Hostname: page-component-745bb68f8f-l4dxg Total loading time: 0 Render date: 2025-02-10T14:03:06.045Z Has data issue: false hasContentIssue false
  • English
  • Français

OPTIMAL CONTROL OF A MAKE-TO-STOCK SYSTEM WITH ADJUSTABLE SERVICE RATE

Published online by Cambridge University Press:  19 September 2006

Maria E. Mayorga ,
Hyun-Soo Ahn  and
J. George Shanthikumar
Maria E. Mayorga
Affiliation:
Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, CA 94720
Hyun-Soo Ahn
Affiliation:
Ross School of Business, University of Michigan, Ann Arbor, MI 48109, E-mail: hsahn@umich.edu
J. George Shanthikumar
Affiliation:
Department of Industrial Engineering and Operations Research, University of California at Berkeley, Berkeley, CA 94720
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a multiclass make-to-stock system served by a single server with adjustable capacity (service rate). At any point in time, the decision-maker must determine the capacity level, make a production decision (i.e., whether to produce an item to stock or to satisfy a backorder), and make a rationing decision (i.e., whether to satisfy a new order from stock or place it on backorder). In this article we characterize the structure of optimal capacity adjustment, production, and stock rationing policy for both finite- and infinite-horizon problems. We show that an optimal policy is monotone in current inventory and backorder levels, and we characterize its properties. In a numerical study we compare the optimal policy with heuristic policies and show that the savings from using an optimal policy can be significant.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 4 , October 2006 , pp. 609 - 634
Copyright
© 2006 Cambridge University Press

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

REFERENCES

Cabrill, T.B. (1974). Optimal control of a maintenance system with variable service rates. Operations Research 22(4): 736–745.Google Scholar
Cohen, M.A., Kleindorfer, P.R., & Lee, H.L. (1988). Service constrained (s, S) inventory systems with priority demand classes and lost sales. Management Science 34(4): 482–499.Google Scholar
de Véricourt, F., Karaesman, F., & Dallery, Y. (2002). Optimal stock allocation for a capacitated supply system. Management Science 48(11): 1486–1501.Google Scholar
Eberly, J. & Van Mieghem, J.A. (1997). Multi-factor dynamic investment under uncertainty. Journal of Economic Theory 75: 345–387.Google Scholar
Frank, K.C., Zhang, R.Q., & Duenyas, I. (2003). Optimal inventory policies in systems with priority demand classes. Operations Research 51(6): 993–1002.Google Scholar
George, J.M. & Harrison, M.J. (2001). Dynamic control of a queue with adjustable service rate. Operations Research 49(5): 720–731.Google Scholar
Ha, A.Y. (1997). Stock-rationing policy for a make-to-stock production system with several demand classes and lost sales. Management Science 43(3): 1093–1103.Google Scholar
Ha, A.Y. (1997). Stock-rationing policy for a make-to-stock production system with two priority classes and backordering. Naval Research Logistics 44: 457–472.Google Scholar
Ha, A.Y. (2000). Stock rationing in an M/Ek /1 make-to-stock queue. Management Science 46(1): 77–87.Google Scholar
Lippman, S.A. (1975). Applying a new device in the optimization of exponential queueing systems. Operations Research 23: 687–710.Google Scholar
Mayorga, M.E. & Ahn, H.-S. (2004). Optimal control of a make-to-stock production system with adjustable service rate. Working Paper, University of California, Berkeley.
Nahmias, S. & Demmy, W. (1981). Operating characteristics of inventory systems with rationing. Management Science 27(11): 1236–1245.Google Scholar
Narongwanich, W., Duenyas, I., & Birge, J.R. (2002). Optimal portfolio of reconfigurable and dedicated capacity under uncertainty. Working Paper, University of Michigan, Ann Arbor.
Porteus, E.L. (1982). Conditions for characterizing the structure of optimal strategies in infinite horizon dynamic programs. Journal of Optimization Theory and Applications 36: 419–432.Google Scholar
Sobel, M.J. & Zhang, R.Q. (2001). Inventory policies for systems with stochastic and deterministic demand. Operations Research 49: 157–162.Google Scholar
Van Mieghem, J.A. (1998). Investment strategies for flexible resources. Management Science 44(8): 1071–1078.Google Scholar
Weber, R. & Stidham, S. (1987). Optimal control of service rates in networks of queues. Advances in Applied Probability 19: 202–218.Google Scholar