste powder factories (n). Finally, the allocation of shrimp waste powder products from shrimp The Simulated Annealing (SA) algorithm emerged simul- waste powder factories (n) to the poultry and livestock food taneously in two different works (Kirkpatrick et al. 1983; markets is performed in segment 5 (Fig. 12). For more Cerny´ 1985). This algorithm is centered on the process of information about the priority-based method, refer to obtaining a crystalline structure in which a slow cycle of (Cheraghalipour et al. 2018). cooling and heating (annealing) passes (Deroussi 2016; Talbi 2009). Eskandari-Khanghahi et al. (2018), Torkaman 4.2 Metaheuristics et al. (2018) and Fahimnia et al. (2018) used SA to solve supply chain problems. SA is a single-solution algorithm During the last years, scholars have used numerous meta- whereby it takes an initial solution as the best solution in heuristic methods to solve NP-hard problems and attain a the ﬁrst place. Therefore, it looks into the vicinity of this prominently proper solution. Timesaving, useful for more Fig. 7 The proposed chromosome for the SSC network 123 Shrimp closed-loop supply chain network design 7409 Fig. 8 The random values and priority-based chromosome of segment one Fig. 9 The random values and priority-based chromosome of segment two Fig. 10 The random values and priority-based chromosome of segment three Fig. 11 The random values and priority-based chromosome of segment four Fig. 12 The random values and priority-based chromosome of segment ﬁve solution for the likely best solution. The pseudo code of the studies (Golshahi-Roudbaneh et al. 2017; Fathollahi-Fard SA algorithm is as follows (Fig. 14): et al. 2018a; Cheraghalipour et al. 2018). This algorithm, which is based on the feeding behavior of a dabbling duck, 4.2.3 Keshtel algorithm (KA) namely Keshtel, is introduced by Hajiaghaei-Keshteli and Aminnayeri (2013). Keshtels habitually search for food in Keshtel Algorithm (KA) is a novel metaheuristic algorithm superﬁcial water. Once a Keshtel meets a food source, its recently used by many researchers to develop numerous neighbors miraculously come close and swirl in a circle 123 7410 B. Mosallanezhad et al. Fig. 13 The Pseudo-Code of GA Fig. 15 The Pseudo-Code of KA metaheuristic algorithms draw many researchers’ attraction to improve the intensiﬁcation and diversiﬁcation phases of Fig. 14 The Pseudo-Code of SA the algorithms using various hybrid ones (Hajiaghaei- way. After the consumption of food, they look for another Keshteli and Fathollahi Fard 2018). In this study, two hybrid algorithms are exercised, including HGASA and place containing better food source, and they act in the same way once the food is found. As far as the absence of HKASA. These two hybrids are combination of GA and KA as two distinct population-based techniques together proper food source in the place, this iterative process continues. Then, each Keshtel disbands and searches dif- with SA as a single-solution algorithm. In the following subsections, detailed explanations of HGASA and HKASA ferent spots in the lake for a food source. Similarly, when one of the Keshtels ﬁnds food, its neighbors approach and are provided. repeat the same process as above. KA, akin to other pop- 4.3.1 Hybrid of genetic algorithm and simulating ulation-based metaheuristic algorithms, begins with an annealing (HGASA) initial population, known as Keshtels. Initial Keshtels break up to three categories including N1 entails lucky Keshtels, which are some Keshtels that ﬁnd the food faster As mentioned earlier, GA has two operators for intensiﬁ- cation and diversiﬁcation of the algorithm. SA, as an than others do. Worst solutions are gathered as N3 popu- lation, and are regenerated randomly in each iteration. acceptance phase, can be implemented as mutation phases. In this approach, SA creates competition between parents After ﬁnding better food, a new lucky Keshtel is replaced for each lucky Keshtel; otherwise, the swirling process will and offsprings in a way that ﬁrst all parents and offsprings are compared. If offsprings have better ﬁtness value com- be carried on. N2 represents Keshtels that move between N1 and N3 population. Obviously, N1 is responsible for pared to their parents, they are accepted; otherwise, we accept offsprings according to the acceptance criteria in SA intensiﬁcation in KA, and N2 and N3 ensure the diversi- algorithm. This procedure helps HGASA to evade from ﬁcation phase. Figure 15 sketches the pseudo-code of our local optimum (Zhu and Weng 2012). KA (Fathollahi-Fard and Hajiaghaei-Keshteli 2018a,2018b; Hajiaghaei-Keshteli and Aminnayeri, 2013). 4.3.2 Hybrid of Keshtel algorithm and simulating annealing (HKASA) 4.3 Hybrid metaheuristics As shown in Sect. 4.2.3, KA beneﬁts from two strong In recent studies, a great development in nature-based metaheuristics can be seen. The advantages of the different operators, namely swirling and moving, for the 123 Shrimp closed-loop supply chain network design 7411 intensiﬁcation phase. In such phase of KA, Keshtels in N3 Table 3 Other model parameters tuning group are replaced by new random Keshtels. Although the Parameter Values Unit randomization step in KA is endorsed by different studies f Uniform * [10, 30] Dollar ($) (Golshahi-Roudbaneh et al. 2017; Fathollahi-Fard et al. l f Uniform * [20, 42] Dollar ($) 2018a; Cheraghalipour et al. 2018), SA is able to improve Cx Uniform * [80, 110] Dollar per Ton this procedure in each iteration. Hence, our proposed ij Cy 0 Uniform * [60, 90] Dollar per Ton HKASA approves new random Keshtels either they i j because they have better ﬁtness than prior ones or if they Cu Uniform * [55, 75] Dollar per Ton jk pass the acceptance criteria of the SA algorithm. Ca Uniform * [45, 58] Dollar per Ton jl Cb Uniform * [62, 80] Dollar per Ton km Cd Uniform * [35, 45] Dollar per Ton lm 5 Computational results Cf Uniform * [35, 45] Dollar per Ton kn Cf Uniform * [25, 40] Dollar per Ton ln In the following section, the parameters value for each Cl Uniform * [40, 50] Dollar per Ton np random test is determined. Taguchi experimental design k Uniform * [5, 10] Tons method is used to tune parameters of the metaheuristics. k Uniform * [10, 25] Tons Eventually, to evaluate the performance of the proposed kd Uniform * [12, 30] Tons model, a case study is conducted. kf Uniform * [6, 18] Tons kw Uniform * [8, 25] Tons 5.1 Data generation ks Uniform * [1, 3] Tons a [0.1, 0.12, 0.15] Percentage A set of test problems with different dimensions are con- b [0.90, 0.93, 0.97] Percentage sidered to endorse the proposed model. Here, 15 test n [0.95, 0.93, 0.97] Percentage problems are designed. Table 2 shows the test problems Db Uniform * [12, 30] Tons generated to achieve the purpose of this study. The test Dp Uniform * [2, 4] Tons problems are indiscriminately deﬁned by using the parameters shown in Table 3. It should be mentioned that the approximated value of each parameter is estimated and extracted on the basis of the Iran Fisheries Organization databanks. Table 2 The structure of nine test problems for the various 5.2 Parameters tuning dimensions Test # Index Tuning the parameters in metaheuristics is a crucial phase because it may lead to a wasteful execution of the meta- ii’ j k l m n p heuristics if the parameters are not set rightfully (Fathol- Small-Size 1 2 3 3 4 2 3 2 2 lahi-Fard and Hajiaghaei-Keshteli 2018a). Although there 2 453 525 25 are numerous researchers who tested all possible combi- 3 879 977 98 nations of factors for parameter tuning (Jabbarizadeh et al. 4141212 111311 1211 2009; Naderi et al. 2008; Al-Aomarm and Al-Okaily 2006), 5141615 131115 1612 when the number of factors increase in a problem, their Medium-Size 6 22 26 20 21 29 22 26 27 ﬁndings are disclosed to be inefﬁcient. Henceforward, for 7273030 322833 3431 parameters tuning purpose, we use the efﬁcient Taguchi 8364847 363648 4446 experimental design method, developed by Taguchi 9534857 534155 4852 (1986). The parameters and their levels for the algorithms 10 64 66 69 62 61 61 66 64 have been evolved from (Fathollahi-Fard et al. 2018b). For Large-Size 11 84 80 83 87 78 84 85 90 each factor, three levels are taken into account to design the 12 93 102 98 104 104 97 97 107 experiments. In GA and SA, we have four parameters with 13 129 197 133 113 128 118 147 149 three levels, and for KA, we take ﬁve factors with three 14 209 159 189 241 190 172 205 213 levels into account. The hybrid cases, HKASA and 15 339 323 287 307 328 301 318 255 HGASA, contain seven factors with three levels, and six factors and three levels, respectively. Thus, L is 123 7412 B. Mosallanezhad et al. recommended as a proper array for both SA and KA and distribution centers, wholesalers, factories, shrimp waste also L for GA. powder factories, poultry and livestock food market, and In this study, we generated, for the sake of validating the customers in Khuzestan province. proposed model, 15 test problems put into three categories, At this point, we will attempt to solve the problems by consisting of small-size, medium-size, and large-size. our ﬁve the different algorithms, GA, SA, KA, HKASA, Hence, the orthogonal array has been run for each test and HGASA. Note that the parameters are ﬁxed but the size problem using Minitab software. Owing to the size dif- of test problems alters during the analysis. In fact, when a ference of each problem, the Relative Percentage Deviation factory is added to the dimension of the model, all related (RPD) or mean of means is operated to compare the results. parameters are selected through Table 3. To assess the The RPD is deﬁned as follows for minimization problems: performance of the metaheuristic algorithms, four mea- sures including RPD, one-way ANOVA, hitting time, and Alg Min sol sol RPD ¼ ð22Þ the computational time of the algorithms are considered, as Min Sol shown in Table 5 (Fig. 16). where Min is the best solution among all solutions and sol Figures 17, 18 and 19 depict the objective function Alg is the result of algorithm. The mean RPD is com- sol behavior for various problem sizes. It is obvious that there puted on the basis of the RPDs from the objective values. are slight differences between the values obtained by the Also, the optimal levels for metaheuristic algorithm are different algorithms. Within this, it is clear that in terms of summarized in Table 4. the cost values, SA and HKASA act better than the rest of the algorithms. 