Optimal capacity rationing policy for a container leasing system with multiple kinds of customers and substitutable containers
Yang, X; Zhang, J; Jiao, W; et al.Yan, H
Date: 19 May 2022
Article
Journal
Management Science
Publisher
Institute for Operations Research and Management Sciences
Publisher DOI
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 ...
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.
Management
Faculty of Environment, Science and Economy
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