Pricing of Contractual Shipments and Slot Allocation in Container Liner Shipping under Stochastic Environment

Abstract

This study aimed to propose an optimization model for slot allocation and contractual pricing that considers spot and contractual shipments and empty container repositioning under a stochastic environment. In that respect, a two-stage stochastic non-linear programming modelwas proposed. The model considers contractual pricing that is overlooked by previous studies. Experimentation results revealed that decreasing market demand and spot market prices could cause serious profit loss while creating a high level of idle capacity.With the increasing market demand, capacity utilization reaches saturation at 90% requiring a capacity increase in the service. In the increasing market, slots allocated to empty containers get reduced while taking advantage of other options for empty container supply. Experimentation of symmetric uncertainty revealed that the range of uncertainty should be minimized since it creates a serious loss in profits and capacity utilization. Calculations also demonstrated that the applications of the stochastic modeling solutions would provide higher profit margins than the solutions of their deterministic equivalents. The model can easily be applied to the real-life situations of container liner services for managing and optimization of their service capacities as well as determining optimum contractual prices.

Keywords

• Container shipping
• contractual pricing
• slot allocation
• revenue management
• capacity management

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