Inventory control of service parts in the final phase: A central depot and repair kits

We consider an appliance manufacturer's problem of controllng the inventory of a service part in its final phase. That phase begins when the production of the appliance using that part is discontinued (time 0), and ends when the last service contract on that appliance expires. Thus, the planning horizon is deterministic and known. Parts are stocked in repair kits that repairmen carry to jobsites. If enough parts are available, then each kit contains one and the surplus is stocked at a central warehouse. Otherwise, some kits contain a service part but others do not. The objective is to minimize the total expected undiscounted costs of replenishment, inventory holding, penalty (for ‘broken’ jobs), and disposal (of unused parts at the end of the planning horizon). There is no set-up cost for ordering. However, if a part is not ordered at time 0, its price will be higher. We propose an ordering policy consisting of an initial order-up-to-level at time 0, and a subsequent series of decreasing order-up-to-levels for various intervals of the planning horizon. We present a (partly graphical) method of calculating the optimal policy, along with a numerical example.