Bi-objective min-flow problem with capacity and flow constraints

Abstract

A network flow algorithm for a bi-criteria version of the manpower scheduling and resource allocation problem is developed. In such a study it is desired to find the ‘minimum’ total ‘flow’ through the network, where ‘flow’ is represented by a two-component cost vector and ‘minimum’ is interpreted in the sense of a vector-minimum. Thus, a set of non-dominated solutions is obtained. The method efficiently generates both individual (criterion) optima and bi-criteria solutions in a single pass. A simple example is presented.