Slot allocation and exchange for container shipping alliance under profit-sharing agreement and uncertain demand

Abstract

Shipping alliance has become a prevalent cooperation form among major container shipping companies in recent decades. By forming an alliance, shipping companies can exchange their container slots to better satisfy the shipping demand and improve capacity utilization. This paper considers the slot allocation and exchange for a shipping alliance with consideration of profit-sharing agreement and uncertain demand. The profit-sharing agreement indicates the profit segmentation that should be kept by each alliance member among the total alliance profit. To tackle this problem, a two-stage stochastic programming model is subsequently developed to maximize the total profit of the alliance and minimize the deviation of the profit percentage of each member from the prescribed value indicated in the profit-sharing agreement. In the first stage, the number of slots allocated and exchanged within the alliance is determined. In the second stage, after the uncertain shipping demand is realized, each alliance member separately determines their container shipping plan to obtain profit. A tailored pattern-search-based solution algorithm is developed to solve the model. A series of numerical experiments demonstrate the applicability of the programming model and deliver several interesting managerial insights.