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On seeking efficient Pareto optimal points in multi-player minimum cost flow problems with application to transportation systems. (English) Zbl 1426.90227
Summary: In this paper, we propose a multi-player extension of the minimum cost flow problem inspired by a transportation problem that arises in modern transportation industry. We associate one player with each arc of a directed network, each trying to minimize its cost function subject to the network flow constraints. In our model, the cost function can be any general nonlinear function, and the flow through each arc is an integer. We present algorithms to compute efficient Pareto optimal point($$s$$), where the maximum possible number of players (but not all) minimize their cost functions simultaneously. The computed Pareto optimal points are Nash equilibriums if the problem is transformed into a finite static game in normal form.
##### MSC:
 90C29 Multi-objective and goal programming 90C35 Programming involving graphs or networks 90B06 Transportation, logistics and supply chain management