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The  Inventory Routing Problem  (IRP) is an integrated logistic problem arising in several industries (e.g. petrochemical, grocery, soft drink and automotive). A vendor decides the optimal delivery strategy for a set of customers, taking into account their inventory policies and avoiding product stock-out in a finite and discrete time horizon. Delivery strategy includes the time and size of deliveries in order to minimize the total delivery cost. Most commonly studied are IRP real cases where a single homogeneous product with deterministic but time-varying demand is delivered over a finite time horizon. This paper is focused on an efficient methodology for industrial problems where a vendor resupplies a set of customers of heterogeneous products (as in the supermarket distribution industry). In this context, the paper reports on an effort facing the inventory routing problem for multi-category products per customer in conjunction with different inventory policies per category. The paper is motivated by real applications arising in the food engineering field. For instance, industries dealing with food’s distribution to stores located in a given geographic area. The planning strategy is formulated as a linear model. The core of the decision problem consists in determining both the delivery route and the corresponding day of activation along the time horizon. A decomposition of the problem into two phases has been proposed. A suitable penalty cost modeled by simulating the possibility of having an early or delayed product delivery on the delivery day returned from the inventory model (e.g. Economic Order Quantity) is the key feature of the first phase. In the second phase, deliveries are scheduled on a daily basis by taking into account the time windows associated to each customer. This is accomplished by using a constructive heuristic algorithm for the vehicle routing problem with time windows. Computational results on some realistic instances are presented and discussed.

Multi-Product Inventory-Routing Problem in the Supermarket Distribution Industry