A Fuel Distribution Problem – Application of New Multi-item Inventory Routing Formulation

This paper presents a new approach to solving the inventory routing problem. This approach could be classified as a first cluster -second route. In the first step a new formulation of mixed integer programming is used to determine the partitioning of customers as well as dates and quantities of deliveries. Then, using any algorithm for solving the traveling salesperson problem the optimal routes for each partition are determined. Although in the first step the set partitioning model is applied, one of the main components of the objective function is approximate routes length. While the routing and inventory costs are considered parallel, the formulation is not so complex compared to classical approaches with exact route length calculation. The presented formulation has been used to solve the problem of determining a delivery plan from a fuel base to 36 fuel stations of one network operating in Poland. In addition in this formulation more than one item is taken into consideration.