Annals of Operations Research

Gaivoronski, A.; Messina, E.; Sciomachen, A.

doi: 10.1007/BF02038859pmid: N/A

In this paper, we are concerned with an algorithm which combines the generalized linear programming technique proposed by Dantzig and Wolfe with the stochastic quasigradient method in order to solve stochastic programs with recourse. In this way, we overcome the difficulties arising in finding the exact values of the objective function of recourse problems by replacing them with the statistical estimates of the function. We present the basic steps of the proposed algorithm focusing our attention on its implementation alternatives aimed at improving both the convergence and computational performances. The main application areas are mentioned and some computational experience in the validation of our approach is reported. Finally, we discuss the possibilities of parallelization of the proposed algorithmic schemes.

Smith, J.; Chikhale, Nikhil

doi: 10.1007/BF02038860pmid: N/A

In this paper, we examine a class of nonlinear, stochastic knapsack problems which occur in manufacturing, facility or other network design applications.Series, merge-and-split topologies of series-parallelM/M/1/K andM/M/C/K queueing networks with an overall buffer constraint bound are examined. Bounds on the objective function are proposed and a sensitivity analysis is utilized to quantify the effects of buffer variations on network performance measures.

Sagastizábal, C.

doi: 10.1007/BF02038861pmid: N/A

We study here a set of quasi-variational inequalities related to inventory/production stochastic problems. We mainly focus our attention on two subjects: (i) From a theoretical point of view, we compare the advantages of global controls versus a decentralized approach via a model of an inventory serial system with Gaussian demand. (ii) We consider discretized systems, we solve the simple model of (i), and we apply a similar technique for solving a more complex system with Poissonian demand. The centralized approach naturally leads to large-scale problems; we solve them using a fast algorithm of resolution with very good performances. We conclude with some numerical results.

Neck, Reinhard; Karbuz, Sohbet

doi: 10.1007/BF02038862pmid: N/A

In this paper, we determine optimal budgetary and monetary policies for Austria using a small macroeconometric model. We use a Keynesian model of the Austrian economy, called FINPOL1, estimated by ordinary least squares, which relates the main objective variables of Austrian economic policies, such as the growth rate of real gross domestic product, the rate of unemployment, the rate of inflation, the balance of payments, and the ratio of the federal budget deficit to GDP, to fiscal and monetary policy instruments, namely expenditures and revenues of the federal budget and money supply. Optimal fiscal and monetary policies are calculated for the model under a quadratic objective function using the algorithm OPTCON for the optimum control of nonlinear stochastic dynamic systems. Several control experiments are performed in order to assess the influence of different kinds of uncertainty on optimal budgetary and monetary policies. Apart from deterministic optimization runs, different assumptions about parameter uncertainties are introduced; the results of these different stochastic optimum control experiments are compared and interpreted.