Capacity management for a leasing system with different equipment and batch demands

Abstract

This work explores the admission and capacity allocation for a leasing system with two types of equipment and three kinds of batch demands: elementary-specified, premium-specified and unspecified demands. The demands arrive following mutually independent Poisson processes and the rental duration of equipment follows a negative exponential distribution. The lessor can satisfy partially the specified demands with the required type of equipment and satisfy partially the unspecified demands with any type of equipment. The objective is to maximise the expected discounted revenue. We formulate this problem as a Markov Decision Process, prove the anti-multimodularity of the value function and characterise the structure of the optimal policy. We show that the optimal policy has a simple structure and is characterised by state-dependent rationing and priority thresholds. Moreover, a solution algorithm is proposed to calculate the optimal policy. We study the impacts of the system state on the optimal action, and find that the optimal action has limited sensitivity to the system state. Numerical studies are conducted to compare the performance of the optimal policy with that of two heuristic methods and to derive some managerial insights by analysis. We further discuss batch acceptance.