Search

Manufacturing network flow (MNF) is a generalized network model that can model more complicated manufacturing scenarios, such as the synthesis of different materials to one product and/or the distilling of one material to many different products. Minimum distribution cost flow problem (MDCF) is a simplified version of MNF optimization problems, in which a general supplier wants to proportionally distribute certain amount of a particular product from a source node to several retailers at different destinations through a distribution network. A network simplex algorithm has been outlined in recent years for solving a special case of MDCF. In this paper, we characterize the network structure of the bases of the MDCF problem and develop a primal simplex algorithm that exploits the network structure of the problem. These results are extensions of those of the ordinary network flow problems. In conclusion, some related interesting problems are proposed for future research.Manufacturing network flow (MNF) is a generalized network model that can model more complicated manufacturing scenarios, such as the synthesis of different materials to one product and/or the distilling of one material to many different products. Minimum distribution cost flow problem (MDCF) is a simplified version of MNF optimization problems, in which a general supplier wants to proportionally distribute certain amount of a particular product from a source node to several retailers at different destinations through a distribution network. A network simplex algorithm has been outlined in recent years for solving a special case of MDCF. In this paper, we characterize the network structure of the bases of the MDCF problem and develop a primal simplex algorithm that exploits the network structure of the problem. These results are extensions of those of the ordinary network flow problems. In conclusion, some related interesting problems are proposed for future research.

Abstract In this paper, we consider weighted inverse minimum spanning tree problems under Hamming distance. Three models are considered: unbounded case, unbounded case with forbidden edges, and general bounded case. In terms of the method for minimum-weight node cover problem on bipartite graph, we present their respective strongly polynomial algorithms.