The Inventory Routing Problem with Priorities and Fixed Heterogeneous Fleet

Abstract

This paper presents a new combinatorial optimization problem, the inventory routing problem with priorities, and a fixed heterogeneous fleet. In this problem, a particular set of customers has to be served before the rest of the customers using vehicles with different capacities. The problem is inspired by the current situation faced by a specialized gas distribution company in the northeast region of Mexico. The company produces and distributes three main products, although this paper focuses only on the oxygen distribution problem. The company delivers oxygen to industrial customers, as well as hospitals and other medical facilities. Due to Mexican government regulations, the company requires prioritizing deliveries to hospitals and medical facilities over its industrial customers. Therefore, the company is obliged to satisfy the customers demand considering inventory levels and priority constraints while minimizing the inventory and routing cost. An integer programming model is proposed to solve the problem. The model minimizes the total distribution cost while considering inventory level, priority constraints, and a fixed fleet of vehicles with different capacities. Finally, computational experiments were carried out using benchmark instances to validate the correctness of the proposed model and to analyze the effect of priorities on the total distribution cost. Finally, actual customers of the company were selected to show the effectiveness of the proposed model to solve real-world problems.