| Container liner shipping(liner shipping for short)is the main body of the global marine trade of industrial goods and general consumer goods,and an essential pillar of the remodeling of the worldwide supply chain system.Under the circumstances that the economic,trade,and geopolitical frictions between China and the United States continued to heat up,the ongoing global epidemic(COVID-19)continued,and the Russian-Ukrainian conflict broke out,which had not happened in a century.The liner shipping market has become increasingly competitive with the promotion and implementation of liner shipping alliance strategies and the popularization and application of online booking technology.There has been homogeneous competition between duopoly shipping companies along many identical or similar ocean routes or ocean route networks.In the ocean liner shipping spot market with rapidly changing demand,dynamically setting or adjusting freight rates has become the key for shipping companies to improve liner shipping revenue and maintain market competitiveness.Therefore,the research on the dynamic pricing optimization of the duopoly spot market of ocean liner shipping is a core problem that shipping companies urgently solve.Since liner shipping has developed online booking and real-time quotation businesses,the existing pricing mechanism lacks flexibility,which makes it difficult to meet the current practical requirements of shipping companies.It is also relatively rare to find research on the dynamic pricing of duopoly spot markets for ocean liner shipping.Therefore,based on the typical situation in the duopoly spot market of liner shipping:(1)Two oligopolistic shipping companies compete directly on the same route with no other related network routes in the region;(2)Two oligopolistic shipping companies compete directly on the same route,and they also operate other network routes with overlapping segments with the direct competition routes in the region;(3)Two oligopolistic shipping companies compete on some of the same differentiated routes at the origin-destination(OD)ports in the region;(4)Two oligopolistic shipping companies have a dual decision-making period in the liner shipping spot market voyages and pricing decisions.Based on these four situations,this dissertation studies the dynamic pricing of the ocean liner shipping duopoly spot market,as follows:(1)Aiming at the problem of spot market dynamic pricing of liner shipping under the competition of two oligopoly shipping companies on the same route,the collection period is divided into several periods based on the analysis of how time and competition affect spot market transportation demand.The spot market dynamic pricing model under the competition on the same route is established.Combining the convexity assumption of the generalized Nash problem and the KKT condition,the model solution method is designed.The equilibrium solution of the spot market dynamic pricing game of two oligopoly shipping companies is obtained.The rationality and effectiveness of the model and algorithm are verified with test cases of different scales.Through the sensitivity analysis of price sensitivity,market competition intensity,OD pairs quantity,and other factors,the impact of the above factors on the dynamic pricing decision of the duopoly spot market under the same route situation and the shipping company’s voyage revenue is explored.(2)Aiming at the dynamic pricing problem in the spot market under the competition between two oligopoly shipping companies on the overlapping segment network routes,a cargo flow allocation scheme based on the proportion of travel time on the overlapping segments is proposed.A dynamic pricing model for the spot market with multi-OD time slots considering the overlapping segment network routes is established.The nature of the equilibrium solution of the game is analyzed by using the Lagrangian function and the KKT conditional property.The linear complementary and KKT conditional system solution method based on the generalized Nash equilibrium problem is designed.The equilibrium solutions of the game are obtained for dynamic pricing in the spot market of two oligopoly shipping companies.The rationality and effectiveness of the model and algorithm are verified by using the trans-Pacific regional network route as an example.Through the sensitivity analysis of booking time,competition intensity,and price sensitivity,the impact of the above factors on the pricing decision in the duopoly spot market with overlapping segments and the revenue of shipping companies’ voyages is explored.(3)Aiming at the dynamic pricing problem in the spot market under the competition situation between two oligopolistic shipping companies on differentiated ocean routes,two types of demand functions,competitive and non-competitive,are proposed by analyzing the effects of factors such as route network structure,booking cycle,vessel capacity and each OD port on transportation revenue on container tariffs and vessel capacity control.A time-phased dynamic pricing and capacity control nonlinear mixed integer generalized Nash equilibrium game model is established.The KKT condition system of the continuous differentiable generalized Nash equilibrium problem is used as the initial feasible solution.The best response decomposition algorithm with provable convergence is designed.The rationality and validity of the model and algorithm are verified by using the trans-Pacific route network as an example.Through sensitivity analysis of factors such as competition intensity,customer price sensitivity,and potential demand in the spot market,the impact of the above factors on the duopoly oligopoly spot market pricing decision and ocean shipping line voyage revenue under the differentiation scenario is explored.(4)Aiming at the problem of dynamic pricing in the duopoly spot market under the difficulty of accurately predicting the demand for both voyage departures and return trips,the dual decision period for voyage departures and return trips is designed based on the spatial and temporal differences between the voyage departures and return trips of ocean liner shipping.Using dynamic game theory,the discrete state transfer equation is introduced to establish a dynamic pricing game model based on a dual decision period in a duopoly spot market in a spatio-temporal network.The KKT conditional system is constructed after applying the augmented Hamiltonian function to the model relaxation.Based on the transformation of the model into a linear complementary problem and the solution to obtain the initial solution,the regularized best response decomposition algorithm is designed.The rationality and effectiveness of the model and algorithm are verified by an example.Through sensitivity analysis of factors such as competition intensity,customer price sensitivity,and potential demand in the spot market,the impact of the above factors on the pricing decision of the duopoly spot market and the voyage revenue of the shipping company in the dual decision period scenario is explored.The results of this research indicate that:(1)By adopting a dynamic pricing policy in different periods according to the customer demand laws of the spot market,shipping companies can effectively improve the spot market revenue of liner shipping.(2)In the duopoly competitive market,the profits of two shipping companies do not decline with the increase in competition intensity.Shipping companies that operate routes with more ports can obtain more customers in the fierce market to offset the losses caused by the price war.Therefore,the strategic alliance and route differentiation of shipping companies can help reduce the adverse effects of competition.(3)The dual decision period dynamic pricing model in the duopoly spot market effectively resolves the problem of predicting demand for both outbound and inbound voyages at the same time.This helps maximize revenue for ocean liner shipping.The conclusion of this research enriches and improves the research results of dynamic pricing of ocean liner shipping,which is of significant practical significance for effectively managing the dynamic changes of the liner shipping market,seeking sustainable profitability and improving market competitiveness,and provides significant enlightenment for shipping companies to solve the transportation capacity allocation through real-time quotation and online booking. |
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