Modifications of the Two-Stage Transportation Problem and Their Applications

Mathematical models of linear and Boolean linear programming for the balanced two-stage transportation problem and its two modifications are analyzed. The first modification takes into account the upper limits on the capacity of intermediate points, and the second modification allows choosing a fixed number of intermediate points, less than their total number. For all the cases, the necessary and sufficient conditions for the consistency of the systems of linear constraints of the corresponding mathematical programming problems are justified. Examples of applying the modifications for the optimal set partitioning, the p-median graph problem, and the problem of optimal arrangement of a given number of storages are considered. The results of the computing experiments using the Gurobi and CPLEX solvers and the AMPL modeling language are presented.