Optimum Solution Structure for a Repairable Inventory Problem

This paper proves that the optimum solution structure for an n-period repairable inventory problem is completely defined by three period dependent values: θ n , the repair-up-to-level; δ n , the purchase-up-to-level; and θ n + ξ n , the scrap-down-to-level. The specific problem examined includes fixed periodic reviews, instantaneous delivery of purchased and repaired units, backlogging of unsatisfied demand, random demand for serviceables, random return of repairables with any relationship being permitted between demand and returns and a convex differentiable cost function. The basic solution methodology is a backward dynamic programming technique in two dimensions with the Kuhn-Tucker saddle point theorems applied in each stage.