5.3 Applied example The RPD is a reliable criterion that can be deﬁned to evaluate and compare the quality of the solution for the In this section, applied instances are exercised to corrob- algorithms. Here, RPD is the relative deviation of the orate the pertinency of the model and solving methodology. outcome of each algorithm from the optimal result among To this end, ﬁfteen test problems in different dimension the ﬁve implemented approaches. These results for each scales are solved with tuned parameters of each meta- test size are shown in Fig. 20. In terms of RPD, HKASA heuristic (Table 2). Among these examples, the second shows better performance than all other algorithms for all example is inspired by a small-sized case in southern the three categories. Another avenue to evaluate the per- Khuzestan province situated in southern Iran. Khuzestan formance of the proposed metaheuristic algorithms is using province is surrounded by the Persian Gulf and has several one-way Analysis of Variance (ANOVA) to account for rivers such as Arvand river, Karun river, etc. Thus, it has any statistically signiﬁcant differences between the RPD of marine access with shrimp production capacity as well as the algorithms. RPD is a response variable and all ﬁve numerous ﬁshery farms which are active in this province. metaheuristics algorithms are factors. Two hypotheses are In the real-case example, four shrimp catching location is considered for the ANOVA test. The p-value for ANOVA considered. These four location are Karun river in Ahvaz, test is equal to zero; therefore, it can be concluded that Arvand river in Abadan, Bahmanshir river in Abadan, and there are statistically signiﬁcant differences in the RPDs. Musa Bay in Mandar-e-Emam. Five shrimp farms exist in For more precise analysis, the means plot and the least Ahvaz, Abadan, Mahshahr, Shadegan, and Hendijan. Other signiﬁcant difference (LSD) intervals at 95% conﬁdence details on the case study are shown in Fig. 16 as a symbolic level are presented in Figs. 21, 22 and 23 for small-size, scheme for SSC network which contains producers, medium size, and large size problems, respectively. In Table 4 Best levels of each algorithm Algorithms GA SA KA Notation Max P P N Max Sub T T Max N PN PN S It c m pop It It 0 damp It pop 1 2 max Optimal Level 800 0.8 0.1 100 800 30 1500 0.90 800 150 0.3 0.2 4 Algorithms HKASA HGASA Notation Max N PN PN S T T Max N Pc Pm T T It pop 1 2 max 0 damp It pop 0 damp Optimal Level 800 150 0.4 0.2 4 2000 0.9 800 100 0.9 0.15 2000 0.88 123 Shrimp closed-loop supply chain network design 7413 Table 5 The objective function (OF), RPD, hitting time (HT), and computational time (CT) value for each algorithm Tests Algorithms GA SA KA OF RPD HT CT OF RPD HT CT OF RPD Small-Size 1 7723.55 0.0000 23.76 42.42 7723.55 0.0000 8.99 15.76 7723.55 0.0000 2 11,486.71 0.0115 34.84 55.31 11,474.06 0.0104 10.41 19.64 11,355.86 0.0000 3 33,071.25 0.0091 65.24 95.94 32,786.31 0.0004 17.92 33.81 32,875.03 0.0031 4 44,948.50 0.0204 84.64 120.92 44,497.55 0.0101 21.28 42.57 44,050.55 0.0000 5 48,576.65 0.0370 101.89 134.06 46,845.50 0.0000 25.84 46.14 47,155.25 0.0066 Medium-Size 6 69,285.68 0.0492 166.74 213.77 66,034.25 0.0000 42.52 70.86 67,681.41 0.0249 7 119,697.27 0.0276 257.80 303.29 116,568.78 0.0007 49.32 98.63 116,819.47 0.0029 8 186,768.95 0.0408 344.59 396.09 180,103.55 0.0037 74.12 132.36 179,703.90 0.0014 9 218,473.50 0.0279 421.41 468.23 213,292.05 0.0036 93.63 158.70 212,849.85 0.0015 10 267,487.35 0.0424 558.19 613.40 258,446.40 0.0072 125.46 212.64 256,610.55 0.0000 Large-Size 11 327,230.00 0.0227 766.77 782.41 319,968.75 0.0000 260.72 266.04 321,759.40 0.0056 12 374,918.20 0.0119 894.35 912.60 370,492.55 0.0000 315.87 319.06 372,906.50 0.0065 13 517,371.39 0.0128 1275.40 1301.42 511,829.17 0.0020 435.53 439.93 511,997.58 0.0023 14 770,929.47 0.0282 2146.73 2190.54 751,002.95 0.0016 722.96 730.27 751,635.90 0.0025 15 1,162,159.40 0.0188 3755.28 3831.92 1,143,016.73 0.0020 1251.89 1264.53 1,143,265.08 0.0022 Tests Algorithms KA HKASA HGASA HT CT OF RPD HT CT OF RPD HT CT Small-Size 1 63.36 105.61 7723.55 0.0000 59.11 113.68 7723.55 0.0000 33.44 58.66 2 78.13 137.07 11,433.53 0.0068 87.25 164.62 11,483.66 0.0113 43.81 75.54 3 129.34 244.03 32,774.11 0.0000 145.87 270.14 32,938.22 0.0050 69.31 130.76 4 156.19 294.69 44,103.75 0.0012 180.47 353.87 44,735.86 0.0156 88.97 164.76 5 186.82 322.11 46,949.73 0.0022 211.51 391.68 47,725.03 0.0188 94.42 181.58 Medium-Size 6 307.12 511.86 66,985.99 0.0144 315.49 595.27 67,679.93 0.0249 157.71 286.75 7 414.96 715.44 116,482.36 0.0000 528.89 944.45 118,167.34 0.0145 230.78 404.88 8 481.74 875.88 179,446.81 0.0000 577.09 1049.26 183,489.91 0.0225 271.53 532.42 9 584.13 1123.32 212,534.96 0.0000 811.59 1352.66 215,945.37 0.0160 353.75 631.69 10 723.28 1418.20 256,664.71 0.0002 913.81 1791.79 263,043.70 0.0251 466.15 832.42 Large-Size 11 1911.65 1930.96 320,464.56 0.0015 2139.02 2160.63 323,693.09 0.0116 1045.87 1056.44 12 2226.55 2249.04 371,293.06 0.0022 2388.58 2412.71 372,812.47 0.0063 1228.82 1241.23 13 5593.82 5650.32 510,829.88 0.0000 5796.85 5915.15 514,748.03 0.0077 1719.46 1754.55 14 8535.54 8621.76 749,793.22 0.0000 8827.05 9007.19 761,187.19 0.0152 2883.86 2942.72 15 9008.35 9192.19 1,140,700.17 0.0000 9253.90 9442.76 1,152,920.42 0.0107 5031.70 5134.38 small-size problems, there is negligible difference between ﬁrst time at which each algorithm obtains the best solution. the performance of SA, KA, and HKASA (Fig. 21). As Figure 24 demonstrates the hitting time comparison for the shown in Fig. 22, in medium-size cases, KA outperformes proposed algorithms. We can conclude that the increment all other algorithms. Finally, the best performance among of the hitting time coincides with the augmentation of all algorithms belongs to HKASA for large-size problems problems sizes. Apparently, the growth rate of hitting time (Fig. 23). in KA and HKASA is more than that of GA, SA, and Hitting time is a tool used to investigate the speed of HGASA. algorithms in different problem sizes. It is deﬁned as the 123 7414 B. Mosallanezhad et al. Fig. 18 Objective function behavior for medium size problem Fig. 16 The Khuzestan province Fig. 19 Objective function behavior for large size problem Fig. 17 Objective function behavior for small size problem The last measure used to check the performance of our algorithms is the computation time. Figure 25 displays the information related to the computational time for all algorithms. Not surprisingly, the SA obviously has the least computational time and after followed by the GA, HGASA, Fig. 20 RPD comparison for the algorithms KA, and HKASA. 123 Shrimp closed-loop supply chain network design 7415 Fig. 21 Means plot and LSD intervals for the algorithms for small- size problems Fig. 24 Hitting time comparison for all algorithms Fig. 22 Means plot and LSD intervals for the algorithms for medium- size problems Fig. 25 Computational time comparison for each algorithm on the functional capability of the proposed model and provide a managerial insight, a sensitivity analysis on the major parameters are performed. Since the HKASA demonstrated to be one of the most efﬁcient algorithms with respect to different metrics, it has been applied here for the sensitivity analysis. Also, we selected the large-size experimental instance 14 as a test problem. Thus, we create three scenarios for sensitivity analysis in which we exam- Fig. 23 Means plot and LSD intervals for large-size problems ine the behavior of cost function under the change of capacity parameters, production/waste rate, and demands 5.4 Sensitivity analyses for each sector. The ﬁrst scenario explores the changes in the production In general, Sensitivity analysis is used to show how output variables change based on the variation of input parame- capacity of shrimp ﬁsher (k ), the production capacity of ters. In mathematical programming terms, sensitivity shrimp farmer (k ), the holding capacity at distribution analysis is a way to explore the effect of changes in the center (kd ), the production capacity of factory (kf ), hold- values of parameters on objective function. To shed light ing capacity at wholesaler (kw ), and production capacity 123 7416 B. Mosallanezhad et al. Table 6 The sensitivity analyses of ﬁrst experiment Capacity parameters Change (Tons) Objective function Capacity parameters Change (Tons) Objective function k 5 769,926.8 kw 5 779,183.9 i k 10 783,700.1 10 797,546.8 15 801,480.7 15 846,795.2 20 818,035.9 20 850,225.3 25 827,072.0 25 891,046.9 30 844,424.0 30 921,267.4 35 851,024.2 35 932,732.1 k 5 763,474.2 kf 5 804,315.5 0 l 10 771,854.0 10 826,209.1 15 790,678.5 15 873,524.1 20 807,244.2 20 929,484.0 25 813,515.6 25 954,929.7 30 824,121.2 30 963,600.9 35 834,273.1 35 984,758.3 kd 5 782,171.2 ks 5 758,695.0 j n 10 802,838.9 10 764,547.2 15 853,042.6 15 786,475.8 20 871,198.6 20 793,884.7 25 913,713.3 25 804,632.3 30 947,666.9 30 817,834.7 35 956,833.4 35 828,637.4 Fig. 26 Objective function behavior for sensitivity analysis (ﬁrst scenario) of shrimp waste powder factory (ks ). In this scenario, each objective function also increases. However, there is sig- parameter varies between 5 to 35 tons and other parameters niﬁcant difference between the effect of factories, distri- are kept unaltered. The performance of the objective bution centers, and wholesalers on the objective function in function with respect to the change of capacity parameters comparison with the other factors. So, it can be inferred are shown in Table 6 and Fig. 26. As shows Fig. 26 with that the capacity of shrimp production factories, distribu- the increase in the amount of capacity of each sector, the tion centers, and wholesalers should be determined 123 Shrimp closed-loop supply chain network design 7417 carefully to avoid risky increase in the cost of the supply signiﬁcant effect on the overall cost of the supply chain chain network. network than the shrimp waste powder demand. The second scenario seeks for the effect of changes in shrimp waste rate by the wholesaler (a ), shrimp produc- tion rate by factories (b ), and shrimp waste powder pro- 6 Managerial insights duction rate by factories (n ). Here, we consider the decrease in shrimp waste rate by wholesaler, and increase The purpose of this paper was to provide a supply chain in both shrimp production rate by factories, and shrimp network for both shrimp products engendered by marine waste powder production. The results of this scenario are and aquaculture. The strength of this model consists in the presented in Table 7 and Fig. 27. According to Fig. 27,we novelty of returning shrimp waste made by wholesalers and realize that all considered factors are positively associated shrimp factories as raw material to shrimp waste powder with an increase in the objective function value. However, factories. The use of the suggested supply chain network shrimp production rate of factory is reasonably effective can signiﬁcantly help in providing the governors and sea- rather than the others. food industries managers with guidelines on how to take The last scenario investigates the inﬂuence of shrimp strategic decisions. Iran has great potential capacity in product demand by customers (Db ), and shrimp waste seafood and aquaculture production such as skilled aca- powder demand by poultry and livestock food market demic experts, affordable industrial requirement such as (Dp ) on the supply chain network cost. The results of the facilities, oil and fuel, human resources. Moreover, it has third scenario are separately calculated for customer’s the most substantial advantage of direct access to three marine zones (the Persian Gulf, Gulf of Oman, and the demands and shrimp waste powder demand and shown in Table 8 and Fig. 28. The results indicate that whenever the Caspian Sea) and its great capability of establishing aquaculture projects in these locations. According to the demand in both sides vary increasingly, there is advance in optimum objective function value. Additionally, it is statistical evidences, developing countries and speciﬁcally Iran, have not yet approached to their satisfactory derived from Fig. 27 that demands of customers have more achievements in seafood industry, especially with respect to shrimp products. Indeed, we believe that countries like Iran should take advantage of its great opportunities and Table 7 The sensitivity analysis of second scenario competencies in seafood industry to boost its economy by Production and waste rate Change Objective gaining remarkable proﬁts and avoiding losses of parameters (%) function capabilities. Going in this direction, the model has assumed potential 1 a 0.80 759,524.5 locations for the distribution center, wholesaler, shrimp 0.85 770,902.4 factories, and shrimp waste powder factory. So, the ﬁnd- 0.87 796,687.0 ings of this model can help investors and governors to get 0.90 814,296.2 the best location to optimally distribute and transport 0.93 873,755.0 shrimp products throughout the network. Moreover, shrimp 0.95 917,694.4 industries can ﬁnd it advantageous, on the basis of this 0.97 934,031.2 study, to enrich their business by recycling the shrimp b 0.80 772,198.0 wastes, if they still didn’t implement such technology, with 0.85 781,315.0 further beneﬁts to the environment. 