Nonlinear pricing for stochastic container leasing system

Abstract

With the substantial upsurge of container traffic, the container leasing company thrives on the financial benefits and operational flexibility of leasing containers requested by shippers. In practice, container lease pricing problem is different from the consumer product pricing in consideration of the fair value of container, limited customer types and monopolistic supply market. In view of the durability of container and the diversified lease time and quantity, the pricing is a challenging task for the leasing company. This paper examines the monopolist's nonlinear pricing problems in static and dynamic environments. In particular, the leasing company designs and commits a menu of price and hire quantity/time pairs to maximize the expected profit and in turn customers choose hire quantities/time to maximize their surpluses according to their hire preferences. In a static environment, closed-form solutions are obtained for different groups of customers with multiple types subject to capacity constraint. In a dynamic environment, we address two customer types and derive closed-form solutions for the problem of customers with hire time preference. Further, we show that the effect of the capacity constraint increases with time of the planning horizon when customers have the same hire time preference; while in the case with different hire time preferences, the capacity constraint has opposite effects on the low and high type customers. Last, the case of customers with hire quantity preference is discussed. We focus on the lease with alternative given sets of hire time and use dynamic programming to derive the numerical optimal hire time sequence.

Dynamic allocation and pricing for capacitated stochastic container leasing systems with dynamic arrivals

“…Different from them, we study the dynamic rationing and pricing problem in the container leasing industry by considering its features in terms of multiple-unit demand, monopolistic supply, and long-standing customer relationships. The main differences between the present study and that conducted by Jiao et al (2016) are as follows. (1) We consider that customers first arrive at the company stochastically, which is more realistic in practice, and we also compare the effect of the case with dynamic arrivals and the case with simultaneous arrivals on the optimal allocation policy.…”

“…Benigno et al (2012) applied the revenue management approach to discuss a truck rental problem through dynamic programming formulations and derived primal and dual acceptance policies. Jiao et al (2016) examined nonlinear pricing problems for a monopolist in static and dynamic environments in the context of container leasing industry. In a static environment, they derived the closed-form solutions for the problem under different customer groups with multiple types.…”

“…The above revenue management papers except for Jiao et al (2016) either assume the unit demand request (car rental and truck rental) or consider short-life cycle products (video rental) where the leasing company's rationing and pricing decisions are independent of the lease history. Different from them, we study the dynamic rationing and pricing problem in the container leasing industry by considering its features in terms of multiple-unit demand, monopolistic supply, and long-standing customer relationships.…”

“…(1) We consider that customers first arrive at the company stochastically, which is more realistic in practice, and we also compare the effect of the case with dynamic arrivals and the case with simultaneous arrivals on the optimal allocation policy. (2) We present an explicit expression of the capacity constraint in the case with the same hire time preference, whereas only a recursive formula was derived by Jiao et al (2016) from the capacity constraint in the same case. (3) We provide management insights for leasing companies based on the optimal allocation and pricing policy.…”

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

“…According to the United Nations Conference on Trade and Development (UNCTAD 2022), global container port throughput has experienced outstanding growth from 541.76 million TEU in 2010 to 807.33 million TEU in 2019, which shows the increasing demand from shipping companies for containers. Shipping companies either purchase from the trading market to acquire their own fleet or lease from container leasing firms in order to enjoy benefits such as cost saving, quick response to demand changes, and high flexibility (Jiao et al 2016).…”