A solution approach to minimal average cost flow problem with lower and upper bounds on flows

Abstract

As a variant of minimal cost flow problem, the minimal average cost flow problem with lower and upper bounds on flows (MACFLUB) is to search the feasible flow with minimal average cost in network with lower and upper arc capacities and fixed network cost. Only three methods are available in the literature to solve the special cases of MACFLUB, and they cannot be applied to the general case. This paper reduces the MACFLUB to the minimization of a function with U-shaped curve, and develops an algorithm named MACFLUB-MCMFA as more generalized solution approach based on minimal cost maximal flow algorithm. Computational study validates that the MACFLUB-MCMFA algorithm is a robust and efficient approach to solving the MACFLUB.