We consider a distribution problem in which a set of products has to be shipped from a supplier to several retailers in a given time horizon. Shipments from the supplier to the retailers are performed by a vehicle of given capacity and cost. Each retailer determines a minimum and a maximum level of the inventory of each product, and each must be visited before its inventory reaches the minimum level. Every time a retailer is visited, the quantity of each product delivered by the supplier is such that the maximum level of the inventory is reached at the retailer. The problem is to determine for each discrete time instant the retailers to be visited and the route of the vehicle. Various objective functions corresponding to different decision policies, and possibly to different decision makers, are considered. We present a heuristic algorithm and compare the solutions obtained with the different objective functions on a set of randomly generated problem instances.
The paper describes a model for the optimal management of periodic deliveries of a given commodity. The goal is to schedule the deliveries according to feasible combinations of delivery days and to determine the scheduling and routing policies of the vehicles in order to minimize over the planning horizon the maximum number of vehicles simultaneously employed, i.e., the fleet size. Heuristic algorithms are proposed and computational experience is reported.
In this paper we consider a complex production-distribution system, where a facility produces (or orders from an external supplier) several items which are distributed to a set of retailers by a fleet of vehicles. We consider Vendor-Managed Inventory (VMI) policies, in which the facility knows the inventory levels of the retailers and takes care of their replenishment policies. The production (or ordering) policy, the retailers replenishment policies and the transportation policy have to be determined so as to minimize the total system cost. The cost includes the fixed and variable production costs at the facility, the inventory costs at the facility and at the retailers and the transportation costs, that is the fixed costs of the vehicles and the traveling costs. We study two different types of VMI policies: The order-up-to level policy, in which the order-up-to level quantity is shipped to each retailer whenever served (i.e. the quantity delivered to each retailer is such that the maximum level of the inventory at the retailer is reached) and the fill-fill-dump policy, in which the order-up-to level quantity is shipped to all but the last retailer on each delivery route, while the quantity delivered to the last retailer is the minimum between the order-up-to level quantity and the residual transportation capacity of the vehicle. We propose two different decompositions of the problem and optimal or heuristic procedures for the solution of the subproblems. We show that, for reasonable initial values of the variables, the order in which the subproblems are solved does not influence the final solution. We will first solve the distribution subproblem and then the production subproblem. The computational results show that the fill-fill-dump policy reduces the average cost with respect to the order-up-to level policy and that one of the decompositions is more effective. Moreover, we compare the VMI policies with the more traditional Retailer-Managed Inventory (RMI) policy and show that the VMI policies significantly reduce the average cost with respect to the RMI policy.
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