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.

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 maximize the expected discounted revenue. We formulate this problem as a Markov decision process, prove the anti-multimodularity of the value function, and characterize the structure of the optimal policy. We show that the optimal policy has a simple structure and is characterized 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.

In recent years, many retailers sell their products through not only offline but also online platforms. The sales of perishable goods on e-commerce platforms recorded phenomenal growth in 2020. However, some retailers are overconfident and order more products than the optimal ordering quantity, resulting in great losses due to product decay. In this paper, we apply the newsvendor model to analyze the impacts of overconfident behavior on the retailer’s optimal pricing and order quantity decisions and profit. Our model provides the overconfident retailer with a feasible and effective method to adjust optimal ordering and pricing decisions. Through numerical studies, we examine the retailer’s optimal decisions under the scenarios of complete rationality, over-estimation, and over-precision. We find that the over-estimation retailer always orders more products than the optimal order quantity, and the over-precision retailer always orders fewer products than the optimal order quantity. Under some conditions, overconfidence hurts the retailer’s revenue to a large extent. Therefore, it is beneficial for the overconfident retailer to adjust its order quantity according to our research findings.

No abstract