A stochastic fleet composition problem

In this paper, we consider the problem of forming a new vehicle fleet, consisting of multiple vehicle types, to cater for uncertain future requirements. The problem is to choose the number of vehicles of each type to purchase so that the total expected cost of operating the fleet is minimized. The total expected cost includes fixed and variable costs associated with the fleet, as well as hiring costs that are incurred whenever vehicle requirements exceed fleet capacity. We develop a novel algorithm, which combines dynamic programming and the golden section method, for determining the optimal fleet composition. Numerical results show that this algorithm is highly effective, and takes just seconds to solve large-scale problems involving hundreds of different vehicle types.