We address the combined problem of allocating a scarce resource among several locations, and planning deliveries using a fleet of vehicles. Demands are random, and holding and shortage costs must be considered in the decision along with transportation costs. We show how to extend some of the available methods for the deterministic vehicle routing problem to this case. Computational results using one such adaptation show that the algorithm is fast enough for practical work, and that substantial cost savings can be achieved with this approach. T HIS PAPER addresses the combined problem of allocating a scarce resource available at some central depot among several locations (or "customers"), each experiencing a random demand pattern, while deciding which deliveries are to be made by each of a set of vehicles and in what order. This problem is an extension of the standard vehicle routing problem (VRP). There, one must design a set of vehicle routes of minimal total cost, leaving from and eventually returning to the depot, while satisfying capacity constraints and meeting customer requirements. These requirements almost universally include exogenously determined, deterministically known delivery sizes. Most existing resource allocation models, on the other hand, assume a cost function that is smooth as well as separable and additive in the activities. As a consequence, their application to physical distribution problems is confined to situations where all delivery points receive individual deliveries rather than being served in routes. There are many situations where the vehicle schedules and the delivery sizes are (or should be) determined simultaneously. Such is often the case, for example, when at each location the demand for the resource is random. Here, the deliveries serve to replenish the inventories to levels that appropriately balance inventory carrying and shortage costs, but thereby incur transportation costs as well. This type of problem is the major focus of the paper. Subject classification: 331 inventory allocation/VRP, 831 vehicle routing/inventory.
Some of the first work on the IRP with stochastic demands is due to REF .
A Combined Vehicle Routing and Inventory Allocation Problem
Oper. Res.
Oper. Res.
Computer Science Mathematics