0.87 809,166.8 Another managerial implication of this study is con- 0.90 844,649.4 cerned with shrimp factories. The managers of these fac- 0.93 883,909.9 tories can apply this model to improve their ﬁxed opening 0.95 929,412.0 and transportation costs and manage production ﬂows and 0.97 963,853.9 supply chain activities. As a result, the optimized supply n 0.80 754,590.4 chain network design leads to pay the lowest cost and to 0.85 757,163.4 deliver the highest service level. These two privileges bring 0.87 773,967.9 competitive advantages over similar supply chains espe- 0.90 785,521.4 cially in the countries around the Persian gulf. For instance, 0.93 846,851.0 the managers can ﬁt their production capacities and 0.95 906,538.0 demand of market with the suggested constraints in the 0.97 914,806.3 model. Furthermore, the sensitivity analysis on demands and the other data together with the setting parameters can 123 7418 B. Mosallanezhad et al. Fig. 27 Objective function behavior for sensitivity analysis (second scenario) Table 8 The sensitivity analysis of third scenario Demand parameters Change (Tons) Objective function Demand parameters Change (Tons) Objective function Db 5 749,793.2 Dp 2 758,002.2 m p 10 772,005.9 4 768,611.9 15 826,632.0 6 777,863.1 20 837,372.3 8 801,915.1 25 854,960.8 10 813,052.0 30 889,661.5 12 838,650.6 35 902,351.3 14 846,043.5 Fig. 28 Objective function behavior for sensitivity analysis (third scenario) give valuable insights to the supply chain decision-makers. can be exploited by the managers of shrimp production The last but not the least, managers always seek for efﬁ- industries to solve their speciﬁc, or similar variants, of cient ways to solve their problems and make decision network design. successfully. This study offered several metaheuristics that 123 Shrimp closed-loop supply chain network design 7419 Regarding the methodological viewpoint, this study 7 Conclusion and future works developed a combination of efﬁcient classic, modern, and hybrid metaheuristics to increase the quality of problem Lately, due to the incessant progress of aquaculture pro- solving. The sensitivity analyses are inspired from the most duction, international markets, and changes in customers’ related and recent studies such as Cheraghalipour et al. desires, seafood business has been astoundingly developed. (2019) and Abdi et al. (2019). In many developed and developing countries, seafood There could be diverse extension on the presented work constitutes the most critical parts of people’s daily diet. for future studies. From mathematical modeling view, the Shrimp products is a desirable seafood among many pop- model can involve the multi-objective aspect by adding a ulations, and it represents a signiﬁcant amount of food product quality function by considering shelf-life of shrimp intake in different societies. Shrimp products is either products and arrival time of orders (see e.g. Bortolini et al. caught from marine environment like seas and rivers, or 2016), a function measuring the satisfaction level of the farmed in aquaculture systems. So, designing a proper manufacturer, market and customers (e.g. Gholami et al. supply chain network for shrimp productions can offer 2016) and shortage/responsiveness functions in the supply many beneﬁts for decision-makers, organizations, facto- chain (e.g. Gen et al. 2006). ries, or even markets to improve the functionality of supply The model could be also extended to cover a multi- chain. Thus, this paper introduced a mathematical model period settings by adopting shrimp maturity assumptions or for the SSC network to retrieve the desirable goals of even catching timeline. It might not be necessary to ﬁg- optimizing the total cost of whole network while respecting ure the model as a multi-product network because although a set of operational restrictions. there are different types of shrimp in the marine or aqua- The solution the proposed model has been ensured by culture production, they are sold in a single deal. However, three renowned metaheuristic algorithms: GA, SA, and if this is not the case in some markets then prospective KA. Additionally, two hybrid metaheuristic algorithms, researchers can think about designing multi-product including HGASA and HKASA, that embed the advantages models. of SA algorithm, were proposed. Thereafter, the Taguchi Another valuable extension of this study is to consider method was used to tune and set the parameters of the the sustainability paradigm to make the model more algorithms with the aim of achieving their better perfor- comprehensive. Therefore, future researches may need to mance. An applied example with 15 test problems was cover social, environmental, and economical aspects and generated considering the application of the SSC to the include them in terms of constraints into the model. Iranian real case, and four measures were used to compare Moreover, in real-world settings uncertainty and ambiguity the results of the designated algorithms. Even though the is common for different aspect of the supply chain network algorithms have shown different behavior with respect to especially demand of markets. For future considerations, the considered measures, the results show that KA and the model can be formulated as a stochastic model under HKASA had satisfactory performance, over the others, in uncertain condition of demands and other important solving the problem under exam. In additions, the results parameters (e.g. Beraldi et al. 2000). Finally, further show the applicability of the suggested SSC network in advances can be achieved even in the context of solution practice and to the effectiveness of proposed methodologies. For instance, developing stochastic and metaheuristics. robust metaheuristic and heuristic approaches that can Principally, this study presented practical and method- efﬁciently deal with the uncertain and multi-objective ological contributions. From the practical standpoint, this nature of the model can be a striking avenue. paper proposed a mathematical model for designing a SSC network as sought-after seafood and increasingly thriving market. The capability of the model is used to handle the Funding Open access funding provided by the Qatar National forward ﬂow of shrimp product from marine catching or Library. aquaculture production to distribution centers then to wholesalers and shrimp factories, and afterward to markets. Declarations It also manages the reverse ﬂow of waste product from wholesalers and shrimp factories to shrimp powder facto- Conflict of interest Author Behzad Mosallanezhad declares that he ries and to livestock and poultry food markets. The model has no conflict of interest. Author Mostafa Hajiaghaei-Keshteli helps to satisfy both the demands of shrimp products in declares that he has no conflict of interest. Author Chefi Triki markets and demand of by-products originated from waste declares that he has no conflict of interest. shrimps while it deals with the capacity restriction of the Ethical approval This article does not contain any studies with human distributors, factories, and particularly shrimp production. participants or animals performed by any of the authors. 123 7420 B. Mosallanezhad et al. Open Access This article is licensed under a Creative Commons Butterworth K (1985) Practical application of linear/integer program- Attribution 4.0 International License, which permits use, sharing, ming in agriculture. J Oper Res Soc 36(2):99–107 adaptation, distribution and reproduction in any medium or format, as Caixeta-Filho JV (2006) Orange harvesting scheduling management: long as you give appropriate credit to the original author(s) and the a case study. 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Publisher: Springer Journals
Copyright: Copyright © The Author(s) 2021
ISSN: 1432-7643
eISSN: 1433-7479
DOI: 10.1007/s00500-021-05698-1
Publisher site: See Article on Publisher Site

Abstract

Recent developments in food industries have attracted both academic and industrial practitioners. Shrimp as a well-known, rich, and sought-after seafood, is generally obtained from either marine environments or aquaculture. Central prominence of Shrimp Supply Chain (SSC) is brought about by numerous factors such as high demand, market price, and diverse ﬁsheries or aquaculture locations. In this respect, this paper considers SSC as a set of distribution centers, wholesalers, shrimp processing factories, markets, shrimp waste powder factory, and shrimp waste powder market. Subsequently, a mathematical model is proposed for the SSC, whose aim is to minimize the total cost through the supply chain. The SSC model is NP-hard and is not able to solve large-size problems. Therefore, three well-known metaheuristics accompanied by two hybrid ones are exerted. Moreover, a real-world application with 15 test problems are established to validate the model. Finally, the results conﬁrm that the SSC model and the solution methods are effective and useful to achieve cost savings. Keywords Closed-loop supply chain Supply chain design Metaheuristics Seafood Shrimp 1 Introduction management activities. Signiﬁcantly, it includes coordina- tion and collaboration with channel partners as well, which Over the past two decades, a great deal of attention is can be suppliers, intermediaries, third-party service provi- devoted to varied types and approaches in Supply Chains to ders, and customers. In essence, supply chain management reach a more suitable solution to create competitive integrates supply and demand management within and advantages for companies, governments, and parties. across companies’’ (Hanne and Dornberger 2017). According to the literature, the supply chain is stated as In today’s world, one of the leading sectors in developed series of facilities that provide the ﬁnal products (Haji- and developing countries is food industries. Food produc- aghaei-Keshteli and Sajadifar 2010; Hajiaghaei-Keshteli tion and distribution have become enough efﬁcient in et al 2011). Moreover, the Council of Supply Chain various aspects to satisfy the growing demands (Sharma Management Professionals (CSCMP) deﬁnes the Supply et al. 2018). The Food Supply Chain (FSC) is resemblance Chain Management (SCM) as: ‘‘SCM encompasses the to any other supply chain, since it made up of several planning and management of all activities involved in stages (production, handling and storage, processing and sourcing and procurement, conversion, and all logistic packaging, distribution, and consumption). Final goods move along the FSC from the producers to reach con- sumers through pre- and post-production actions, and under quality and time-conscious work (Govindan et al. 2017; & Cheﬁ Triki [email protected] Wunderlich and Martinez 2018). However, it can be sep- arated in many ways, since poorly timed distribution in Tecnologico de Monterrey, Escuela de Ingenierıa y Ciencias, FSC makes perishable products unusable. It holds, thus, a Puebla, Mexico prominent situation in the global marketplace and has Division of Engineering Management and Decision Sciences, impacts on society and also the economy of countries College of Sciences and Engineering, Hamad Bin Khalifa (Govindan et al. 2017). University, Doha, Qatar Seafood Supply Chain (SFSC) can be classiﬁed as a Department of Engineering Innovation, University of special FSC, that needs momentous consideration. Health Salento, Lecce, Italy 123 7400 B. Mosallanezhad et al. beneﬁts of seafood are hidden to no one. Indeed, scientists chain over the time (Fathollahi-Fard et al. 2017). Nowa- and organizations believe that seafood teems with sub- days, the economic and environmental concerns arising stantial nutritional values and assures food security due to from the growing demand for shrimp has led to a wide- the fact that over a third of global population beneﬁt from spread discussion regarding the performance within the its protein sources. Furthermore, it is predicted that ﬁsh- shrimp supply (Lin and Wu 2016). Shrimp, like any other eries and aquaculture are taken into account as prominent ﬁsh product, is perishable food. Hence, several important protein sources by 2050 as the population increases (Tab- factors have an indispensable inﬂuence on shrimp supply bakh and Freeland-Graves 2016; Schiller et al. 2018). network. Quality of product in distribution, speed, and Among seafoods, shrimps are a main source of protein efﬁciency in the design of supply network, and ﬁnally time and have low hazardous saturated fat and