Bicriteria network flow problems: Integer case

The authors consider a bicriteria network flow problem with flow variables restricted to integer values. The set of efficient solutions to the problem can be obtained by adopting a bicriteria integer programming technique. The purpose of this paper is to present a new technique which capatalizes on the network structure and the unimodular property of the incidence matrix. The procedure uses efficient solutions to the continuous version of the bicriteria network flow problem and parametric programming in order to generate the efficient solutions to the bicriteria integer network flow problem. The performance of the algorithm is also discussed.