Abstract
This paper deals with the optimal control of a one-machine two-product manufacturing system with setup changes, operating in a continuous time dynamic environment. The system is deterministic. When production is switched from one product to the other, a known constant setup time and a setup cost are incurred. Each product has specified constant processing time and constant demand rate, as well as an infinite supply of raw material. The problem is formulated as a feedback control problem. The objective is to minimize the total backlog, inventory and setup costs incurred over a finite horizon. The optimal solution provides the optimal production rate and setup switching epochs as a function of the state of the system (backlog and inventory levels). For the steady state, the optimal cyclic schedule is determined. To solve the transient case, the system's state space is partitioned into mutually exclusive regions such that with each region, the optimal control policy is determined analytically.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bai, S. X. and Elhafsi, M. (1993), “Real-Time Scheduling of a Manufacturing System with Non-Resumable Setup Changes,” Research Report 93-28. Department of Industrial and Systems Engineering. University of Florida.
Bai, S. X. and Elhafsi, M. (1996), “Transient and Steady State Analysis of a Manufacturing System with Setup Changes,” Journal of Global Optimization 8, 349–378.
Buzacott, J. A. and Ozkarahan, I. A. (1983), “One- and Two-Stage Scheduling of Two Products with Distributed Inserted Idle Time: The Benefits of a Controllable Production Rate,” Naval Research Logistics Quarterly 30, 675–696.
Caramanis, M., Sharifnia, A., Hu, J. and Gershwin, S. B. (1991), “Development of a Science Base for Planning and Scheduling Manufacturing Systems,” Proceedings of the 1991 NSF Design and Manufacturing Systems Conference, The University of Texas at Austin, January 9–11, 1991.
Carreno, J. J. (1990), “Economic Lot Scheduling for Multiple Products on Parallel Identical Processors,” Management Science 36, 348–358.
Connolly, S. (1992), “A Real-Time Policy for Performing Setup Changes in a Manufacturing System,” Master's Thesis, MIT Operations Research Center, May, 1992; MIT Laboratory for Manufacturing and Productivity. Report LMP-92-0005.
Dobson, G. (1987), “The Economic Lot Scheduling Problem: Achieving Feasibility Using Time-Varying Lot Sizes,” Operations Research 35, 764–771.
Elhafsi, M. and Bai, S. X. (1996a), “The Common Cycle Economic Lot Scheduling Problem with Backorders: Benefits of Controllable Production Rates.” To appear in Journal of Global Optimization.
Elhafsi, M. and Bai, S. X. (1996b), “Optimal Production and Setup Control of a Dynamic Two-Product Manufacturing System: Analytical Solution.” To appear in Journal of Computers and Mathematical Modelling.
Elmaghraby, S. E. (1978), “The Economic Lot Scheduling Problem (ELSP): Review and Extensions,” Management Science 24, 587–598.
Gallego, G. (1989), “Real-Time Scheduling of Several Products on a Single Facility With Setups and Backorders,” Ph.D. Thesis, School of OR&IE, Cornell University, Ithaca, NY.
Gershwin, S. B. (1993), Manufacturing Systems Engineering. Prentice Hall, Inc.
Goyal, S. K. (1984), “Determination of Economic Production Quantities for a Two-Product Single Machine System,” International Journal of Production Research 22, 121–126.
Hu, J. and Caramanis, M. (1992), “Near Optimal Set-up Scheduling for Flexible Manufacturing Systems,” Proceedings of the Third Renselaer Polytechnic Institute International Conference on Computer Integrated Manufacturing, