(632g) Optimization and Analysis Methods for Maritime Inventory Routing

Authors: 
Dong, Y., University of Wisconsin-Madison
Maravelias, C. T., University of Wisconsin-Madison
Jerome, N. F., BP plc

Inventory routing problem (IRP) appears in various chemical supply chains (SCs), when distribution routing and scheduling decisions are made with considerations of inventories at suppliers/customers. Based on travel distances, real-time inventories and forecasted production/consumption profiles of suppliers and customers, we optimize the routes, schedules, and loading/discharging amounts, while ensuring that the inventory levels are kept within a certain range. Compared with the traditional order call-in scheme, integration of distribution routing and scheduling together with inventory control helps to reduce the distribution cost, which accounts for a large fraction of the total operating cost of the distribution SC. One important type of IRP, which finds applications in the petro-chemical sector, is the maritime inventory routing problem (MIRP), where multiple products are transported between supplier ports and customer ports, so that the upper and lower inventory level constraints of these ports are satisfied. The travel time between ports normally takes several days. Each port in the SC network has its own access windows during which a loading or discharging is allowed, which also adds more complexity to the problem.

In this work, we propose a discrete-time Mixed-Integer-Programming (MIP) model, and develop a suite of methods and tools to aid decision-making in MIRP. First, in addition to travel distance, heterogeneous vessels and access windows, we also consider soft windows, and penalized overflow and underflow. The objective is to minimize the overall cost, which includes travelling cost, material holding cost, overflow/underflow cost and vessel rental cost. Second, we present new methods to accurately calculate rental cost based on rental modes (short-term or long-term). Third, we develop tools that help the user to easily manipulate data as well as the resulting schedules and re-optimize seamlessly. Finally, to give some insights on the SC performance under uncertainty, we present results from an analysis based on different scenarios generated based on (1) different rental modes, (2) uncertainty in consumption/production forecast, (3) uncertainty in vehicle availability, and (4) expanded access windows. We show that the proposed framework can lead to significant savings.