Hostname: page-component-7b9c58cd5d-6tpvb Total loading time: 0 Render date: 2025-03-15T12:08:15.043Z Has data issue: false hasContentIssue false
  • English
  • Français

A CONTINUOUS REVIEW MODEL WITH GENERAL SHELF AGE AND DELAY-DEPENDENT INVENTORY COSTS

Published online by Cambridge University Press:  09 October 2015

Awi Federgruen  and
Min Wang
Awi Federgruen
Affiliation:
Graduate School of Business, Columbia University, 3022 Broadway New York, NY 10025, USA E-mail: af7@columbia.edu
Min Wang
Affiliation:
LeBow College of Business, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA E-mail: min.wang@drexel.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We analyze a continuous review inventory model with the marginal carrying cost of a unit of inventory given by an increasing function of its shelf age and the marginal delay cost of a backlogged demand unit by an increasing function of its delay duration. We show that, under a minor restriction, an (r, q)-policy is optimal when the demand process is a renewal process, and a state dependent (r, q)-policy is optimal when the demand is a Markov-modulated renewal process. We also derive various monotonicity properties for the optimal policy parameters r* and r* + q*.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 29 , Issue 4 , October 2015 , pp. 507 - 525
Copyright
Copyright © Cambridge University Press 2015 

References

1. Aviv, Y. & Federgruen, A. (1999). The value-iteration method for countable state Markov decision processes, Operations Research Letters 24: 223–234.Google Scholar
2. Axsäter, S. (1990). Simple solution procedures for a class of two-echelon inventory problems. Operations Research 38: 64–69.Google Scholar
3. Axsäter, S. (1993). Exact and approximate evaluation of batch-ordering policies for two-level inventory systems. Operations Research 41: 777–785.Google Scholar
4. Bather, J.A. (1966). A continuous time inventory model. Journal of Applied Probability 3: 538–549.Google Scholar
5. Benjaafar, S., Cooper, W.L., & Mardan, S. (2011). Production-inventory systems with imperfect advance demand information and updating. Naval Research Logistics 58(2): 88–106.Google Scholar
6. Bertsekas, D. (2005). Dynamic Programming and Optimal Control, Vol 1. Nashua, NH: Athena Scientific.Google Scholar
7. Browne, S. & Zipkin, P. (1991). Inventory models with continuous stochastic demands. Annals of Applied Probability 1: 419–435.Google Scholar
8. Chao, X., Xu, Y., & Yang, B. (2012). Optimal policy for a production-inventory system with setup cost and average cost criterion. Probability in the Engineering and Informational Sciences 26: 457–481.Google Scholar
9. Chao, X. & Zhou, S.X. (2006). Joint inventory-and-pricing strategy for a stochastic continuous-review system. IIE Transactions 38: 401–408.Google Scholar
10. Chen, F. & Song, J.-S. (2001). Optima policies for multechelon inventory with Markov-modulated demand. Operations Research 49: 226–234.Google Scholar
11. Chen, F., & Zheng, Y.-S. (1993). Inventory models with general backorder costs. European Journal of Operations Research 65(2): 175–186.Google Scholar
12. Chen, X. & Simchi-Levi, D. (2006). Coordinating inventory control and pricing strategies with random demand and fixed ordering cost: the continuous review model. Operations Research Letters 34: 323–332.Google Scholar
13. Dai, J.G. & Yao, D. (2012). Brownian inventory models with convex holding cost (part 1): Average-optimal controls. Stochastic Systems 3: 442–499.Google Scholar
14. Federgruen, A. & Lee, C.-Y. (1990). The dynamic lot size model with quantity discount. Naval Research Logistics 37: 707–713.Google Scholar
15. Federgruen, A. & Schechner, Z. (1983). Cost formulas for continuous review inventory models with fixed delivery lags. Operations Research 31(5): 957–965.Google Scholar
16. Federgruen, A. & Wang, M. (2012). Inventory subsidy versus supplier trade credit. Working paper, Columbia University.Google Scholar
17. Federgruen, A. & Wang, M. (2013). Monotonicity properties of stochastic inventory systems. Annals of Operations Research 208: 155–186.Google Scholar
18. Federgruen, A. & Wang, M. (2015). Inventory model with shelf age and delay dependent inventory costs. Operations Research 63(3): 701–715.Google Scholar
