Routing trains through railway stations: complexity issues

Article Abstract:

A problem in routing trains through railway stations is mathematically described using an integer linear program. The challenge involved the possibility of routing trains through a station such that there are no conflicting pairs of trains, the trains can be coupled or uncoupled as required and that several service requirements are fulfilled. It was shown that only a subset of the sections of the track and routing possibilities are needed in evaluating the feasibility of a specific train routing arrangement.

Operations research, Management science, Railroads, Integer programming, Chaos theory, Chaotic systems, Feasibility studies

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A differential game model of a market of substitutable products

Article Abstract:

A differential game model is formulated for a market selling substitutable products. A feedback Nash equilibrium (FNE) solution for the game is determined to avoid time-inconsistency. The model is demonstrated for symmetric companies which have terminal valuations and can operate in market for an unlimited period of time. A set of state-dependent equilibrium strategies are determined. The model is also extended to a stochastic formulation and to an infinite time horizon specification.

Differential games, Substitute products

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The reduced form of a game

Article Abstract:

The reduced form of a normal form game was analyzed in terms of its unicity and resolution. Utilization of a game reduction approach designed by Mertens revealed the unicity of the reduced form of a normal form game. A direct combinatorial-geometric interpretation of the reduced form of a game was also established and was used in obtaining an algorithm that will calculate the reduced form.

Research and Development in the Physical, Engineering, and Life Sciences, Mathematics, Algorithms

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