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CONTROL POLICIES FOR INVENTORY SYSTEMS WITH PERISHABLE ITEMS: OUTSOURCING AND URGENCY CLASSES

Published online by Cambridge University Press:  22 June 2005

Shaul K. Bar-Lev ,
David Perry  and
Wolfgang Stadje
Shaul K. Bar-Lev
Affiliation:
Department of Statistics, University of Haifa, 31905 Haifa, Israel
David Perry
Affiliation:
Department of Statistics, University of Haifa, 31905 Haifa, Israel
Wolfgang Stadje
Affiliation:
Department of Mathematics and Computer Science, University of Osnabrück, 49069 Osnabrück, Germany, E-mail: wolfgang@mathematik.uni-osnabrueck.de
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Abstract

We consider control policies for perishable inventory systems with random input whose purpose is to mitigate the effects of unavailability. In the basic uncontrolled system, the arrival times of the items to be stored and the ones of the demands for those items form independent Poisson processes. The shelf lifetime of every item is finite and deterministic. Every demand is for a single item and is satisfied by the oldest item on the shelf, if available. The first controlled model excludes the possibility of unsatisfied demands by introducing a second source of fresh items that is completely reliable and delivers without delay whenever the system becomes empty. In the second model, there is no additional ordering option by outsourcing. However, to avoid the most adverse effects of unavailability, the demands are classified into different categories of urgency. An incoming demand is satisfied or not according to its category and the current state of the system. For both models, we determine the steady-state distribution of the virtual outdating process, which is then used to derive the relevant cost functionals: the steady-state distribution and expected value of the number of items in the system, the rate of outdatings, as well as, for model 1, the rate of special orders from the external source and, for model 2, the rate of unsatisfied demands.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 19 , Issue 3 , July 2005 , pp. 309 - 326
Copyright
© 2005 Cambridge University Press

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References

REFERENCES

Azouri, K. & Brill, P.H. (1986). An application of the system-point method to inventory models under continuous review. Journal of Applied Probability 23: 778–789.Google Scholar
Berman, O. & Sapna, K.P. (2002). Optimal service rates of a service facility with perishable inventory systems. Naval Research Logistics 49: 464–482.Google Scholar
Goh, C.R.S., Greenberg, R.S., & Matsuo, H. (1993). Perishable inventory systems with batch arrivals and demands. Operations Research Letters 13: 1–8.Google Scholar
Kalpakam, S. & Arivarignan, G. (1988). A continuous review perishable inventory model. Statistics 19: 389–398.Google Scholar
Kalpakam, S. & Sapna, K.P. (1994). Continuous review (s,S) inventory system with random lifetimes and positive lead times. Operations Research Letters 16: 115–119.Google Scholar
Kalpakam, S. & Shanthi, S. (2000). A perishable system with modified (S − 1,S) policy and arbitrary processing times. Computers and Operations Research 28: 453–471.Google Scholar
Kalpakam, S. & Shanthi, S. (2000). A perishable system with modified base stock policy and random supply quantity. Computations in Mathematics with Applications 39: 79–89.Google Scholar
Kaspi, H. & Perry, D. (1983). Inventory system of perishable commodities. Advances in Applied Probability 15: 674–685.Google Scholar
Lian, Z. & Liu, L. (1999). A discrete-time model for perishable inventory systems. Annals of Operations Research 87: 103–116.Google Scholar
Liu, L. (1990). (s,S) continuous review models for inventory with random lifetimes. Operations Research Letters 9: 161–167.Google Scholar
Liu, L. & Lian, Z. (1999). (s,S) continuous review models for products with fixed lifetimes. Operations Research 47: 150–158.Google Scholar
Liu, L. & Shi, D.-H. (1999). An (s,S) model for inventory with exponential lifetimes and renewal demands. Naval Research Logistics 46: 39–56.Google Scholar
Liu, L. & Yang, T. (1999). An (s,S) random lifetime inventory model with a positive lead time. European Journal of Operations Research 113: 52–63.Google Scholar
Lian, Z. & Liu, L. (2001). Continuous review perishable inventory systems: Models and heuristics. IIE Transactions 33: 809–822.Google Scholar
Nahmias, S. (1982). Perishable inventory theory: A review. Operations Research 30: 680–708.Google Scholar
Nahmias, S., Perry, D., & Stadje, W. (2004). Actuarial valuation of perishable inventory systems. Probability in the Engineering and Information Sciences 18: 219–232.Google Scholar
Nahmias, S., Perry, D., & Stadje, W. (2004). Perishable inventory systems with variable input and demand rates. Mathematical Methods of Operations Research 60: 155–162.Google Scholar
Nandakumar, P. & Morton, T.E. (1993). Near myopic heuristics for the fixed-life perishable problem. Management Science 39: 1490–1498.Google Scholar
Perry, D. (1999). Analysis of a sampling control scheme for a perishable inventory system. Operations Research 47: 966–973.Google Scholar
Perry, D. & Posner, M.J.M. (1989). Control policies for two classes of inventory systems via a duality-equivalence relationship. Probability in the Engineering and Informational Sciences 3: 561–579.Google Scholar
Perry, D. & Stadje, W. (1999). Perishable inventory systems with impatient demands. Mathematics and Methods in Operations Research 50: 77–90.Google Scholar
Perry, D. & Stadje, W. (2000). An inventory system for perishable items with by-products. Mathematics and Methods in Operations Research 51: 287–300.Google Scholar
Perry, D. & Stadje, W. (2000). Inventory systems for goods with censored random lifetimes. Operations Research Letters 27: 21–27.Google Scholar
Perry, D. & Stadje, W. (2001). Disasters in Markovian inventory systems for perishable items. Advances in Applied Probability 33: 61–75.Google Scholar
Perry, D. & Stadje, W. (2003). Duality of dams via mountain processes. Operations Research Letters 31: 451–458.Google Scholar
Petruzzi, N.C. & Dada, M. (1999). Pricing and the newsvendor problem: A review with extensions. Operations Research 47: 183–194.Google Scholar
Raafat, R. (1991). Survey of literature on continuously deteriorating inventory models. Journal of the Operational Research Society 42: 27–37.Google Scholar
Tekin, E., Gürler, Ü., & Berk, E. (2001). Age-based vs. stock level control policies for a perishable inventory system. European Journal of Operations Research 134: 309–329.Google Scholar
Williams, C.L. & Patuwo, B.E. (1999). A perishable inventory model with positive lead times. European Journal of Operations Research 116: 352–373.Google Scholar
Williams, C.L. & Patuwo, B.E. (2004). Analysis of the effect of various unit costs on the optimal incoming quantity in a perishable inventory model. European Journal of Operations Research 156: 140–147.Google Scholar