Scheduling Tasks and Vehicles in FMSs — Network Flow Model

A problem of simultaneous task scheduling and vehicle routing in a flexible flow shop, is considered. The problem of finding a feasible vehicle schedule for the given machine schedule is reduced to the one of finding a maximum flow in the a three-partite network. On the other hand, if a minimum number of vehicles is looked for, then the problem must be reduced to the one of finding maximal flow of a minimum cost in the network with irregular cost function.