Abstract
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.
Highlights
Purchasing a vehicle fleet is one of the most expensive capital investments a company or organization can make
Purchasing too few vehicles will result in excessive hiring costs, as additional vehicles will need to be hired whenever vehicle requirements exceed fleet capacity
Many optimization problems related to fleet composition have been discussed in the literature; see, for example, [3, 6, 7, 8, 11] and the references cited therein
Summary
Purchasing a vehicle fleet is one of the most expensive capital investments a company or organization can make. Number of (owned) type-i vehicles used during period t = min{vit, pi} Number of type-i vehicles hired during period t = max{vit − pi, 0}.
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