A goal programming model for the stability analysis of a maritime inventory routing replanning problem

Abstract

This paper aims to provide insight into the stability of solutions to a multi-product maritime inventory routing problem (MIRP) when replanning due to the occurrence of unexpected events. The MIRP determines vessel routes while ensuring that port inventory levels remain within operational thresholds. In today's global economy, supply chains are often vast and complex. Managing inventory and routes for multiple products across international waters is a daunting task. The MIRP provides a framework for optimizing these complex supply chain networks. Four stability metrics are available to evaluate the stability of the adjusted plans. The problem is modeled using a goal programming approach to consider all stability metrics simultaneously. Then, 30 instances from the literature are solved using CPLEX. It is shown that there are significant differences when all stability metrics, as opposed to a single one, are considered simultaneously, which can lead to better agreement between the vendor and the retailer in decision making. A cost analysis is performed to examine the impact of the cost increase on the stability of the other metrics. The key finding is that when all stability metrics are considered simultaneously, a 5 % increase in cost can result in 7.5 % fewer changes to replanned solutions, while this rate is less than half when the stability metrics are considered individually. This highlights the significance of evaluating all metrics simultaneously instead of analyzing each metric separately.

Keywords

• Goal programming
• Stability metrics
• Replanning
• Maritime inventory routing