A dynamic pricing model of container liner shipping with overlapping legs on shipping network in a duopoly competition market

ABSTRACT

Container liner shipping is an important backbone for international trade marine transportation of industry products. After the 2008 financial crisis and especially with the recent COVID-19 pandemic, the international liner shipping has been at a low ebb. It has experienced an overall imbalance in the supply and demand of transportation capacity, prolonged recession periods, and low-level fluctuations in freight rates. Moreover, the imbalance between supply and demand has been extremely prominent and the operating cost has risen drastically. Therefore, competition between liner companies has grown fiercer. To reduce operating costs and increase their market share and shipping competitiveness, container liner companies have strengthened their cooperation and formed shipping liner alliances. With dominant ocean carriers and the merger of the carriers′ industry, the carrier competition exhibits an oligopolistic nature. The capital-intensive nature of regular shipping services has led to fierce competition between shipping lines. Low service differentiation in liner shipping implies that competition in this industry is mainly on a cost or price (freight rate) basis. Therefore, how to formulate reasonable container liner freight rates has become a core decision-making issue for shipping companies in an oligopolistic market. Furthermore, with the advent of online booking systems, such as the one operated by Maersk Line, adjusting realtime prices can become less costly, which will make a dynamic pricing strategy possible and necessary. In view of this, this paper focuses on the dynamic pricing strategy of container liner shipping in a duopoly market. This paper makes the following contributions to the literature. (1) It contributes to the literature by expanding the current literature by exploring the dynamic pricing problem that extends from a single origin-destination (OD) stream to multiple OD streams under a liner shipping network. (2) A time-phrased dynamic pricing game strategy is proposed to solve the pricing problem of liner shipping networks with overlapping legs based on the principle of discrete-time dynamic generalized Nash equilibrium. Shipping lines face two types of customer demands long-term contractual demand and spot market demand. The price of the longterm demand is often fixed and contracted once a year, whereas the price of spot market demand may be agreed upon between shipping lines and shippers (or freight forwarders) dynamically on a daily or weekly basis. The regularity of liner shipping services indicates that liner services are perishable products, which means that unutilized vessel slots will lose the opportunity to generate revenue. Therefore, it is vital for a shipping line to seek an appropriate pricing strategy to maximize its revenue in the competitive and uncertain spot market. In addition, a container liner shipping network operates on multiple routes, and there are overlapping legs. The container freight rates of an OD that flows on different routes should be consistent without affecting the distribution ratio of the customer′s cargo transportation between the overlapping legs of each route. Therefore, from the perspective of customer classification, the focus of container liner shipping pricing decisions is mainly on the dynamic pricing of spot market customers. Based on the actual operation of liner shipping companies in multiple ports and the characteristics of customer classification, this paper studies the dynamic pricing problem of container liner shipping with overlapping legs on a shipping network in a duopoly competition market. The correlations between price sensitivity of customers and competition intensity with container shipping demand and freight rates in a spot market were analyzed. In accordance with the impact of a change in freight rate on freight flow distribution in overlapping segments of the shipping network, a time-phased dynamic pricing model for container liner shipping in a duopoly competition spot market was established while considering the factors of ma ket competition and the rival′s pricing strategy. The model has the essential feature of the generalized Nash equilibrium problem, that is, each participant′ s strategy is dependent on the competitor′s strategy. To prove the existence and uniqueness of the Nash equilibrium solution, the K-T method was employed to solve the discrete-time dynamic pricing model. The research results are as follows. (1) Adopting the dynamic pricing strategy will significantly increase the revenue of the two duopoly shipping companies. (2) The shipping company′s transportation revenue is negatively correlated with the intensity of market competition, and the container freight rate decreases as the intensity of competition in the duopoly market increases. (3) When the intensity of market competition is weak, the shipping company′s transportation revenue has a negative correlation with the customer′s price sensitivity. However, when the market competition is intense, the shipping company′s transportation revenue has a positive correlation with the customer′ s price sensitivity. The meaningful management implications of this paper are as follows. (1) To improve transportation revenue, shipping companies should adopt a flexible dynamic pricing strategy for customers in the duopoly competition spot market by dividing the canvassing period into several periods. (2) Shipping companies should strengthen cooperation by forming liner alliances. This will not only prevent price wars but also reduce the negative impact of market competition intensity on freight rates. (3) Shipping companies should adopt a time-phased pricing strategy to minimize the adverse impact of the price sensitivity of some urgent customers whose canvassing period is approaching on the demand for container transportation so that the shipping company′s transportation revenue would significantly improve © 2022, Journal of Industrial Engineering and Engineering Management. All Rights Reserved.