Managing equipment rentals: Unreliable fleet, impatient customers, and finite commitment capacity

In this paper, we discuss fleet size decisions of an equipment rental firm. The availability of the rental equipment depends on the fleet size of the firm and has a direct impact on its profitability. In our setting, we allow for partial backordering, reneging, and finite commitment capacity. Moreover, we explicitly consider the breakdown possibility of the available equipment fleet. We develop an efficient recursive algorithm to solve the underlying two‐dimensional stochastic single‐player model. Our algorithm determines the global optimal fleet size of the firm for the same reneging and equipment return rates. Our extensive managerial insights quantify the behavior of various performance measures in the single‐player model with regard to repair performance of the firm, customer impatience level, traffic intensity, and equipment rental revenue. We demonstrate that by applying our model to a real case, there is a potential of more than a 4% (400,000 USD) increase in total daily profits. Extending our model to a two‐player game, we propose an approximation heuristic to derive closed‐form solutions to estimate equilibrium fleet sizes under complete information. Using our heuristic as the initial solution, we develop a simulation model to determine the exact equilibrium fleet sizes and draw a detailed comparison between the two‐player and single‐player models.