energy, making delivery and maintenance of cold chain result in the them a healthful preference as well as a desirable food commercial success of the supply chain network (Buritica around the world. In many developing countries, shrimps et al. 2017). Consequently, designing and optimizing the are served as a traditional meal and as a luxurious food in SSC network can help governments, investors, and active developed countries (Alam 2016). Over the past years, food parties to satisfy market demands, and to overcome and agricultural organization (FAO) statistics show that obstacles in the supply chain, and in general can boost the consumption of shrimp in developed countries like performance of the whole chain. China, the United States, and the United Kingdom is This study designs a mathematical modeling and opti- sharply increased, whereas in developing countries such as mization structure that focus on the SSC network. To the Iran, this amount is less than a kilogram per capita per year best of our knowledge, there is no prior study involving (See: Fig. 1). mathematical modeling for SSC network design. The main Iran has a prodigious potential of shrimp production in goal of the SSC model is to minimize the total cost. its both freshwater and marine resources, which drives Moreover, since the SSC model is characterized by the from 1800 km long coastline of the Persian Gulf and the hard complexity in solving large-scale problems, three Gulf of Oman and also appropriate condition for the ﬁshery recognized metaheuristic algorithms and two hybrid on this coastline. More than 2000 shrimp species are heuristics are conducted to address this issue and to analyze identiﬁed worldwide, ﬁve of which are caught and aqua- the model. Furthermore, to achieve better performance of cultured in Iran (See: Fig. 2) (Harlioglu and Farhadi 2016; these algorithms, the corresponding parameters are tuned Schiller et al. 2018). by using the Taguchi method. Statistics indicate that 82% of the total global pro- The remainder of this paper is structured as follows. duction of shrimp belongs to the Asian countries such as Section 2 entails the related literature review on FSC and SFSC. Our SSC mathematical model is proposed and for- China, Thailand, Vietnam, Indonesia, Malaysia, India, and Bangladesh. Moreover, Ecuador, Peru, Mexico, mulated in Sect. 3. The solution methods and computa- Honduras, Guatemala, Brazil, Nicaragua, Venezuela, and tional results are reported in Sect. 4 and Sect. 5, Belize have a 16% portion and the rest is owned by respectively. Finally, conclusions and suggestions for Saudi Arabia, Madagascar, and Australia (Alam 2016). future works are addressed in Sect. 6. As FAO ﬁshery statistics show, in 2016, the total global production of shrimp is approximately 8,671,358 tons with 59.74% of aquaculture production and 40.26% of 2 Literature marine capture. Shrimp is a crucial component of the coastal ﬁsheries resources in Iran, and FAO statistics This section is dedicated to the literature review on FSC illustrate that shrimp production between 2003 and 2016 and recent pertinent works on SFSC. has distinctly been grown and shrimp aquaculture has exceeded marine harvests. For example shrimp culture 2.1 Food supply chain (FSC) production approaches, in 2014, 22,500 tons (See: Figs. 3, 4). Mostly, food can be divided into two main categories: Supply Chain Network Design (SCND) facilitates perishable food (e.g. fruits, vegetables, ﬁshery, aquaculture making strategic decisions and plays a crucial role in the products, meats, etc.) and non-perishable (e.g. canned, supply chain performance. Moreover, its competitive ben- pickled, dehydrate, dried products). Recently, several eﬁts affect the operational and tactical levels of the supply studies investigated perishable food supply chain for fresh fruits (Cheraghalipour et al. 2018; Soto-Silva et al. 2016), agricultural (Borodin et al. 2016), and dairy (Sel et al. 2015) come along with different components of the supply chain such as inventory, resources location-allocation, http://www.fao.org/ﬁshery/statistics/collections/en. 123 Shrimp closed-loop supply chain network design 7401 Fig. 1 Developed Countries shrimp supply quantity versus Iran (kg/capita/year) (FAO Fishery Stats) Fig. 2 Shrimps species in Iran [FAO Aquatic Species Information (http://www.fao.org/ﬁshery/collection/cultured-species/en) planning and scheduling, production, and distribution One of the ﬁrst studies on perishable food supply chain (Musavi and Bozorgi-Amiri 2017; Govindan et al. 2014; was conducted by Stoecker et al. (1985). They used linear Attanasio et al. 2007; Kaasgari et al. 2017; Dai et al. 2018; integer programming for maximizing the proﬁt and for Triki 2016; Wu et al. 2018). planning the farm’s crop, livestock, and labor decisions. Miller et al. (1997) provided a simple and a fuzziﬁed linear 123 7402 B. Mosallanezhad et al. Fig. 3 World shrimp production statistics (capture and aquaculture) (FAO Fishery Stats) Fig. 4 Iran shrimp production statistics (capture and aquaculture) (FAO Fishery Stats) programs to produce scheduling of fresh tomato packing- With the aim of maximizing revenues under production house, then, they compared the costs obtained by each and distribution decisions, an operational model was sug- model. Ten Bergeet al. (2000) proposed an explorative gested by Ahumada and Villalobos (2011). Tan and model at the whole farm level that effectively integrates C¸o¨mden (2012) proposed a planning model to handle the component knowledge at a crop or animal level. Then, case random supply of annual fruits and vegetables from farms studies in dairy farming, ﬂower bulb industry, and arable and random demands of the retailers, which are results of farming were provided. A mathematical model was pre- the uncertainty of harvest time, and uncertainty of weekly sented by Caixeta-Filho (2006) who developed a linear demand, respectively. A simulation model for perishable optimization model with chemical, biologic, and logistic fruit and vegetables supply chain was presented by constraints for quality of harvested Brazilian’s oranges. Teimoury et al. (2013) to investigate behaviors and rela- Ferrer et al. (2008) recommended a mixed-integer linear tionships of supply chain and supply, demand and price programming model containing harvest scheduling, labor interactions. Agustina et al. (2014) studied a mixed-integer allocation, and routing decisions on wine grape harvesting linear model of vehicle scheduling and routing at a cross- operations by considering both operational costs and grape docking center for perishable food supply chains to mini- quality. Arnaout and Maatouk (2010) focused on a vine- mize earliness, tardiness, inventory holding, and trans- yard harvesting problem in developing countries to portation cost. A planning model for apples orchards was improve wine quality and reduce the operational costs. proposed by Gonza´lez-Araya et al. (2015) to minimize Additionally, they utilized heuristics for better assigning of labor costs, equipment use, loss of fruit quality, and also harvesting days to different grape blocks and validated the satisfying packing plants demand. The implementation of proposed model by solving several numerical examples. this model on three orchards in Chile showed a 16% Their results showed that their model is prominently able to decrease in the labor costs and loss of income. reduce harvesting costs. Rocco and Morabito (2016) suggested a production and logistics planning linear model for the Brazilian tomato 123 Shrimp closed-loop supply chain network design 7403 processing industry, which includes tactical planning have incredible capabilities for producing especial seafood decisions like the size of tomato area, selection of tomato like shrimps. There is an extraordinary domestic and types, transporting harvests, and so on. Three optimization oversea market demand for shrimp which can ensure a models for purchasing, transporting, and storing fresh proper income. So, designing a SSC can be a good start and produce were studied by Soto-Silva et al. (2017) to ensure a preliminary preparation to accomplish this mission. The an annual supply of fresh apple. An average of 8% savings accurate analysis reported in Table 1 determines the gaps in the real costs of purchasing, storing, and transporting that highlight the signiﬁcance of this paper. The main arisen from conducting a real case study in apple dehy- contributions of this study can be summarized as follows: dration in the Maule region of Chile has been achieved. • This study presented a seven-level MILP supply chain Cheraghalipour et al. (2018) provided a citrus closed-loop network for shrimp product including marine ﬁshery supply chain model to minimize costs and maximize and aquaculture product resources, distributors, whole- responsiveness to customers’ demand. One of the most salers, factories, markets (customers), shrimp waste recent food supply chain model was introduced by Ma powder factories and poultry and livestock food market. et al. (2019). They focused on the three-echelon supply • For the ﬁrst time, the proposed network considered chain for seasonal fresh products consisting of one sup- potential factories which use the collected waste of plier, third-party logistics service providers, and one shrimp products as input for their process. retailer. • In this study, the cost minimization of the network is considered while satisfying the demand of shrimp 2.2 Recent related works on seafood supply products and in the same time supplying the demands of chain (SFSC) poultry and livestock food market. • The above review has shown that all previous related During the last few decades, only a limited number of works have focused either on marine or aquaculture researchers and academics have studied SFSC in miscel- products; however our proposed model took both the laneous ways. In a preliminary study of SFSC problems, products into account with interesting industrial sights. Forsberg (1996) pointed out a multi-period linear pro- • The literature review has emphasized that most of the gramming approach to the production-planning of ﬁsh supply chain and logistics studies were based on NP- farms. In addition, Forsberg (1999) developed a multi-pe- hard models (Jo et al. 2007; Zheng et al. 2013; Deng riod linear programming model for ﬁsh growth that opti- et al. 2017). Hence, metaheuristic algorithms are the mizes the harvest. Sanders et al. (2003) suggested a compulsory and the best way to solve large-scale production model of white sturgeon caviar and meat for networks (Rocco and Morabito 2020; Wang et al. various management conditions. Using the network-ﬂow 2013). Therefore, this research not only takes advan- approach, Yu et al. (2009) implemented a nonlinear tages of classic and modern metaheuristics but also mathematical model of partial harvesting. Cisternas et al. develops two hybrid metaheuristics to solve the (2013) designed an integer programming model to improve suggested NP-hard problem. resource usage, planning, and economic evaluation of grow-out centers. The results obtained from implementing This paper addresses a new model to help the managers this model in one of the Chile’s largest salmon farmers of shrimp production industries in designing an optimal showed a 18% reduction in net maintenance cost together supply chain network for shrimp products. It also under- with several qualitative beneﬁts. Bravo et al. (2013) takes wastes generated in two main levels of network i.e. wholesalers and shrimp factories. The decisions to be taken employed mixed integer programming to propose two models for the production planning in salmon farming within this study consist of: suffering from a range of biological, economic, and health- • How many and which distribution points, wholesalers, related constraints. Bakhrankova et al. (2014) developed a shrimp factories, and shrimp waste powder factories stochastic production-planning model to overcome raw should be selected and established? material supply and product market price uncertainties. • How