Backorders optimization in a one-warehouse N-identical retailer distribution system. (English) Zbl 0655.90020
This article examines the allocation of safety stock between sectors in a one-warehouse N-retailer distribution system which follows a (Q,R) inventory replenishment policy. In particular, the so-called “portfolio” motive for holding warehouse safety-stock inventory is investigated. Two optimization problems involving the tradeoff between average system inventory investment and customer service, i.e., customer backorders, are considered and shown to be equivalent to a simpler optimization problem involving the tradeoff between customer service and system safety stock. Equivalence implies that the set of optimal policies for the simpler optimization problem provides all of the optimal policies for the more complex ones. This equivalence result is applied to the DS model [see B. L. Deuermeyer and the second author, TIMS Stud. Manage. Sci. 16, 163-193 (1981; Zbl 0469.90031)] of the distribution system under study. Bounds on the set of optimal policies are provided. A heuristic for minimizing expected backorders with respect to a constraint on average system on-hand inventory is introduced, and empirical tests described. The heuristic, which prescribes little warehouse on-hand inventory, appears to be near optimal for the DS model. A simulation study supports this “near-zero” inventory prescription for the warehouse.
MSC:
| 90B05 | Inventory, storage, reservoirs |
Keywords:
allocation of safety stock; one-warehouse N-retailer distribution system; inventory replenishment; Bounds; set of optimal policies; heuristic; simulationCitations:
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