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Algorithm for the stochastic generalized transportation problem

100%

Anholcer M.

2012

tom Vol. 22, No. 4

9--20

The equalization method for the stochastic generalized transportation problem has been presented. The algorithm allows us to find the optimal solution to the problem of minimizing the expected total cost in the generalized transportation problem with random demand. After a short introduction and literature review, the algorithm is presented. It is a version of the method proposed by the author for the nonlinear generalized transportation problem. It is shown that this version of the method generates a sequence of solutions convergent to the KKT point. This guarantees the global optimality of the obtained solution, as the expected cost functions are convex and twice differentiable. The computational experiments performed for test problems of reasonable size show that the method is fast.

Stochastic Generalized Transportation Problem with discrete distribution of demand

100%

ANHOLCER M.

tom 23

nr 4

9-19

The generalized transportation problem (GTP) allows us to model situations where the amount of goods leaving the supply points is not equal to the amount delivered to the destinations (this is the case, e.g. when fragile or perishable goods are transported or complaints may occur). A model of GTP with random, discretely distributed, demand has been presented. Each problem of this type can be transformed either into the form of a convex programming problem with a piecewise linear objective function, or a mixed integer LP problem. The method of solution presented uses ideas applied in the method of stepwise analysis of variables and in the equalization method.