much shrimp products and shrimp waste powder As can be noticed from the recent literature, SFSC has should be transported within the network? been considered in different manners and for various • How do shrimp production and shrimp waste powder products. Real-world issues and case-based methods is the optimally ﬂow in the network? main factor to design an industrial problem for SSC net- works. In our case, we formulated the SSC network We believe that the mangers can extensively beneﬁt from the suggested mathematical model and its results to according to both the nature and characteristics of the product and due to its importance in Iran and even in make strategic decisions regarding the quality of shrimp today’s food world industry. Developing countries like Iran ﬂow in the supply network while minimizing the total cost. 123 7404 B. Mosallanezhad et al. Table 1 Comparison of previous studies with the current study Author(s) Year Type of Modeling Objective product Yu and 2005 Shrimp Linear Scheduling (the harvesting and restocking time) for maximizing total proﬁt throughout the Leung planning horizon, with biological and economic constraints Yu et al 2006 Shrimp Linear Production scheduling for maximizing the net revenue under different constraints Kumar et al 2006 Fish Multi- Minimization of service costs, late deliveries, and unfulﬁlled demands objective Pathumnakul 2009 Shrimp Mixed Minimization of overall inventory costs of the chain et al Integer Linear Jensen et al 2010 Fish Linear Maximization of ﬁsh supply chain proﬁt Blanchard 2013 Shrimp Non-Linear Determination of the optimal harvesting times and corresponding optimal harvesting et al fractions for Maximization of the total revenue Abedi and 2016 Fish Mixed Optimal purchase, production and distribution of ﬁsh farm for maximization of the total Zhu Integer proﬁt of the supply chain Linear Lin and Wu 2016 White Theoretical Optimal price and inventory level to maximize proﬁt Shrimp Models Tabrizi et al 2018 Warm- Non-Linear Maximization of the total proﬁt Water Fish This study 2020 Shrimp Mixed Minimization of the supply chain costs Integer Linear Additionally, since numerous countries do not have yet the livestock food in addition to the required nutrients for technology to convert shrimp waste to poultry and live- shrimp farming. stock food, this study can give guidelines to the mangers and governors on how to invest their resources to set up a 3.2 Assumptions shrimp waste powder factories in highly potential areas. The following real assumptions are set in the proposed SSC network: 3 Proposed model • The SSC model is a single-period, single-product mixed integer linear programming model. 3.1 Problem description • The locations of the ﬁsheries, aquacultures, and customers are considered ﬁxed. On the other hand, The present SSC network embodies producers (shrimp the distribution centers, wholesalers, factories, and ﬁshers and farmers), distribution centers, wholesalers, markets are assumed as potential locations. processing centers (factories), shrimp waste powder fac- • Market demands must be satisﬁed. tories, poultry and livestock food market, and customers. • It is supposed that there is shrimp waste and also there As can be observed in Fig. 5, captured or aquacultured is demand for the shrimp powder. shrimps are shipped in this network from the producing • Shrimp products are transported and preserved in cold locations (ﬁshery locations and aquacultures) to the dis- containers. tribution centers. The distribution centers, depending on their capacities, send shrimps to the wholesaler and fac- tories. Furthermore, factories, after peeling, packing or 3.3 Model notations canning, and freezing should transport ﬁnished goods to the ﬁnal customers. Finally, shrimp wastes collected from both The indices, parameters, and decision variables for the wholesalers and factories are shipped to shrimp waste mathematical model are presented as follows: powder factories. These factories make poultry and 123 Shrimp closed-loop supply chain network design 7405 V Quantity of product transported from factory l to Indices lm customer m i = 1,2,…,I The production location (shrimp ﬁsher) R Quantity of waste shrimp transported from kn i’ = 1,2,…,I’ The production location (shrimp farm) wholesaler k to shrimp waste powder factory n j = 1,2,…,J The potential point of the distribution center G Quantity of waste shrimp transported from factory l ln k = 1,2,…,K The potential location for the wholesaler to shrimp waste powder factory n l = 1,2,…,L The potential location for the factory B Quantity of shrimp waste powder transported from np m = 1,2,…,M The customer index factory n to market p n = 1,2,…,N The potential site for shrimp waste powder factory Ih Quantity of stored shrimp by distribution center j p = 1,2,…,P The poultry and livestock food market Dis Equal to 1 if distribution center j is opened at the elected location, 0 otherwise Parameters Wh Equal to 1 if wholesaler k is opened at the elected f Fixed cost of opening factory l k location, 0 otherwise f Fixed cost of opening shrimp waste powder factory n Fr Equal to 1 if factory l is opened at the elected Cx Transport cost per unit of product from shrimp ij location, 0 otherwise ﬁshers i to distribution center j Wp Equal to 1 if shrimp waste powder factory n is Cy 0 Transport cost per unit of product from shrimp i j opened at the elected location, 0 otherwise farmers i’ to distribution center j Cu Transport cost per unit of product from distribution jk center j to wholesaler k Ca Transport cost per unit of product from distribution jl center j to factories l 3.4 Shrimp supply chain mathematical model Cb Transport cost per unit of product from wholesaler km k to customer m Cd Transport cost per unit of product from factory l to The schematic view of the SSC network is illustrated in lm customer m Fig. 6. The proposed mixed integer linear programming Cf Transport cost per unit of shrimp waste from kn model of the SSC problem is formulated as follows: wholesaler k to shrimp waste powder factory n • Objective Function Cf Transport cost per unit of shrimp waste from factory ln The objective function of the SSC is to minimize the l to shrimp waste powder factory n total cost including ﬁxed opening costs and trans- Cl Transport cost per unit of shrimp waste powder from np portation costs by means of Eq. (1). factory n to market p k Production capacity of shrimp ﬁsher i "# " 0 L N I J X X XX k 0 Production capacity of shrimp farmer i’ MinZ ¼ f Fr þ f Wp þ Cx X l l n ij ij kd Holding capacity at distribution center j l¼1 n¼1 i¼1 j¼1 kf Production capacity of factory l I J J K XX XX kw Holding capacity at wholesaler k þ Cy 0 X þ Cu U k i j 0 jk jk i j i ¼1 j¼1 j¼1 k¼1 ks Production capacity of shrimp waste powder factory J L n XX þ Ca S jl jl a Shrimp waste rate by wholesaler k j¼1 l¼1 b Shrimp production rate by factory l K M L M XX XX n Shrimp waste powder production rate by factory n þ Cb W þ Cd V km km lm lm k¼1 m¼1 l¼1 m¼1 Db Shrimp product demand by customer m K N XX Dp Shrimp waste powder demand by poultry and þ Cf R kn kn livestock food market p k¼1 n¼1 Decision L N N P XX XX variables þ Cf G þ Cl B ln np np ln n¼1 n¼1 p¼1 l¼1 X Quantity of product transported from shrimp ﬁsher i ij to distribution center j ð1Þ X 0 Quantity of product transported from shrimp farmer i j i to distribution center j U Quantity of product transported from distribution • Constraint jk center j to wholesaler k S Quantity of product transported from distribution jl center j to factory l Dis 1 ð2Þ W Quantity of product transported from wholesaler k to km j¼1 customer m 123 7406 B. Mosallanezhad et al. Fig. 5 The Proposed SSC Network Fig. 6 The graphic view of SSC network K L I I X X X X U þ S X þ X 8j 2 J ð6Þ jk jl ij i j k¼1 l¼1 i¼1 I¼1 X k 8i 2 I ð3Þ ij i j¼1 Wh 1 ð7Þ k¼1 J X 0 0 0 0 Fr 1 ð8Þ X k 8i 2 I ð4Þ l 0 0 i j i l¼1 j¼1 I I X X X U kw Wh 8k 2 K ð9Þ jk k k X þ X 0 kd Dis 8j 2 J ð5Þ ij j j i j j¼1 i¼1 I¼1 123 Shrimp closed-loop supply chain network design 7407 Constraint (9) indicates the quantity of products to be S kf Fr 8l 2 L ð10Þ jl l l transported from the distribution centers to the factories j¼1 should respect the holding capacity of each factory, if it is K L opened. Likewise, constraint (10) applies to the wholesaler. X X W þ V Db 8m 2 M ð11Þ km lm m Constraint (11) ensures that the quantity of product trans- k¼1 l¼1 ported from wholesaler and factories to each customer is J M X X less or equal to the demand at customers side. Constraint ðÞ 1 a U ¼ W 8k 2 K ð12Þ k jk km (12) ensures that products transported from distribution j¼1 m¼1 centers to wholesalers minus wasted shrimp product are J M equal to the amount of product transported from whole- X X b S ¼ V 8l 2 L ð13Þ jl lm salers to customers. Constraint (13) ensures that shrimp j¼1 m¼1 production by factories is equal to the quantity of product N transported from factories to customers. Constraint (14) Wp 1 ð14Þ n determines that at least one shrimp waste powder factory n¼1 should be activated. Constraint (15) ensures the respect of K L X X the shrimp waste powder factories capacities. Constraint R þ G ks Wp 8n 2 N ð15Þ kn ln n n (16) ensures that wasted shrimp product transported from k¼1 l¼1 distribution centers to wholesalers is equal to waste prod- J N X X ucts transported from wholesalers to shrimp waste powder a U ¼ R 8k 2 K ð16Þ k jk kn factories. Constraint (17) ensures the ﬂow balance of the j¼1 n¼1 waste shrimps between factories and shrimp waste powder J N X X factories. Constraint (18) establishes the equality between ðÞ 1 b S ¼ G 8l 2 L ð17Þ jl ln the produced shrimp waste powder and the quantity of j¼1 n¼1 product transported to poultry and livestock food market. K L P Constraint (19) guarantees the demand satisfaction of the X X X R þ G n ¼ B 8n 2 N ð18Þ kn ln np n poultry and livestock food market. Finally, constraints (20) k¼1 l¼1 p¼1 represent the 0/1 restriction on the binary variables and constraints (21) enforce the non-negativity of the continu- B Dp 8p 2 P ð19Þ np p ous decision variables. n¼1 The above model results to be a mixed-integer linear Dis ; M ; Fr ; Wp 2fg 0; 1 8j 2 J; k 2 K; l 2 L; n 2 N model whose size increases quickly with the number of j k l n shrimp ﬁshers, farms, distribution centers, wholesalers, ð20Þ shrimp factory, customers, shrimp waste powder factories X ; X 0 ; U ; S ; W ; V ; R ; G ; B 0 ij jk jl km lm kn ln np i j and poultry and livestock food markets. Consequently, we 0 0 8i 2 I; i 2 I ; j 2 J; k 2 K; l 2 L; m 2 M; n 2 N; p 2 Pt will suggest in the sequel metaheuristic algorithms to solve 2 T real-world instances of SSC problems in a reasonable time. ð21Þ Constraint (2) states that at least one distribution center 4 Solution approach should be opened. Constraint (3) state that the quantity of products transported from shrimp ﬁshers to distribution As mentioned earlier, real-world supply chain network centers should be less than or equal to the production problems are complex and result to be NP-hard for large- capacity of each producer. Similarly, constraint (4) applies scale instances (Jo et al. 2007; Zheng et al. 2013; Deng to the shrimp farmers case. Constraint (5) indicates that the et al. 2017). Using exact methods to solve these problems quantity of products transported from the producers to the would be time-consuming and inefﬁcient especially for distribution centers should be less than or equal to the large-size problems (Rocco and Morabito 2020; Wang holding capacity of each distribution center, if it is opened. et al. 2013). In this study, the Genetic Algorithm (GA), Constraint (6) implies that the quantity of products trans- Simulated Annealing (SA) and Keshtel Algorithm (KA) are ported from the distribution centers to the wholesalers and employed to solve the problems. Moreover, two hybridized factories should not exceed the quantity of products algorithms including Hybrid of Genetic Algorithm with transported from the producers to distribution centers. Simulating Annealing (HGASA) and Hybrid of Keshtel Constraints (7) and (8) determine that at least one whole- Algorithm with Simulating Annealing (HKASA) are uti- saler and one factory should be opened, respectively. lized to ﬁnd the sub-optimal solution. In the sequel, the 123 7408 B. Mosallanezhad et al. encoding and decoding approaches used in the meta- complex problems, and avoidance of local optimum are the heuristic algorithms are explained. most outstanding advantages of these methods (Van Engeland et al. 2018; Diarrassouba et al. 2019; and 4.1 Encoding and decoding Fathollahi-Fard et al. 2020). For example, in order to solve the order acceptance and supply chain scheduling problem, Among the numerous approaches for encoding solutions in Sarvestani et al. (2019) applied GA and Variable Neigh- metaheuristics, we use the recent priority-based method borhood Search (VNS). Youseﬁ et al. (2018) used GA to (Cheraghalipour et al. 2018). Here, the proposed chromo- tackle the ﬁxed-charge transportation problem. Govindan some for the SSC network and application of the priority- et al. (2015) designed a sustainable supply chain problem based method for satisfying all the constraints is enlight- for order allocation and sustainability including stochastic ened using a small-size example. Assume that the numbers demand and used a multi-objective metaheuristic approach of shrimp ﬁshers, shrimp farms, distribution locations, to solve the given problem. This study utilizes the beneﬁts wholesaler, factories, customers, and shrimp waste powder of metaheuristic algorithms and develops three meta- factories, and poultry and livestock food markets are 2, 3, heuristic algorithms including GA, SA, KA as well as two 3, 2, 2, 3, 2, and 2, respectively. The proposed chromosome hybrid metaheuristics i.e. HGASA and HKASA to solve is a matrix with one row and (i ? i’ ? 