Slot allocation with minimum quantity commitment in container liner revenue management: A robust optimization approach

Purpose - The purpose of this paper is to propose robust optimization models addressing the container slot allocation problem with minimum quantity commitment (MQC) under uncertain demand, which is faced by international companies export to USA. Design/methodology/approach - A novel robust optimization approach handling linear programming (LP) with right-hand-side uncertainty is developed by incorporating new parameters: uncertainty level, infeasibility tolerance and reliability level. Two types of uncertainty, namely, bounded uncertainty and symmetric uncertainty are considered, respectively. Findings - The present work finds that the expected revenue increases as the uncertainty level and the MQC decrease, as well as the infeasibility tolerance and the reliability level increase, no matter which type of uncertainty is considered. Research limitations/implications - Typically, the capacity constraints in a container shipping model should include two major restrictions: (1) number of slots and (2) total weight of loaded and empty containers. However, this study only addresses the first restriction for simplicity. It is recommended that future research explore the optimal solutions with additional restriction (2). Originality/value - This paper fills a theoretical and practical gap for the problem of slot allocation with MQC in container liner revenue management. Deterministic and tractable mixed integer LP is formulated to derive robust solutions which immunes to demand uncertainty. Illustrative examples are presented to test the proposed models. The present work provides practical and solid advice and examples which demonstrates the application of the proposed robust optimization approach for logistics managers.