Application of Stochastic Linear Programming in the Solution of a Transportation Problem

Document Type : Original Article

Authors

1 Eng. Mathematics Department, Military Technical Collage-Cairo, Egypt.

2 Prof. Dr. in Eng. Mathematics Department, Military Technical Collage-Cairo, Egypt.

3 Assoc. Prof. in Eng. Mathematics Department, Military Technical Collage-Cairo, Egypt.

4 Dr. in Military Technical Research Center-Cairo, Egypt.

Abstract

Abstract:
Stochastic Linear Programming (SLP), has a great importance due to its various applications in real life. In particular, the two-stage SLP or, sometimes, recourse programming. We used the two-stage SLP to describe the common transportation problem in case of random levels of supplies and demands. The randomness in the supplies and demands levels gives more realistic description of the problem. The random parameters in such problems may be continuously or discretely distributed. Indeed, there are many algorithms used to solve such problems in both continuous and discrete cases. The L-shape algorithm is the most commonly used in the discrete case two-stage SLP, but the problem in this method is the need for large computer memory to perform the iterations in such problems which have large numbers of decision variables. We give an example of such transportation problems and carry out using two distinct designs for the problem. One, using a subcontract with very high cost as penalty for demands not met. The other, using a virtual extra-demand at each supplier and these extra amounts act like supplying the over-demands. In each design, we calculate the total expected cost once using the expectation of each random variable, and another using the most likely realization of each random variable. We perform analysis of variance ANOVA to compare the four treatments from statistical point of view. Detailed results were illustrated for each design. All computations were performed with Matlab R2014a and MS-Excel2014.

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