Period and phase of customer replenishment – A new approach to the strategic inventory/routing problem

The delivery of inventory to customers involves the use of vehicles for which purchase or lease agreements may need to be signed months or even years before the start of actual delivery operations. Such long lead times make it impractical to build a fleet incrementally and motivated study of the Strategic Inventory Routing Problem (SIRP). SIRP focuses on estimating, in advance of the start of actual delivery operations, the minimum size (or cost) vehicle fleet required to supply inventory from a central depot to spatially dispersed customers. A fundamental difference between SIRP and the associated tactical IRPs (route an existing fleet, given knowledge of actual customer inventory levels) is that all possible realizations of the tactical problem must be considered, at least implicitly, when solving SIRP. This paper generalizes Larson's approach for SIRP through the use of period and phase of customer replenishment as additional decision variables. Routing solutions based on customer-specific period and phase of replenishment are developed for a simple model of the tactical routing problems the fleet will eventually encounter. Estimates of the fleet size required are developed on the basis of these routing solutions. The period/phase approach can be generalized to take long-term operating costs into account. Computational tests show that the new approach yields significant reductions in solution cost when the vehicle is large enough to replenish several customers in a single trip and/or when there is significant variation in the maximum inter-replenishment intervals of the customers.