Abstract
We study a manufacturing firm that builds a product to stock to meet a random demand. If there is a positive surplus of finished goods, customers make their purchases without delay and leave. If there is a backlog, the customers are sensitive to the quoted lead time and some choose not to order if they feel that the lead time is excessive. A set of subcontractors, who have different costs and capacities, are available to supplement the firm's production capacity. We derive a feedback policy that determines the production rate and the rate at which the subcontractors are requested to deliver products. The performance of the system, when it is managed according to this policy, is evaluated.
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Abernathy, F.H., J.T. Dunlop, J.H. Hammond, and D.Weil. (1999). A Stich in Time: Lean Retailing and the Transformation of Manufacturing-Lessons from the Apparel and Textile Industries. New York: Oxford University Press.
Abernathy, F.H., J.T. Dunlop, J.H. Hammond, and D. Weil. (2000). “Control Your Inventory in a World of Lean Retailing.” Harvard Business Review, November-December, 169-176.
Bielecki, T. and P.R. Kumar. (1988). “Optimality of Zero-Inventory Policies for Unreliable Manufacturing Systems.” Operations Research 36(4), 532–541.
Bradley, J. (1999). “Optimal Control of an M/M/1 Subcontracting Model.” Technical report, Cornell University.
Bradley, J. and P. Glynn. (2000a). “Managing Capacity and Inventory Effectively in Manufacturing Systems.” Technical report, Cornell University.
Bradley, J. and P. Glynn. (2000b). “Managing the Manufacturer-Subcontractor Relationship and the Manufacturer's Optimal Capacity, Inventory, and Subcontracting Policies.” Technical report, Cornell University.
Fleming, W., S. Sethi, and H. Soner. (1987). “An Optimal Stochastic Production Planning with Randomly Fluctuating Demand.” SIAM Journal of Control Optimization 25, 1495–1502.
Fukuda, Y. (1964). “Optimal Policies for the Inventory Problem with Negotiable Lead-Time.” Management Science 4, 690–708.
Gershwin, S. and B. Tan. (2001). “Production Control with Backlog-Dependent Demand.” Unpublished manuscript.
Gershwin, S.B. (1992-1993). “Extension of FMS Scheduling Model.” Unpublished note.
Gershwin, S.B. (1994). Manufacturing Systems Engineering. Prentice-Hall. See http://web.mit.edu/manuf-sys/www/gershwin.errata.html for corrections.
Gershwin, S.B. (2000). “Design and Operation of Manufacturing Systems-the Control-Point Policy.” IIE Transactions 32(2), 93–103.
Ghosh, M., A. Araposthathis, and S. Markus. (1993). “Optimal Control of Switching Diffusions with Applications to Flexible Manufacturing Systems.” SIAM Journal of Control Optimization 31, 1183–1204.
Hu, J. (1995). “Production Rate Control for Failure Prone Production with no Backlog Permitted.” IEEE Transactions on Automatic Control 40(2), 291–295.
Huang, L., J. Hu, and P. Vakili. (1999, May 16-20). “Optimal Control of a Multi-State Manufacturing System: Control of Production Rate and Temporary Increase in Capacity.” In Second Aegean International Conference on Analysis and Modeling of Manufacturing Systems, pp. 191–198. http:// www.samos.aegean.gr/icsd/secaic/.
Kimemia, J.G. and S.B. Gershwin. (1983). “An Algorithm for the Computer Control of Production in a FlexibleManufacturing Systems.” IIE Transactions 15(4), 353–362. Reprinted in Modeling and Control of Automated Manufacturing Systemsby A.A. Desrochers, IEEE Computer Society Press Tutorial, 1990.
Krichagina, E.V., S.X.C. Lou, and M.I. Taksar. (1994). “Double Band Policy for Stochastic Manufacturing Systems in Heavy Traffic.” Mathematics of Operations Research 19(3), 560–597.
Nelder, J. and R. Mead. (1965). “A Simplex Method for Function Minimization.” Computer Journal 7, 308–313.
Olsder, G.J. and R. Suri. (1980, December). “Time-Optimal Control of Flexible Manufacturing Systems with Failure Prone Machines.” In Proceedings of the 19th IEEE Conference on Decision and Control, Albuquerque, NM
Perkins, J. and R. Srikant. (2001). “Failure-Prone Production Systems with Uncertain Demand.” IEEE Transactions on Automatic Control. to appear.
Puzo, M. (1969). The Godfather. G.P. Putnam's Sons.
Schweppe, F., M. Caramanis, R. Tabors, and R. Bohn. (1988). Spot Pricing of Electricity. Boston: Kluwer Academic.
Sethi, S.P. and G.L. Thompson. (2000). Optimal Control Theory: Applications to Management Science and Economics (2 ed.). Dordrecht: Kluwer Academic.
Tan, B. (1997). “Variance of the Throughput of an N-Station Production Line with no Intermediate Buffers and Time Dependent Failures.” European Journal of Operational Research 101(3), 560–576.
Tan, B. (2002a). “Managing Manufacturing Risks by Using Capacity Options.” Journal of the Operations Research Society 53(2), 232–242.
Tan, B. (2002b). “Production Control of a Pull System with Production and Demand Uncertainty.” IEEE Transactions on Automatic Control 47(5), 779–783.
Tan, B. and S.B. Gershwin. (2001). “On Production and Subcontracting Strategies for Manufacturers with Limited Capacity and Volatile Demand.” Working Paper Series ORC 354-01, Massachusetts Institute of Technology, Operations Research Center.
Van Mieghem, J.A. (1999). “Coordinating Investment, Production, and Subcontracting.” Management Science 45(7), 954–971.
Whittemore, A. and S. Saunders. (1977). “Optimal Inventory under Stochastic Demand with Two Supply Options.” SIAM Journal of Applied Mathematics 32, 293–305.
Yan, H., S. Lou, S. Sethi, A. Gardel, and P. Deosthali. (1996, May). “Testing the Robustness of Two-Boundary Control Policies in Semiconductor Manufacturing.” IEEE Transactions on Semiconductor Manufacturing 9(2), 285–288.
Zhang, V. (1995). “Ordering Policies for an Inventory System with Supply Flexibility.” PhD. thesis, Department of Industrial Engineering and Engineering Management, Stanford University.
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Tan, B., Gershwin, S.B. Production and Subcontracting Strategies for Manufacturers with Limited Capacity and Volatile Demand. Annals of Operations Research 125, 205–232 (2004). https://doi.org/10.1023/B:ANOR.0000011192.23903.7f
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DOI: https://doi.org/10.1023/B:ANOR.0000011192.23903.7f