19. Federgruen, A. & Zheng, Y.S. (1992). An efficient algorithm for computing an optimal (r, Q) policy in continuous review stochastic inventory systems. Operations Research 40(4): 808–813.Google Scholar
20. Gayon, J., Benjaafar, S., & de Véricourt, F. (2009). Using imperfect advance demand information in production-inventory systems with multiple customer classes. Manufacturing & Service Operations Management 11(1): 128–143.Google Scholar
21. Gupta, D. & Wang, L. (2009). A stochastic inventory model with trade credit. Manufacturing Service Operations Management 11(1): 4–18.Google Scholar
22. Hadley, G. & Whitin, T. (1963). Analysis of inventory systems. Englewood Cliffs, NJ: Prentice-Hall.Google Scholar
23. Huh, W.T., Janakiraman, G., Muharremoglu, A., & Sheopuri, A. (2011). Optimal policies for inventory systems with a generalized cost model. Operations Research 59(4): 1040–1047.Google Scholar
24. Iglehart, D. & Karlin, S. (1962). Optimal policy for dynamic inventory process with nonstationary stochastic demands. In Studies in Applied Probability and Management Science (Arrow, K., Karlin, S., Scarf, H., Eds). Chapter 8, Stanford, CA: Stanford University Press.Google Scholar
25. Karlin, S. (1960). Dynamic inventory policy with varying stochastic demands. Management Science 6: 231–258.Google Scholar
26. Levi, R., Roundy, R., Shmoys, D., & Sviridenko, M. (2008). A constant approximation algorithm for the one-warehouse multi-retailer problem. Management Science 54: 763–776.Google Scholar
27. Muharremoglu, A. & Tsitsiklis, J. (2008). A single-unit decomposition approach to multi-echelon inventory systems. Operations Research 56(5): 1089–1103.Google Scholar
28. Naddor, E. (1966). Inventory Systems. New York: Wiley.Google Scholar
29. Nagarajan, M. & Rajagopalan, S. (2008). Contracting under vendor managed inventory systems using holding cost subsidies. Production and Operations Management 17(2): 200–210.Google Scholar
30. Nahmias, S., Perry, D., & Stadje, W. (2004). Actual valuation of perishable inventory systems. Probability in the Engineering and Information Sciences 18: 219–232.Google Scholar
31. Perry, D. & Stadje, W. (1999). Perishable inventory systems with impatient demands. Mathematical Methods of Operations Research 50: 77–90.Google Scholar
32. Richardson, H. (1995). Control your costs then cut them. Transportation and Distribution 36(12): 94–96.Google Scholar
33. Rosling, K. (2002). Inventory cost rate functions with nonlinear shortage costs. Operations Research 50(6): 1007–1017.Google Scholar
34. Sahin, I. (1979). On the stationary analysis of continuous review (s, S) inventory systems with constant lead times.Operations Research 27: 717–730.Google Scholar
35. Sahin, I. (1983). On the continuous review (s; S) inventory model under compound renewal demand and random lead times. Journal of Applied Probability 20: 213–219.Google Scholar
36. Shaked, M. & Shanthikumar, J.G. (2007). Stochastic Orders. New York: Springer.Google Scholar
37. Shi, J., Katehakis, M.N., Melamed, B., & Xia, Y. (2014). Production-Inventory systems with lost sales and compound Poisson demands. Operations Research 6(5): 1048–1063.Google Scholar
38. Song, J.-S. & Zipkin, P. (1993). Inventory control in a fluctuating demand environment. Operations Research 41: 351–370.Google Scholar
39. Stauffer, G., Massonnet, G., Rapine, C., & Gayon, J.-P. (2011). A simple and fast 2-approximation for deterministic lot-sizing in one warehouse multi-retailer systems. Proceedings of the Twenty-Second Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), 67–79.Google Scholar
40. Tijms, H.C. (1972). Analysis of (s, S): Inventory Models. Mathematical Centre Tracts 40, Amsterdam: Mathematical Centre.Google Scholar
41. Tijms, H.C. (2003). A First Course in Stochastic Models. West Sussex, England: Wiley.Google Scholar
42. Xu, Y. & Chao, X. (2009). Dynamic pricing and inventory control for a production system with average profit criterion. Probability in the Engineering and Informational Sciences 23: 489–513.Google Scholar
43. Zheng, Y.S. (1991). A simple proof for optimality of (s, S) policies in infinite-horizon inventory systems. Journal of Applied Probability 28(4): 802–810.Google Scholar
44. Zipkin, P. (1986). Stochastic leadtimes in continuous time inventory models. Naval Research Logistics 33: 763–774.Google Scholar
45. Zipkin, P. (2000). Foundations of Inventory Management. New York: McGraw Hill-Irwin.Google Scholar