Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-23T17:38:42.279Z 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: [email protected]
Min Wang
Affiliation:
LeBow College of Business, Drexel University, 3141 Chestnut Street, Philadelphia, PA 19104, USA E-mail: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

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 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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