Possibilistic Minimum-cost Flow Problem
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To illustrate the applications of the proposed fuzzy approaches, the minimum-cost flow (MCF) problem was investigated and several examples were solved. Minimum-cost flow problem is a general form of network flow problem, whose aim is to find the least cost of shipments of commodities through capacitated network in order to satisfy demands at certain nodes from available supplies at other nodes. The results from the study of this general problem can be applied to many other network problems such as transportation, maximum flow, assignment, shortest path, and transshipment problems. In addition, the results from these kind of study frequently offer bounds or rough estimates to more complicated network problems such as the Chinese postman problem [Pearn 1994]. Therefore, the MCF problem plays a crucial role in the understanding of network flow. Furthermore, the MCF is also very practical and has been applied to a number of real-world problems such as multi-stage production and inventory planning, mold allocation, nurse scheduling, project assignment, and automobile routing [Ahuja et al. 1993].