In this study, inventory&ndash / routing system of a company operating in Fast Moving Consumer Goods (FMCG) industry is analyzed. The company has decided to redesign distribution system by locating regional warehouses between production plants and customers. The warehouses in the system are all allowed to hold stock without any capacity restriction. The customers are replenished by the warehouse to which they have been assigned. Customer stocks are continuously monitored by the warehouse and deliveries are to be scheduled. In this multi&ndash / item, two-echelon inventory&ndash / distribution system, main problem is synchronizing inventory and distribution decisions. An integrated Mixed Integer Programming optimization model for inventory and distribution planning is proposed with the aim of optimally coordinating inventory management and vehicle routing. The model determines the replenishment periods of items and amount of delivery to each customer / and constructs the delivery routes with the objective of cost minimization. The integrated model is coded in GAMS and solved by CPLEX. The integrated inventory-routing model is simulated with retrospective data of the company. Computational results on test problems are provided to show the effectiveness of the model developed in terms of the performance measures defined. Moreover, the feasible solution obtained for a period is compared to the realized inventory levels and distribution schedules. Computational results seem to indicate a substantial advantage of the integrated inventory-routing system over the existing distribution system.

Le problème d’approvisionnement conjoint (JDP) proposé est un problème de planification des tournées de livraisons sur un horizon de temps décomposé en périodes élémentaires, l’horizon de temps étant la période commune de livraison de tous les produits,. La donnée de ces paramètres permet d’obtenir une formulation linéaire du problème, avec des variables de décision binaires. Le modèle intègre aussi des contraintes de satisfaction de la demande à partir des stocks et des quantités livrées, des contraintes sur les capacités de stockage et de transport.Afin de résoudre aussi le problème de choix des tournées de livraison, il est nécessaire d'introduire dans le modèle des contraintes et des variables liées aux sites visités au cours de chaque tour. Il est proposé de résoudre le problème en deux étapes. La première étape est le calcul hors ligne du coût minimal de la tournée associé à chaque sous-ensemble de sites. On peut observer que pour tout sous-ensemble donné de sites, le cycle hamiltonien optimal reliant ces sites à l'entrepôt peut être calculé à l'avance par un algorithme du problème du voyageur de commerce (TSP). Le but ici n'est pas d'analyser pleinement le TSP, mais plutôt d'intégrer sa solution dans la formulation de JRP. .Dans la deuxième étape, des variables binaires sont associées à chaque tour et à chaque période pour déterminer le sous-ensemble de sites choisi à chaque période et son coût fixe associé. / The proposed joint delivery problem (JDP) is a delivery tour planning problem on a time horizon decomposed into elementary periods or rounds, the time horizon being the common delivery period for all products. The data of these parameters provides a linear formulation of the problem, with binary decision variables. The model also incorporates the constraints of meeting demand from stock and the quantities supplied, storage and transport capacity constraints.In order to also solve the problem of choice of delivery rounds, it is necessary to introduce in the model several constraints and variables related to the sites visited during each round. It is proposed to solve the problem in two steps. The first step is the calculation of the minimum off-line cost of the tour associated with each subset of sites. One can observe that for any given subset of sites, the optimal Hamiltonian cycle linking those sites to the warehouse can be calculated in advance by a traveling salesman problem algorithm (TSP). The goal here is not to fully analyze the TSP, but rather to integrate its solution in the formulation of the JRP. In the second stage, binary variables are associated with each subset and each period to determine the selected subset of sites in each period and its associated fixed cost.