Finding a compromise solution to the transportation problem under uncertainty

Abstract

The paper considers the solution of one combinatorial optimization problem under uncertainty. Its functional in deterministic formulation is a linear convolution of weights and arbitrary characteristics of a feasible solution. A constructive algorithm for its solving is a general linear programming problem solution algorithm. Under the uncertainty we mean the ambiguity of the weight values in the functional we optimize. We propose a new approach for finding a compromise solution by the criterion of minimizing the total weighted excess of “desirable” upper bounds on the optimal values of particular functionals. The basis of this approach is the construction and solution of some linear programming problem. We illustrate this approach on a transportation problem example in conditions of uncertainty. Ref. 15, tabl. 2

Keywords

• Uncertainty
• combinatorial optimization
• compromise solution
• transportation problem of linear programming.