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Backorders optimization in a one‐warehouse N ‐identical retailer distribution system
Author(s) -
Badinelli Ralph D.,
Schwarz Leroy B.
Publication year - 1988
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/1520-6750(198810)35:5<427::aid-nav3220350507>3.0.co;2-u
Subject(s) - safety stock , inventory investment , equivalence (formal languages) , operations research , mathematical optimization , computer science , heuristic , portfolio , stock (firearms) , customer service , inventory theory , inventory control , service level , service (business) , mathematics , economics , business , econometrics , supply chain , marketing , finance , engineering , statistics , mechanical engineering , discrete mathematics
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 Deuermeyer and Schwarz (DS) model 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.