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CONTINUOUS REVIEW INVENTORY MODELS FOR PERISHABLE ITEMS WITH LEADTIMES

Published online by Cambridge University Press:  05 June 2017

Opher Baron ,
Oded Berman  and
David Perry
Opher Baron
Affiliation:
Rotman School of Management, University of Toronto, 105 St. George Street, Toronto, ON M5S 3E6, Canada E-mail: [email protected]
Oded Berman
Affiliation:
Rotman School of Management, University of Toronto, 105 St.George Street, Toronto, ON M5S 3E6, Canada E-mail: [email protected]
David Perry
Affiliation:
Department of Statistics, University of Haifa, Haifa, Israel and Western Galilee College, Israel Email: [email protected]
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Abstract

We consider a continuous review (s, S) model of perishable items with lost sales. Once items are perished the entire inventory drops instantaneously to zero. The total cost includes the cost of: ordering, unsatisfied demand, units destroyed, holding, and fixed cost of perishability. Both the time to perishability and the lead times are assumed to be exponentially distributed while two cases of demand distribution are considered: Poisson and compound Poisson with general demand sizes. We study the average cost criterion and provide computational results on the problem of finding the optimal re-order level, s, and order up-to level, S. None of the known work on the subject is as general as the model presented here. Our analysis leads to several insights on the optimal (s, S) policies for perishable items in the presence of lead times. For example, we demonstrate that the effectiveness of a heuristic that ignores perishability (and is also analyzed here) decreases with the demand variability and that the cost may either increase or decrease with this variability.

Keywords

aging itemsinventoryoperations and supply chainproduction: perishableuncertainty: stochastic
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 34 , Special Issue 3: Analytic Methods in Health Care and in Clinical Trials In Honor and Memory of Lycourgos (Lee) Papayanopoulos , July 2020 , pp. 317 - 342
Copyright
Copyright © Cambridge University Press 2017

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References

1.Arrow, K.A., Harris, T.E., & Marschak, T. (1951). Optimal inventory policy. Econometrica 19(3): 250–272.CrossRefGoogle Scholar
2.Baron, O. (2011). Managing Perishable Inventory. Wiley Encyclopedia of Operations Research and Management Science.CrossRefGoogle Scholar
3.Baron, O., Berman, O., & Perry, D. (2010). Continuous review inventory models for perishable items ordered in batches. Mathematical Methods of Operations Research 72: 217–247.CrossRefGoogle Scholar
4.Berk, E. & Gürler, Ü. (2008). Analysis of the (Q, r) inventory model for perishables with positive lead times and lost sales. Operations Research 56(5): 1238–1246.CrossRefGoogle Scholar
5.Boxma, O.J., Perry, D., & Stadje, W. (2011). The M/G/1+G queue revisited. Queueing Systems 67(3): 207–220.CrossRefGoogle Scholar
6.Chen, X., Pang, Z., & Pan, L. (2014). Coordinating inventory control and pricing strategies for perishable products. Operations Research 62: 284–300.CrossRefGoogle Scholar
7.Gürler, Ü. & Özkaya, B.Y. (2008). Analysis of the (s, S) policy for perishables with a random shelf life. IIE Transactions 40(8): 759–781.CrossRefGoogle Scholar
8.Graves, S. (1982). The application of queueing theory to continuous perishable inventory systems. Management Science 28(4): 400.CrossRefGoogle Scholar
9.Kalpakam, S. & Sapna, K.P. (1994). Continuous review (s, S) inventory system with random lifetimes and positive leadtimes. Operations Research Letters 16: 115–119.CrossRefGoogle Scholar
10.Karaesmen, I., Scheller-Wolf, A., & Deniz, B. (2011). Managing perishable and aging inventories: review and future research directions. InKempf, K., Keskinocak, P., & Uzsoy, R. (eds.), Planning production and inventories in the extended enterprise, international series in operations research & management science. USA: Springer, vol. 151, pp. 393–436.Google Scholar
11.Kleywegt, A.J., Nori, V.S., & Savelsbergh, M.W.P. (2002). The stochastic inventory routing problem with direct deliveries. Transportation Science 36(1): 94–118.CrossRefGoogle Scholar
12.Li, Q., Yu, P., & Wu, X. (2014). Managing perishable inventories in retailing replenishment clearance sales and segregation. Operations Research 64: 1270–1284.CrossRefGoogle Scholar
13.Liu, L. & Shi, D.-H. (1999). An (s, S) model for inventory with exponential lifetimes and renewal demands. Naval Research Logistics 46(1): 39–56.3.0.CO;2-G>CrossRefGoogle Scholar
14.Liu, L. & Yang, T. (1999). An (s,S) random lifetime inventory model with a positive lead time. European Journal of Operational Research 113(1): 52–63.CrossRefGoogle Scholar
15.Nahmias, S. (1982). Perishable inventory theory: a review. Operations Research 30: 680–708.CrossRefGoogle ScholarPubMed
16.Nagarajan, M. & Rajagopalan, S. (2008). Coordination issues in vendor managed inventory systems. Production & Operations Management 17(2): 200–210.CrossRefGoogle Scholar
17.Perry, D. and Asmussen, S. (1995) Rejection rules in the M/G/1 type queue. Queueing Systems 19: 105–130.CrossRefGoogle Scholar
18.Porteus, I.L. (2002). Foundations of Stochastic Inventory Theory. Stanford, CA: Stanford Business Books.Google Scholar
19.Rajan, A., Steinberg, R., & Steinberg, R. (1992). Dynamic Pricing and Ordering Decisions by a Monopolist. Management Science 38: 240–262.CrossRefGoogle Scholar
20.Sheffi, Y. (2005). The resilient enterprise, overcoming vulnerability for competitive advantage. Cambridge: MIT Press.Google Scholar
21.Shi, J.Katehakis, M.N..Melamed, B. & Xia, Y. (2014). Optimal continuous replenishment for a production-inventory system with compound Poisson demands and lost-sales. Operations Research 6(5): 1048–1063.CrossRefGoogle Scholar
22.Song, Y. & Lau, H.C. (2004). A periodic – review inventory model with application to the continuous – review obsolescence problem. European Journal of Operational Research 159: 110–120.CrossRefGoogle Scholar
23.Varghese, T.V. & Krishnamoorthy, A. (2004). Inventory system subject to disaster with general interarrival times. Stochastic Analysis and Applications 5(5): 1315–1326.CrossRefGoogle Scholar
24.Whitin, T.M. (1957). The theory of inventory management. Princeton, NJ: Princeton University Press.Google Scholar
25.Xue, Z., Etti, M., & Yao, D. (2012). Managing Freshness Inventory in Direct Store Delivery Supply Chain. Working paper IEOR Department Columbia University.Google Scholar
26.Zipkin, P.H. (2000). Foundations of inventory management. New York: McGraw-Hill.Google Scholar