New Formulation for an Economic Order Quantity Distribution Policy in Vendor-Managed Inventory Routing Problems

Abstract

In vendor managed inventory systems, logistics decisions are centralized at the vendor, allowing inventory storage and transportation costs to be reduced simultaneously. Operation of such systems requires the solution of a complex combinatorial optimization problem, known as the Inventory Routing Problem (IRP), which involves managing client inventory and determining the frequency and size of product deliveries as well as the route taken by the vehicle over a given planning horizon. We present a new formulation based on an economic order quantity distribution policy for the multivehicle inventory routing problem (MIRP). A mathematical programming model with additional practical constraints was used for the MIRP. A new heuristic approach that breaks the MIRP down into the following two sub-problems was also proposed: one dealing with the scheduling of deliveries and the formation of delivery clusters over the planning horizon, and the second sub-problem, which builds the routes for the delivery clusters using classic route construction heuristics and a procedure for intra-route improvements. Adjustments between routes are performed with the aid of a new large neighborhood search (LNS) strategy. Small, medium-sized and large scenarios with different storage and transportation costs were generated using parameters based on data from the literature. Extensive computational tests were carried out to determine the effectiveness of the proposed distribution policy and the heuristic used.