Optimal Capacity Rationing Policy for a Container Leasing System with Multiple Kinds of Customers and Substitutable Containers

Abstract

In this paper, we consider a container leasing firm that has elementary and premium containers, which are downward substitutable and for use by elementary contract customers (ECCs), premium contract customers (PCCs), as well as walk-in customers (WICs). ECCs can be satisfied by elementary containers or premium ones at discounted prices while PCCs only accept premium containers. WICs can be satisfied by any type of container at different prices. The objective is to maximise the expected total rental revenue by managing its limited capacity. We formulate this problem as a discrete-time Markov Decision Process and show the submodularity and concavity of the value function. Based on this, we show that the optimal policy can be characterised by a series of rationing thresholds, a series of substitution thresholds and a priority threshold, all of which depend on the system states. We further give conditions under which the optimal policy can be simplified. Numerical experiments are conducted to show the impact of the substitution of two items on the revenue, to compare the performance of the optimal policy with those of the commonly used policies and to investigate the influence of arrival rates on the optimal policy. Last, we extend the basic model to consider different rental durations, ECCs’ acceptance behaviour and endogenous prices for WICs. This paper was accepted by Jayashankar Swaminathan, operations management.

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

“…In contrast, we investigate a leasing system that supplies two types of equipment and adopts the partial acceptance policy. Yang et al (2022) examined the optimal rationing policy for a system with two types of Production and Operations Management containers and multiple customer groups with single-unit demand. We extend their work by further considering batch demands where the lessor can partially meet demands.…”

“…Wang et al (2021) studied the joint decision on production and allocation for a queuing system with different customer classes. Yang et al (2022) explored the rationing policy for a leasing company with two types of containers. Differently from the above-quoted works, we consider a capacity management problem with batch demands that can be partially met.…”

“…How to cite this article: Yang, X., Jiao, W., Zhang, J., & Yan, H. (2022). Capacity management for a leasing system with different equipment and batch demands.…”

“…Yang et al. (2022) explored the rationing policy for a leasing company with two types of containers. Differently from the above‐quoted works, we consider a capacity management problem with batch demands that can be partially met.…”

“…Transportation companies need many vehicles to carry goods. However, the majority of works on the capacity management of leasing systems assume unit demand (Savin et al., 2005; Yang et al., 2022).…”