Stability metrics for a maritime inventory routing problem under sailing time uncertainty

Abstract

We study a multi-product maritime inventory routing problem (MIRP) with sailing time uncertainty. We explicitly consider the replanning that happens after uncertainty is revealed. The objective is to determine the stability of the adjusted plans after the occurrence of an uncertain event and to evaluate the effect of incorporating different stability metrics in the rescheduling process. Five stability metrics are introduced, and mathematical formulations of the MIRP incorporating each metric are presented. A reoptimization framework is then used to analyze the impact of each stability metric. Calculations are performed using 360 instances. The main result is that adjustments to the original plan occur at no additional cost almost 50% of the time. If decision makers want a more stable plan, they should accept a 5% cost deterioration, resulting in 20% more stable solutions.