2 9 j ? 3 9 k ? the SSC network design. In the following sections, the 3 9 l ? m ? 2 9 n ? p) columns that can be divided mentioned algorithms are discussed and the pseudo code of column-wise into ﬁve segments. The representation of each algorithm is rendered. proposed chromosome is presented in Fig. 7. Each segment in the proposed chromosome is designed according to the 4.2.1 Genetic algorithm (GA) network illustrated in Fig. 6. After generating the chromosome, whose all members Genetic algorithm (GA) is an outstanding evolutionary are random numbers in the interval of (0,1), all values are algorithm, contributing to solve successfully many appli- transformed into a priority-based matrix. As shown in cations in different ﬁelds. Holland (1992), inspired by the Fig. 8, Segment 1 states the amount of transported products genetic science and natural evolution, developed GA for from shrimp ﬁshers and shrimp farmers (i ? i’) to the the ﬁrst time. GA brings two main operators, including distribution centers (j). As reported in Fig. 9, in Segment 2, crossover and mutation, into play to execute intensiﬁcation products are allocated to wholesalers and shrimp factories and diversiﬁcation in the search process of the algorithm. (k ? l) from the distribution centers (j). According to Additionally, for the proportional selection within the Figs. 10 and 11, in segment 3, the allocation of products algorithm, we apply the probabilistic selection (Talbi from wholesalers and shrimp factories (k ? l) to customers 2009). Our pseudo-code of GA is illustrated in Fig. 13. is conducted and segment 4 obtains the allocation of wasted products from wholesalers and shrimp factories 4.2.2 Simulated annealing (SA) (k ? l) to shrimp waste powder factories (n). Finally, the allocation of shrimp waste powder products from shrimp The Simulated Annealing (SA) algorithm emerged simul- waste powder factories (n) to the poultry and livestock food taneously in two different works (Kirkpatrick et al. 1983; markets is performed in segment 5 (Fig. 12). For more Cerny´ 1985). This algorithm is centered on the process of information about the priority-based method, refer to obtaining a crystalline structure in which a slow cycle of (Cheraghalipour et al. 2018). cooling and heating (annealing) passes (Deroussi 2016; Talbi 2009). Eskandari-Khanghahi et al. (2018), Torkaman 4.2 Metaheuristics et al. (2018) and Fahimnia et al. (2018) used SA to solve supply chain problems. SA is a single-solution algorithm During the last years, scholars have used numerous meta- whereby it takes an initial solution as the best solution in heuristic methods to solve NP-hard problems and attain a the ﬁrst place. Therefore, it looks into the vicinity of this prominently proper solution. Timesaving, useful for more Fig. 7 The proposed chromosome for the SSC network 123 Shrimp closed-loop supply chain network design 7409 Fig. 8 The random values and priority-based chromosome of segment one Fig. 9 The random values and priority-based chromosome of segment two Fig. 10 The random values and priority-based chromosome of segment three Fig. 11 The random values and priority-based chromosome of segment four Fig. 12 The random values and priority-based chromosome of segment ﬁve solution for the likely best solution. The pseudo code of the studies (Golshahi-Roudbaneh et al. 2017; Fathollahi-Fard SA algorithm is as follows (Fig. 14): et al. 2018a; Cheraghalipour et al. 2018). This algorithm, which is based on the feeding behavior of a dabbling duck, 4.2.3 Keshtel algorithm (KA) namely Keshtel, is introduced by Hajiaghaei-Keshteli and Aminnayeri (2013). Keshtels habitually search for food in Keshtel Algorithm (KA) is a novel metaheuristic algorithm superﬁcial water. Once a Keshtel meets a food source, its recently used by many researchers to develop numerous neighbors miraculously come close and swirl in a circle 123 7410 B. Mosallanezhad et al. Fig. 13 The Pseudo-Code of GA Fig. 15 The Pseudo-Code of KA metaheuristic algorithms draw many researchers’ attraction to improve the intensiﬁcation and diversiﬁcation phases of Fig. 14 The Pseudo-Code of SA the algorithms using various hybrid ones (Hajiaghaei- way. After the consumption of food, they look for another Keshteli and Fathollahi Fard 2018). In this study, two hybrid algorithms are exercised, including HGASA and place containing better food source, and they act in the same way once the food is found. As far as the absence of HKASA. These two hybrids are combination of GA and KA as two distinct population-based techniques together proper food source in the place, this iterative process continues. Then, each Keshtel disbands and searches dif- with SA as a single-solution algorithm. In the following subsections, detailed explanations of HGASA and HKASA ferent spots in the lake for a food source. Similarly, when one of the Keshtels ﬁnds food, its neighbors approach and are provided. repeat the same process as above. KA, akin to other pop- 4.3.1 Hybrid of genetic algorithm and simulating ulation-based metaheuristic algorithms, begins with an annealing (HGASA) initial population, known as Keshtels. Initial Keshtels break up to three categories including N1 entails lucky Keshtels, which are some Keshtels that ﬁnd the food faster As mentioned earlier, GA has two operators for intensiﬁ- cation and diversiﬁcation of the algorithm. SA, as an than others do. Worst solutions are gathered as N3 popu- lation, and are regenerated randomly in each iteration. acceptance phase, can be implemented as mutation phases. In this approach, SA creates competition between parents After ﬁnding better food, a new lucky Keshtel is replaced for each lucky Keshtel; otherwise, the swirling process will and offsprings in a way that ﬁrst all parents and offsprings are compared. If offsprings have better ﬁtness value com- be carried on. N2 represents Keshtels that move between N1 and N3 population. Obviously, N1 is responsible for pared to their parents, they are accepted; otherwise, we accept offsprings according to the acceptance criteria in SA intensiﬁcation in KA, and N2 and N3 ensure the diversi- algorithm. This procedure helps HGASA to evade from ﬁcation phase. Figure 15 sketches the pseudo-code of our local optimum (Zhu and Weng 2012). KA (Fathollahi-Fard and Hajiaghaei-Keshteli 2018a,2018b; Hajiaghaei-Keshteli and Aminnayeri, 2013). 4.3.2 Hybrid of Keshtel algorithm and simulating annealing (HKASA) 4.3 Hybrid metaheuristics As shown in Sect. 4.2.3, KA beneﬁts from two strong In recent studies, a great development in nature-based metaheuristics can be seen. The advantages of the different operators, namely swirling and moving, for the 123 Shrimp closed-loop supply chain network design 7411 intensiﬁcation phase. In such phase of KA, Keshtels in N3 Table 3 Other model parameters tuning group are replaced by new random Keshtels. Although the Parameter Values Unit randomization step in KA is endorsed by different studies f Uniform * [10, 30] Dollar ($) (Golshahi-Roudbaneh et al. 2017; Fathollahi-Fard et al. l f Uniform * [20, 42] Dollar ($) 2018a; Cheraghalipour et al. 2018), SA is able to improve Cx Uniform * [80, 110] Dollar per Ton this procedure in each iteration. Hence, our proposed ij Cy 0 Uniform * [60, 90] Dollar per Ton HKASA approves new random Keshtels either they i j because they have better ﬁtness than prior ones or if they Cu Uniform * [55, 75] Dollar per Ton jk pass the acceptance criteria of the SA algorithm. Ca Uniform * [45, 58] Dollar per Ton jl Cb Uniform * [62, 80] Dollar per Ton km Cd Uniform * [35, 45] Dollar per Ton lm 5 Computational results Cf Uniform * [35, 45] Dollar per Ton kn Cf Uniform * [25, 40] Dollar per Ton ln In the following section, the parameters value for each Cl Uniform * [40, 50] Dollar per Ton np random test is determined. Taguchi experimental design k Uniform * [5, 10] Tons method is used to tune parameters of the metaheuristics. k Uniform * [10, 25] Tons Eventually, to evaluate the performance of the proposed kd Uniform * [12, 30] Tons model, a case study is conducted. kf Uniform * [6, 18] Tons kw Uniform * [8, 25] Tons 5.1 Data generation ks Uniform * [1, 3] Tons a [0.1, 0.12, 0.15] Percentage A set of test problems with different dimensions are con- b [0.90, 0.93, 0.97] Percentage sidered to endorse the proposed model. Here, 15 test n [0.95, 0.93, 0.97] Percentage problems are designed. Table 2 shows the test problems Db Uniform * [12, 30] Tons generated to achieve the purpose of this study. The test Dp Uniform * [2, 4] Tons problems are indiscriminately deﬁned by using the parameters shown in Table 3. It should be mentioned that the approximated value of each parameter is estimated and extracted on the basis of the Iran Fisheries Organization databanks. Table 2 The structure of nine test problems for the various 5.2 Parameters tuning dimensions Test # Index Tuning the parameters in metaheuristics is a crucial phase because it may lead to a wasteful execution of the meta- ii’ j k l m n p heuristics if the parameters are not set rightfully (Fathol- Small-Size 1 2 3 3 4 2 3 2 2 lahi-Fard and Hajiaghaei-Keshteli 2018a). Although there 2 453 525 25 are numerous researchers who tested all possible combi- 3 879 977 98 nations of factors for parameter tuning (Jabbarizadeh et al. 4141212 111311 1211 2009; Naderi et al. 2008; Al-Aomarm and Al-Okaily 2006), 5141615 131115 1612 when the number of factors increase in a problem, their Medium-Size 6 22 26 20 21 29 22 26 27 ﬁndings are disclosed to be inefﬁcient. Henceforward, for 7273030 322833 3431 parameters tuning purpose, we use the efﬁcient Taguchi 8364847 363648 4446 experimental design method, developed by Taguchi 9534857 534155 4852 (1986). The parameters and their levels for the algorithms 10 64 66 69 62 61 61 66 64 have been evolved from (Fathollahi-Fard et al. 2018b). For Large-Size 11 84 80 83 87 78 84 85 90 each factor, three levels are taken into account to design the 12 93 102 98 104 104 97 97 107 experiments. In GA and SA, we have four parameters with 13 129 197 133 113 128 118 147 149 three levels, and for KA, we take ﬁve factors with three 14 209 159 189 241 190 172 205 213 levels into account. The hybrid cases, HKASA and 15 339 323 287 307 328 301 318 255 HGASA, contain seven factors with three levels, and six factors and three levels, respectively. Thus, L