Hostname: page-component-89b8bd64d-dvtzq Total loading time: 0 Render date: 2026-05-07T05:38:05.278Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMAL POLICY FOR A PRODUCTION–INVENTORY SYSTEM WITH SETUP COST AND AVERAGE COST CRITERION

Published online by Cambridge University Press:  30 July 2012

Xiuli Chao ,
Yifan Xu  and
Baimei Yang
Xiuli Chao
Affiliation:
Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, MI48109 E-mail: xchao@umich.edu
Yifan Xu
Affiliation:
School of Management, Fudan University, Shanghai 200433, China E-mail: yfxu@fudan.edu.cn
Baimei Yang
Affiliation:
School of Management, Fudan University, Shanghai 200433, China E-mail: yfxu@fudan.edu.cn
Get access Rights & Permissions [Opens in a new window]

Abstract

One of the most fundamental results in inventory theory is the optimality of (s, S) policy for inventory systems with setup cost. This result is established under a key assumption of infinite ordering/production capacity. Several studies have shown that, when the ordering/production capacity is finite, the optimal policy for the inventory system with setup cost is very complicated and indeed, only partial characterization for the optimal policy is possible. In this paper, we consider a continuous review production/inventory system with finite capacity and setup cost. The demand follows a Poisson process and a demand that cannot be satisfied upon arrival is backlogged. We show that the optimal control policy has a very simple structure when the holding/shortage cost rate is quasi-convex. We also develop efficient algorithms to compute the optimal control parameters.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 26 , Issue 4 , October 2012 , pp. 457 - 481
Copyright
Copyright © Cambridge University Press 2012

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.)

Article purchase

Temporarily unavailable

References

1.Benjaafar, S., ElHafsi, M., & Vericourt, D. (2004). Demand allocation in multiple-product, multiple-facility, make-to-stock systems. Management Science 50: 1431–1448.CrossRefGoogle Scholar
2.Chao, X. & Zhou, S.X. (2006). Joint inventory and pricing strategy for a stochastic continuous-review system, IIE Transactions 38: 401–408.CrossRefGoogle Scholar
3.Craven, B.D. (1988). Fractional programming. Berlin: Heldermann.Google Scholar
4.Dharmadhikari, S. & Joag-Dev, K.. (1988). Unimodality, convexity, and applications, San Diego, CA: Academic Press.Google Scholar
5.Federgruen, A. & Zipkin, P. (1986). An inventory model with limited production capacity and uncertain demands I. The average cost criterion. Mathematics of Operations Research 11: 193–207.CrossRefGoogle Scholar
6.Feng, Y. & Sun, J. (2001). Computing the optimal replenishment policy for inventory systems with random discount opportunities. Operations Research 49: 790–795.CrossRefGoogle Scholar
7.Feng, Y. & Xiao, B. (2002). Optimal threshold control in discrete failure-prone manufacturing systems, IEEE Transactions on Automatic Control 47: 1167–1174.CrossRefGoogle Scholar
8.Gallego, G. (1998). New bounds and heuristics for (Q, r) policies. Management Science 44: 219–233.CrossRefGoogle Scholar
9.Gallego, G. & Scheller-Wolf, A. (2000). Capacitated inventory problems with fixed order costs: Some optimal policy structure. European Journal of Operational Research 126: 603–613.CrossRefGoogle Scholar
10.Gallego, G. & Toktay, L.B. (2004). All-or-nothing ordering under a capacity constraint. Operations Research 52: 1001–1002.CrossRefGoogle Scholar
11.Gavish, B. & Graves, S. (1980). A one-product production/inventory problem under continuous review policy, Operations Research 28: 1228–1236.CrossRefGoogle Scholar
12.Ha, A.Y. (1997). Optimal dynamic scheduling policy for a make-to-stock production system, Operations Research 45: 42–53.CrossRefGoogle Scholar
13.Heyman, D.P. (1968). Optimal operating policies for M/G/1 queuing systems, Operations Research 16: 362–382.CrossRefGoogle Scholar
14.Kapuscinski, R. & Tayur, S.R. (1990). Optimal policies and simulation based optimization for capacitated production inventory systems. In Tayur, S.R., Ganeshan, R., & Magazine, M. (eds.), Quantitative models for supply chain management. Kluwer: The Netherlands, pp. 7–40.Google Scholar
15.Kleinrock, L. (1975). Queueing systems, vol. 1: Theory. New York: John Wiley & Sons.Google Scholar
16.Li, L. (1988). A stochastic theory of the firm, Mathematics of Operations Research, 13: 447–465.CrossRefGoogle Scholar
17.Ohnishi, M. (1992). Policy iteration and Newton-Raphson methods for Markov decision processes under average cost criterion. Computers & Mathematics with Applications 24: 147–155.CrossRefGoogle Scholar
18.Puterman, M.L. (1994). Markov decision processes: discrete stochastic dynamic programming, New York: John Wiley & Sons.CrossRefGoogle Scholar
19.Scarf, H. (1960). The optimality of (s,S) policies in the dynamic inventory problem. In Arrow, K., Karlin, S., & Suppes, P. (eds.), Mathematical methods in the social sciences. Stanford, CA, USA: Stanford University Press, pp. 196–202.Google Scholar
20.Shaoxiang, C. (2004). The infinite horizon periodic review problem with setup costs and capacity. Operations Research 52: 409–421CrossRefGoogle Scholar
21.Shaoxiang, C. & Lambrecht. (1996). X–Y band and modified (s, S) policy. Operations Research 44: 1013–1019.CrossRefGoogle Scholar
22.Sobel, M. (1982). The optimality of full-service policies. Operations Research 30: 636–649.CrossRefGoogle Scholar
23.Stidham, S. (2009). Optimal design of queueing systems. Boca Raton, FL: CRC Press.CrossRefGoogle Scholar
24.Tijms, H.C. (2003). A first course in stochastic models. Chichester, UK: John Wiley & Sons, Ltd.CrossRefGoogle Scholar
25.Veatch, M.H. & Wein, L.M. (1996). Scheduling a make-to-stock queue, Operations Resesarch 44: 643–647.Google Scholar
26.Veinott, A. (1966). On the optimality of (s, S) invenotry polidies: New conditions and a new proof. SIAM Journal on Applied Mathematics 14: 1067–1083.CrossRefGoogle Scholar
27.Wein, L.M. (1992). Dynamic scheduling of a make-to-stock queue. Operations Research 40: 724–735.CrossRefGoogle Scholar
28.Wijngaard, J. (1972). An inventory problem with constrained order capacity. TH-Report 72-WSK-63, Eindhoven University of Technology, Eindhoven, The Netherlands.Google Scholar
29.Xu, Y. & Chao, X. (2009). Dynamic pricing and inventory control for a production system with average profit criterion. Probability in Engineering and Informational Sciences 23: 489–513.CrossRefGoogle Scholar
30.Zheng, Y. (1992). On properties of stochastic inventory systems. Management Science 38: 87–103.CrossRefGoogle Scholar
31.Zheng, Y.S. & Zipkin, P. (1990). A queueing model to analyze the value of centralized inventory information, Operations Research 38: 296–307.CrossRefGoogle Scholar