Inventory Policy and Heuristic for Long-Term Multi-product Perishable Inventory Routing Problem with Static Demand

Abstract

This work considers a long-term Perishable Inventory Routing Problem with multiple products, static demand, and single vehicle, in the setting of Vendor Managed Inventory. By analyzing the optimal solutions of long-term cases that can be solved in Python+Gurobi within 2 h, we capture some patterns of optimal solutions. Utilizing these patterns, experiments show that under certain conditions, the mathematical models of multi-product problems could be simplified to single-product problems, which have the same optimal solutions while taking less time to solve. Managerial insights were generated that for products with static demand in the long term, delivery should be arranged at the store level rather than at the product level. Products in the same store should have the same delivery pattern, no matter how different the unit holding costs are. By further analyzing the optimal solutions of the simplified models, we find that optimal value will stabilize in the long term, and the optimal solution is very close to the solution point where total inventory holding cost and transportation cost are close. Based on these findings, we have developed a heuristic that always provides optimal or close-to-optimal solutions with far less computational time, compared with Python+Gurobi.