A robust optimization model for the maritime inventory routing problem

Abstract

Uncertainty is a highly important aspect of maritime transportation. Unforeseen occurrences related to environmental conditions, poor weather, vessel reliability, or port congestion are frequent and have a non-negligible impact on the total time required for vessels to perform (un)loading operations at ports. We study a special case of maritime transportation named the maritime inventory routing (MIR) problem, in which one must determine the routings of vessels while keeping the inventory levels at ports within the operational limits. In this paper, we propose a robust optimization approach that considers the uncertainty in the total time spent by vessels at the ports. This approach allows the trade-off between the risk of infeasibility (i.e., violating inventory limits at ports) and the increase in operational costs due to the protection against uncertainty events to be assessed. To test the proposed methodology, we used a real-world instance based on the MIR problem faced by a Brazilian petroleum company. In this problem, violating the inventory limits at ports causes considerable financial losses due to consequent interruptions in crude oil production. Our approach supports the decision maker to devise more robust plans in which the risk of violating inventory limits is acceptable. In other words, despite the increase in the operational costs associated with more robust solutions, the approach enables the decision maker to avoid much larger potential costs. For the problem considered, we observed that the probability of infeasibility of the proposed solution may be reduced from 87% to 2%, depending on the level of robustness adopted by the decision maker. However, this increased protection causes an increase of up to 13% in the overall costs.

Maritime inventory routing: recent trends and future directions

“…In some real-world applications, such adjustments of loaded volumes may be prohibited for contractual reasons. Diz et al (2019) took into account uncertainty in the time spent at ports, which was a significant part of the total time used by vessels in the real-world case investigated. As costs of violating inventory constraints were large, robust optimization was proposed to reduce the probability of inventory violations.…”

“…Such formulations have been used recently by Diz et al. (2017, 2019), Friske et al. (2022), and Jiang and Grossmann (2015).…”

“…Agra et al (2013a) astutely recognized that a single-commodity MIRP can be viewed as a singlecommodity fixed-charge network flow (FCNF) problem in which the commodity is first supplied at production ports, then flows along the arcs corresponding to the chosen vessel routes, and is finally unloaded at the consumption ports to satisfy demand. Such formulations have been used recently by Diz et al (2017Diz et al ( , 2019, Friske et al (2022), and Jiang and Grossmann (2015). An FCNF formulation has two main advantages over the core model ( 1)-(15).…”

Maritime Inventory Routing Problem Considering Weather Conditions and Tide at Ports

“…Hennig et al investigated the fuel consumption costs of ships in the port during the operations regardless of the amount of their fuel consumption at sea ( 38 ). Diz et al addressed a specific MIRP in which port inventory levels should be maintained within an explicit operational range ( 39 ). Rodrigues et al dealt with an MIRP with uncertainty on the ship’s voyage time ( 40 ).…”

Coastal Shuttle Tanker Scheduling Model Considering Inventory Cost and System Reliability

“…Oil inventory affects not only the operating cost of the system but also the reliability of the system. The maritime operation is heavily influenced by the uncertainty factors, such as poor weather, the breakdown of shuttle tankers, and the port congestion issue [46]. The uncertainty factor could delay the operation and cause the deviation of the pre-determined plan.…”