Combinatorial algorithms for the minimum interval cost flow problem

The aim of minimum the interval cost flow problem (MICFP) is to find the least cost of the shipment of a commodity through a capacitated network in order to satisfy demands at certain nodes from available supplies at other nodes where there exists some vague in vector cost of problem. Interval cost is a common event in uncertainty environments, where statistical data are applied. Moreover they almost play an essential role in fuzzy programming, specially in the case of using their cuts. In this paper, a complete order on intervals is defined and efficient combinatorial algorithms for MICFP are proposed. Digital simulation results show the performance of the proposed algorithms compared with real scenarios.