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

Xufeng Yang (), Juliang Zhang (), Wen Jiao () and Hong Yan ()
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Xufeng Yang: School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China
Juliang Zhang: School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China
Wen Jiao: Centre for Simulation, Analytics and Modelling, University of Exeter Business School, Exeter EX4 4PU, United Kingdom
Hong Yan: College of Management, Zhejiang Shuren University, Hangzhou 310015, China

Management Science, 2023, vol. 69, issue 3, 1468-1485

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.

Keywords: container leasing; capacity rationing; Markov Decision Process; downward substitution (search for similar items in EconPapers)
Date: 2023
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