Multicommodity Network Flow Problems with Overlapping Capacities for Several Products
Typically the models described in the literature for multistage multicommodity distribution-systems assume, that features combining different commodities only occur in the objective. Therefore, in the case of linear or linearized distribution-system design problems the masterproblem decomposes into as many independent subproblems as there are different commodities. Therefore, each of these subproblems can be solved by known standard optimizing algorithms. Contrary to these assumptions real-life applications usually show a lot of constraints concerning two or more products. Frequently, each client has to be assigned to exactly one distribution center (single-source constraint) or there are capacitated resources at the facilities for production and throughput for all commodities or only subsets of the different commodities. Considering these constraints it’s no longer possible to solve the original master-problem as a sequence of independent one-product subproblems.