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C. Lemke (1954)
The dual method of solving the linear programming problemNaval Research Logistics Quarterly, 1
A. Charnes, W. Cooper, G. Symonds (1958)
Cost Horizons and Certainty Equivalents: An Approach to Stochastic Programming of Heating OilManagement Science, 4
A. Charnes, M. Kirby (1967)
Some Special P-Models in Chance-Constrained ProgrammingManagement Science, 14
E. Balas, P. Ivanescu (1964)
On the Generalized Transportation ProblemManagement Science, 11
E. Balas (1966)
The Dual Method for the Generalized Transportation ProblemManagement Science, 12
A Charnes, D. Klingman (1970)
The Distribution Problem with Upper and Lower Bounds on Node Requirements, 16
H. Wagner (1959)
On a Class of Capacitated Transportation ProblemsManagement Science, 5
A. Charnes, W. W. Cooper (1961)
Management Models and Industrial Applications of Linear Programming
A. Charnes, W. Cooper (1954)
The Stepping Stone Method of Explaining Linear Programming Calculations in Transportation ProblemsManagement Science, 1
P. Rivett (1972)
Principles of Operations Research
G. Dantzig (1965)
Linear programming and extensionsThe Mathematical Gazette, 49
A. Charnes, W. Cooper (1963)
Deterministic Equivalents for Optimizing and Satisficing under Chance ConstraintsOperations Research, 11
G. Ross, D. Klingman, H. Napier (1975)
A Computational Study of the Effects of Problem Dimensions on Solution Times for Transportation ProblemsJ. ACM, 22
A. Charnes, D. Klingman (1970)
Note---The Distribution Problem with Upper and Lower Bounds on the Node RequirementsManagement Science, 16
L. R. Ford, D. R. Fulkerson (1961)
An Out‐of‐Kilter Method for Minimal Cost Flow Problems, 9
A. Orden (1956)
The Transhipment ProblemManagement Science, 2
L. R. Ford, D. R. Fulkerson (1962)
Flows in Networks
Egon Balas, P. L. Hammer (1962)
On the Transportation Problem—Part II, 4
F. Glover, David Karney, D. Klingman, A. Napier (1974)
A Computation Study on Start Procedures, Basis Change Criteria, and Solution Algorithms for Transportation ProblemsManagement Science, 20
G. B. Dantzig (1951)
Activity Analysis of Production and Allocation
A. Charnes, W. W. Cooper (1954)
The Stepping Stone Method of Explaining Linear Programming in Transportation Problems, 1
R. Barr, F. Glover, D. Klingman (1974)
An improved version of the out-of-kilter method and a comparative study of computer codesMathematical Programming, 7
A. Charnes, W. Cooper (1959)
Chance-Constrained ProgrammingManagement Science, 6
A. Charnes, M. Kirby (1964)
The Dual Method and the Method of Balas and Ivanescu for Transportation Model, 6
A. Charnes, W. Raike (1966)
One-Pass Algorithms for Some Generalized Network ProblemsOper. Res., 14
The transportation model with supplies (Si) and demands (Di) treated as bounded variables developed by Charnes and Klingman is extended to the case where the Si and Di are independently and uniformly distributed random variables. Chance constraints which require that demand at the jth destination will be satisfied with probability at least βi and that stockout at the ith origin will occur with probability less than αi are imposed. Conversion of the chance constraints to their linear equivalents results in a transportation problem with one more row and column than the original with some of the new arcs capacitated. The chance‐constrained formulation is extended to the transshipment problem.
Naval Research Logistics: An International Journal – Wiley
Published: Mar 1, 1977
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