is 123 7412 B. Mosallanezhad et al. recommended as a proper array for both SA and KA and distribution centers, wholesalers, factories, shrimp waste also L for GA. powder factories, poultry and livestock food market, and In this study, we generated, for the sake of validating the customers in Khuzestan province. proposed model, 15 test problems put into three categories, At this point, we will attempt to solve the problems by consisting of small-size, medium-size, and large-size. our ﬁve the different algorithms, GA, SA, KA, HKASA, Hence, the orthogonal array has been run for each test and HGASA. Note that the parameters are ﬁxed but the size problem using Minitab software. Owing to the size dif- of test problems alters during the analysis. In fact, when a ference of each problem, the Relative Percentage Deviation factory is added to the dimension of the model, all related (RPD) or mean of means is operated to compare the results. parameters are selected through Table 3. To assess the The RPD is deﬁned as follows for minimization problems: performance of the metaheuristic algorithms, four mea- sures including RPD, one-way ANOVA, hitting time, and Alg Min sol sol RPD ¼ ð22Þ the computational time of the algorithms are considered, as Min Sol shown in Table 5 (Fig. 16). where Min is the best solution among all solutions and sol Figures 17, 18 and 19 depict the objective function Alg is the result of algorithm. The mean RPD is com- sol behavior for various problem sizes. It is obvious that there puted on the basis of the RPDs from the objective values. are slight differences between the values obtained by the Also, the optimal levels for metaheuristic algorithm are different algorithms. Within this, it is clear that in terms of summarized in Table 4. the cost values, SA and HKASA act better than the rest of the algorithms. 5.3 Applied example The RPD is a reliable criterion that can be deﬁned to evaluate and compare the quality of the solution for the In this section, applied instances are exercised to corrob- algorithms. Here, RPD is the relative deviation of the orate the pertinency of the model and solving methodology. outcome of each algorithm from the optimal result among To this end, ﬁfteen test problems in different dimension the ﬁve implemented approaches. These results for each scales are solved with tuned parameters of each meta- test size are shown in Fig. 20. In terms of RPD, HKASA heuristic (Table 2). Among these examples, the second shows better performance than all other algorithms for all example is inspired by a small-sized case in southern the three categories. Another avenue to evaluate the per- Khuzestan province situated in southern Iran. Khuzestan formance of the proposed metaheuristic algorithms is using province is surrounded by the Persian Gulf and has several one-way Analysis of Variance (ANOVA) to account for rivers such as Arvand river, Karun river, etc. Thus, it has any statistically signiﬁcant differences between the RPD of marine access with shrimp production capacity as well as the algorithms. RPD is a response variable and all ﬁve numerous ﬁshery farms which are active in this province. metaheuristics algorithms are factors. Two hypotheses are In the real-case example, four shrimp catching location is considered for the ANOVA test. The p-value for ANOVA considered. These four location are Karun river in Ahvaz, test is equal to zero; therefore, it can be concluded that Arvand river in Abadan, Bahmanshir river in Abadan, and there are statistically signiﬁcant differences in the RPDs. Musa Bay in Mandar-e-Emam. Five shrimp farms exist in For more precise analysis, the means plot and the least Ahvaz, Abadan, Mahshahr, Shadegan, and Hendijan. Other signiﬁcant difference (LSD) intervals at 95% conﬁdence details on the case study are shown in Fig. 16 as a symbolic level are presented in Figs. 21, 22 and 23 for small-size, scheme for SSC network which contains producers, medium size, and large size problems, respectively. In Table 4 Best levels of each algorithm Algorithms GA SA KA Notation Max P P N Max Sub T T Max N PN PN S It c m pop It It 0 damp It pop 1 2 max Optimal Level 800 0.8 0.1 100 800 30 1500 0.90 800 150 0.3 0.2 4 Algorithms HKASA HGASA Notation Max N PN PN S T T Max N Pc Pm T T It pop 1 2 max 0 damp It pop 0 damp Optimal Level 800 150 0.4 0.2 4 2000 0.9 800 100 0.9 0.15 2000 0.88 123 Shrimp closed-loop supply chain network design 7413 Table 5 The objective function (OF), RPD, hitting time (HT), and computational time (CT) value for each algorithm Tests Algorithms GA SA KA OF RPD HT CT OF RPD HT CT OF RPD Small-Size 1 7723.55 0.0000 23.76 42.42 7723.55 0.0000 8.99 15.76 7723.55 0.0000 2 11,486.71 0.0115 34.84 55.31 11,474.06 0.0104 10.41 19.64 11,355.86 0.0000 3 33,071.25 0.0091 65.24 95.94 32,786.31 0.0004 17.92 33.81 32,875.03 0.0031 4 44,948.50 0.0204 84.64 120.92 44,497.55 0.0101 21.28 42.57 44,050.55 0.0000 5 48,576.65 0.0370 101.89 134.06 46,845.50 0.0000 25.84 46.14 47,155.25 0.0066 Medium-Size 6 69,285.68 0.0492 166.74 213.77 66,034.25 0.0000 42.52 70.86 67,681.41 0.0249 7 119,697.27 0.0276 257.80 303.29 116,568.78 0.0007 49.32 98.63 116,819.47 0.0029 8 186,768.95 0.0408 344.59 396.09 180,103.55 0.0037 74.12 132.36 179,703.90 0.0014 9 218,473.50 0.0279 421.41 468.23 213,292.05 0.0036 93.63 158.70 212,849.85 0.0015 10 267,487.35 0.0424 558.19 613.40 258,446.40 0.0072 125.46 212.64 256,610.55 0.0000 Large-Size 11 327,230.00 0.0227 766.77 782.41 319,968.75 0.0000 260.72 266.04 321,759.40 0.0056 12 374,918.20 0.0119 894.35 912.60 370,492.55 0.0000 315.87 319.06 372,906.50 0.0065 13 517,371.39 0.0128 1275.40 1301.42 511,829.17 0.0020 435.53 439.93 511,997.58 0.0023 14 770,929.47 0.0282 2146.73 2190.54 751,002.95 0.0016 722.96 730.27 751,635.90 0.0025 15 1,162,159.40 0.0188 3755.28 3831.92 1,143,016.73 0.0020 1251.89 1264.53 1,143,265.08 0.0022 Tests Algorithms KA HKASA HGASA HT CT OF RPD HT CT OF RPD HT CT Small-Size 1 63.36 105.61 7723.55 0.0000 59.11 113.68 7723.55 0.0000 33.44 58.66 2 78.13 137.07 11,433.53 0.0068 87.25 164.62 11,483.66 0.0113 43.81 75.54 3 129.34 244.03 32,774.11 0.0000 145.87 270.14 32,938.22 0.0050 69.31 130.76 4 156.19 294.69 44,103.75 0.0012 180.47 353.87 44,735.86 0.0156 88.97 164.76 5 186.82 322.11 46,949.73 0.0022 211.51 391.68 47,725.03 0.0188 94.42 181.58 Medium-Size 6 307.12 511.86 66,985.99 0.0144 315.49 595.27 67,679.93 0.0249 157.71 286.75 7 414.96 715.44 116,482.36 0.0000 528.89 944.45 118,167.34 0.0145 230.78 404.88 8 481.74 875.88 179,446.81 0.0000 577.09 1049.26 183,489.91 0.0225 271.53 532.42 9 584.13 1123.32 212,534.96 0.0000 811.59 1352.66 215,945.37 0.0160 353.75 631.69 10 723.28 1418.20 256,664.71 0.0002 913.81 1791.79 263,043.70 0.0251 466.15 832.42 Large-Size 11 1911.65 1930.96 320,464.56 0.0015 2139.02 2160.63 323,693.09 0.0116 1045.87 1056.44 12 2226.55 2249.04 371,293.06 0.0022 2388.58 2412.71 372,812.47 0.0063 1228.82 1241.23 13 5593.82 5650.32 510,829.88 0.0000 5796.85 5915.15 514,748.03 0.0077 1719.46 1754.55 14 8535.54 8621.76 749,793.22 0.0000 8827.05 9007.19 761,187.19 0.0152 2883.86 2942.72 15 9008.35 9192.19 1,140,700.17 0.0000 9253.90 9442.76 1,152,920.42 0.0107 5031.70 5134.38 small-size problems, there is negligible difference between ﬁrst time at which each algorithm obtains the best solution. the performance of SA, KA, and HKASA (Fig. 21). As Figure 24 demonstrates the hitting time comparison for the shown in Fig. 22, in medium-size cases, KA outperformes proposed algorithms. We can conclude that the increment all other algorithms. Finally, the best performance among of the hitting time coincides with the augmentation of all algorithms belongs to HKASA for large-size problems problems sizes. Apparently, the growth rate of hitting time (Fig. 23). in KA and HKASA is more than that of GA, SA, and Hitting time is a tool used to investigate the speed of HGASA. algorithms in different problem sizes. It is deﬁned as the 123 7414 B. Mosallanezhad et al. Fig. 18 Objective function behavior for medium size problem Fig. 16 The Khuzestan province Fig. 19 Objective function behavior for large size problem Fig. 17 Objective function behavior for small size problem The last measure used to check the performance of our algorithms is the computation time. Figure 25 displays the information related to the computational time for all algorithms. Not surprisingly, the SA obviously has the least computational time and after followed by the GA, HGASA, Fig. 20 RPD comparison for the algorithms KA, and HKASA. 123 Shrimp closed-loop supply chain network design 7415 Fig. 21 Means plot and LSD intervals for the algorithms for small- size problems Fig. 24 Hitting time comparison for all algorithms Fig. 22 Means plot and LSD intervals for the algorithms for medium- size problems Fig. 25 Computational time comparison for each algorithm on the functional capability of the proposed model and provide a managerial insight, a sensitivity analysis on the major parameters are performed. Since the HKASA demonstrated to be one of the most efﬁcient algorithms with respect to different metrics, it has been applied here for the sensitivity analysis. Also, we selected the large-size experimental instance 14 as a test problem. Thus, we create three scenarios for sensitivity analysis in which we exam- Fig. 23 Means plot and LSD intervals for large-size problems ine the behavior of cost function under the change of capacity parameters, production/waste rate, and demands 5.4 Sensitivity analyses for each sector. The ﬁrst scenario explores the changes in the production In general, Sensitivity analysis is used to show how output variables change based on the variation of input parame- capacity of shrimp ﬁsher (k ), the production capacity of ters. In mathematical programming terms, sensitivity shrimp farmer (k ), the holding capacity at distribution analysis is a way to explore the effect of changes in the center (kd ), the production capacity of factory (kf ), hold- values of parameters on objective function. To shed light ing capacity at wholesaler (kw ), and production capacity 123 7416 B. Mosallanezhad et al. Table 6 The sensitivity analyses of ﬁrst experiment Capacity parameters Change (Tons) Objective function Capacity parameters Change (Tons) Objective function k 5 769,926.8 kw 5 779,183.9 i k 10 783,700.1 10 797,546.8 15 801,480.7 15 846,795.2 20 818,035.9 20 850,225.3 25 827,072.0 25 891,046.9 30 844,424.0 30 921,267.4 35 851,024.2 35 932,732.1 k 5 763,474.2 kf 5 804,315.5 0 l 10 771,854.0 10 826,209.1 15 790,678.5 15 873,524.1 20 807,244.2 20 929,484.0 25 813,515.6 25 954,929.7 30 824,121.2 30 963,600.9 35 834,273.1 35 984,758.3 kd 5 782,171.2 ks 5 758,695.0 j n 10 802,838.9 10 764,547.2 15 853,042.6 15 786,475.8 20 871,198.6 20 793,884.7 25 913,713.3 25 804,632.3 30 947,666.9 30 817,834.7 35 956,833.4 35 828,637.4 Fig. 26 Objective function behavior for sensitivity analysis (ﬁrst scenario) of shrimp waste powder factory (ks ). In this scenario, each objective function also increases. However, there is sig- parameter varies between 5 to 35 tons and other parameters niﬁcant difference between the effect of factories, distri- are kept unaltered. The performance of the objective bution centers, and wholesalers on the objective function in function with respect to the change of capacity parameters comparison with the other factors. So, it can be inferred are shown in Table 6 and Fig. 26. As shows Fig. 26 with that the capacity of shrimp production factories, distribu- the increase in the amount of capacity of each sector, the tion centers, and wholesalers should be determined 123 Shrimp closed-loop supply chain network design 7417 carefully to avoid risky increase in the cost of the supply signiﬁcant effect on the overall cost of the supply chain chain network. network than the shrimp waste powder demand. The second scenario seeks for the effect of changes in shrimp waste rate by the wholesaler (a ), shrimp produc- tion rate by factories (b ), and shrimp waste powder pro- 6 Managerial insights duction rate by factories (n ). Here, we consider the decrease in shrimp waste