Modeling the Gateway Location Problem for Multicommodity Flow Rerouting

Abstract

This paper introduces a new problem, involving the optimal location of a limited number of gateways on the nodes of an uncapacitated network. A multicommodity flow, where each commodity is of single-origin-single-destination type, moves on the network according to its linear objective function c. Gateways are used by the network administrator to reroute flows by obliging each commodity to detour from its c-optimal path and pass by its assigned gateway. Gateways are located and assigned by the administrator so that the resulting c-optimal flows on the detours minimize the administrator’s objective function r. Gateways thus provide the administrator with a mechanism for indirect flow control, so that the flow value according to r is improved with respect to the unregulated scenario. To the authors knowledge, this is a new combinatorial optimization problem, that we call the gateway location problem for multicommodity flow rerouting. We present three alternative formulations and discuss pros and cons of each. Interesting applications arise in the field of hazardous material transportation. The discussion is supported by computational results on realistic instances from this field.