Two-Stage Transportation Problem with Two-Sided Constraints on Consumer Demands and Upper Bounds for Capacity of Intermediate Points

The authors considered a mathematical model of a two-stage transportation problem with two-sided constraints on consumer demands and upper bounds on the capacities of intermediate points. They substantiated the necessary and sufficient conditions for the consistency of the system of linear constraints for the corresponding linear programming problem. The article presents two mathematical models of a two-stage transportation problem to which one can reduce the original model. It also presents the results of computational experiments on applying the problem described to the optimal set partitioning problem using the CPLEX solver from the NEOS server.