Optimal Fleet Composition via Dynamic Programming and Golden Section Search
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This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Journal of Industrial and Management Optimization following peer review. The definitive publisher-authenticated version Loxton, Ryan and Lin, Qun. 2011. Optimal Fleet Composition via Dynamic Programming and Golden Section Search. Journal of Industrial and Management Optimization. 7 (4): pp. 875-890. is available online at: http://dx.doi.org/10.3934/jimo.2011.7.875
In this paper, we consider an optimization problem arising in vehicle fleet management. The problem is to construct a heterogeneous vehicle fleet in such a way that cost is minimized subject to a constraint on the overall fleet size. The cost function incorporates fixed and variable costs associated with the fleet, as well as hiring costs that are incurred when vehicle requirements exceed fleet capacity. We first consider the simple case when there is only one type of vehicle. We show that in this case the cost function is convex, and thus the problem can be solved efficiently using the well-known golden section method. We then devise an algorithm, based on dynamic programming and the golden section method, for solving the general problem in which there are multiple vehicle types. We conclude the paper with some simulation results.
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