rate by wholesaler, and increase The purpose of this paper was to provide a supply chain in both shrimp production rate by factories, and shrimp network for both shrimp products engendered by marine waste powder production. The results of this scenario are and aquaculture. The strength of this model consists in the presented in Table 7 and Fig. 27. According to Fig. 27,we novelty of returning shrimp waste made by wholesalers and realize that all considered factors are positively associated shrimp factories as raw material to shrimp waste powder with an increase in the objective function value. However, factories. The use of the suggested supply chain network shrimp production rate of factory is reasonably effective can signiﬁcantly help in providing the governors and sea- rather than the others. food industries managers with guidelines on how to take The last scenario investigates the inﬂuence of shrimp strategic decisions. Iran has great potential capacity in product demand by customers (Db ), and shrimp waste seafood and aquaculture production such as skilled aca- powder demand by poultry and livestock food market demic experts, affordable industrial requirement such as (Dp ) on the supply chain network cost. The results of the facilities, oil and fuel, human resources. Moreover, it has third scenario are separately calculated for customer’s the most substantial advantage of direct access to three marine zones (the Persian Gulf, Gulf of Oman, and the demands and shrimp waste powder demand and shown in Table 8 and Fig. 28. The results indicate that whenever the Caspian Sea) and its great capability of establishing aquaculture projects in these locations. According to the demand in both sides vary increasingly, there is advance in optimum objective function value. Additionally, it is statistical evidences, developing countries and speciﬁcally Iran, have not yet approached to their satisfactory derived from Fig. 27 that demands of customers have more achievements in seafood industry, especially with respect to shrimp products. Indeed, we believe that countries like Iran should take advantage of its great opportunities and Table 7 The sensitivity analysis of second scenario competencies in seafood industry to boost its economy by Production and waste rate Change Objective gaining remarkable proﬁts and avoiding losses of parameters (%) function capabilities. Going in this direction, the model has assumed potential 1 a 0.80 759,524.5 locations for the distribution center, wholesaler, shrimp 0.85 770,902.4 factories, and shrimp waste powder factory. So, the ﬁnd- 0.87 796,687.0 ings of this model can help investors and governors to get 0.90 814,296.2 the best location to optimally distribute and transport 0.93 873,755.0 shrimp products throughout the network. Moreover, shrimp 0.95 917,694.4 industries can ﬁnd it advantageous, on the basis of this 0.97 934,031.2 study, to enrich their business by recycling the shrimp b 0.80 772,198.0 wastes, if they still didn’t implement such technology, with 0.85 781,315.0 further beneﬁts to the environment. 0.87 809,166.8 Another managerial implication of this study is con- 0.90 844,649.4 cerned with shrimp factories. The managers of these fac- 0.93 883,909.9 tories can apply this model to improve their ﬁxed opening 0.95 929,412.0 and transportation costs and manage production ﬂows and 0.97 963,853.9 supply chain activities. As a result, the optimized supply n 0.80 754,590.4 chain network design leads to pay the lowest cost and to 0.85 757,163.4 deliver the highest service level. These two privileges bring 0.87 773,967.9 competitive advantages over similar supply chains espe- 0.90 785,521.4 cially in the countries around the Persian gulf. For instance, 0.93 846,851.0 the managers can ﬁt their production capacities and 0.95 906,538.0 demand of market with the suggested constraints in the 0.97 914,806.3 model. Furthermore, the sensitivity analysis on demands and the other data together with the setting parameters can 123 7418 B. Mosallanezhad et al. Fig. 27 Objective function behavior for sensitivity analysis (second scenario) Table 8 The sensitivity analysis of third scenario Demand parameters Change (Tons) Objective function Demand parameters Change (Tons) Objective function Db 5 749,793.2 Dp 2 758,002.2 m p 10 772,005.9 4 768,611.9 15 826,632.0 6 777,863.1 20 837,372.3 8 801,915.1 25 854,960.8 10 813,052.0 30 889,661.5 12 838,650.6 35 902,351.3 14 846,043.5 Fig. 28 Objective function behavior for sensitivity analysis (third scenario) give valuable insights to the supply chain decision-makers. can be exploited by the managers of shrimp production The last but not the least, managers always seek for efﬁ- industries to solve their speciﬁc, or similar variants, of cient ways to solve their problems and make decision network design. successfully. This study offered several metaheuristics that 123 Shrimp closed-loop supply chain network design 7419 Regarding the methodological viewpoint, this study 7 Conclusion and future works developed a combination of efﬁcient classic, modern, and hybrid metaheuristics to increase the quality of problem Lately, due to the incessant progress of aquaculture pro- solving. The sensitivity analyses are inspired from the most duction, international markets, and changes in customers’ related and recent studies such as Cheraghalipour et al. desires, seafood business has been astoundingly developed. (2019) and Abdi et al. (2019). In many developed and developing countries, seafood There could be diverse extension on the presented work constitutes the most critical parts of people’s daily diet. for future studies. From mathematical modeling view, the Shrimp products is a desirable seafood among many pop- model can involve the multi-objective aspect by adding a ulations, and it represents a signiﬁcant amount of food product quality function by considering shelf-life of shrimp intake in different societies. Shrimp products is either products and arrival time of orders (see e.g. Bortolini et al. caught from marine environment like seas and rivers, or 2016), a function measuring the satisfaction level of the farmed in aquaculture systems. So, designing a proper manufacturer, market and customers (e.g. Gholami et al. supply chain network for shrimp productions can offer 2016) and shortage/responsiveness functions in the supply many beneﬁts for decision-makers, organizations, facto- chain (e.g. Gen et al. 2006). ries, or even markets to improve the functionality of supply The model could be also extended to cover a multi- chain. Thus, this paper introduced a mathematical model period settings by adopting shrimp maturity assumptions or for the SSC network to retrieve the desirable goals of even catching timeline. It might not be necessary to ﬁg- optimizing the total cost of whole network while respecting ure the model as a multi-product network because although a set of operational restrictions. there are different types of shrimp in the marine or aqua- The solution the proposed model has been ensured by culture production, they are sold in a single deal. However, three renowned metaheuristic algorithms: GA, SA, and if this is not the case in some markets then prospective KA. Additionally, two hybrid metaheuristic algorithms, researchers can think about designing multi-product including HGASA and HKASA, that embed the advantages models. of SA algorithm, were proposed. Thereafter, the Taguchi Another valuable extension of this study is to consider method was used to tune and set the parameters of the the sustainability paradigm to make the model more algorithms with the aim of achieving their better perfor- comprehensive. Therefore, future researches may need to mance. An applied example with 15 test problems was cover social, environmental, and economical aspects and generated considering the application of the SSC to the include them in terms of constraints into the model. Iranian real case, and four measures were used to compare Moreover, in real-world settings uncertainty and ambiguity the results of the designated algorithms. Even though the is common for different aspect of the supply chain network algorithms have shown different behavior with respect to especially demand of markets. For future considerations, the considered measures, the results show that KA and the model can be formulated as a stochastic model under HKASA had satisfactory performance, over the others, in uncertain condition of demands and other important solving the problem under exam. In additions, the results parameters (e.g. Beraldi et al. 2000). Finally, further show the applicability of the suggested SSC network in advances can be achieved even in the context of solution practice and to the effectiveness of proposed methodologies. For instance, developing stochastic and metaheuristics. robust metaheuristic and heuristic approaches that can Principally, this study presented practical and method- efﬁciently deal with the uncertain and multi-objective ological contributions. From the practical standpoint, this nature of the model can be a striking avenue. paper proposed a mathematical model for designing a SSC network as sought-after seafood and increasingly thriving market. The capability of the model is used to handle the Funding Open access funding provided by the Qatar National forward ﬂow of shrimp product from marine catching or Library. aquaculture production to distribution centers then to wholesalers and shrimp factories, and afterward to markets. Declarations It also manages the reverse ﬂow of waste product from wholesalers and shrimp factories to shrimp powder facto- Conflict of interest Author Behzad Mosallanezhad declares that he ries and to livestock and poultry food markets. The model has no conflict of interest. Author Mostafa Hajiaghaei-Keshteli helps to satisfy both the demands of shrimp products in declares that he has no conflict of interest. Author Chefi Triki markets and demand of by-products originated from waste declares that he has no conflict of interest. shrimps while it deals with the capacity restriction of the Ethical approval This article does not contain any studies with human distributors, factories, and particularly shrimp production. participants or animals performed by any of the authors. 123 7420 B. Mosallanezhad et al. Open Access This article is licensed under a Creative Commons Butterworth K (1985) Practical application of linear/integer program- Attribution 4.0 International License, which permits use, sharing, ming in agriculture. J Oper Res Soc 36(2):99–107 adaptation, distribution and reproduction in any medium or format, as Caixeta-Filho JV (2006) Orange harvesting scheduling management: long as you give appropriate credit to the original author(s) and the a case study. J Oper Res Soc 57(6):637–642 source, provide a link to the Creative Commons licence, and indicate Cerny´ V (1985) Thermodynamical approach to the traveling salesman if changes were made. The images or other third party material in this problem: an efﬁcient simulation algorithm. J Optim Theory Appl article are included in the article’s Creative Commons licence, unless 45(1):41–51 indicated otherwise in a credit line to the material. If material is not Cheraghalipour A, Paydar MM, Hajiaghaei-Keshteli M (2018) A bi- included in the article’s Creative Commons licence and your intended objective optimization for citrus closed-loop supply chain using use is not permitted by statutory regulation or exceeds the permitted Pareto-based algorithms. Appl Soft Comput 69:33–59 use, you will need to obtain permission directly from the copyright Cheraghalipour A, Paydar MM, Hajiaghaei-Keshteli M (2019) holder. To view a copy of this licence, visit http://creativecommons. 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Int J Ind Syst Eng Van Engeland J, Belien J, De Boeck L, De Jaeger S (2018) Literature 12(3):259–279 review: strategic network optimization models in waste reverse supply chains. Omega. Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional afﬁliations.

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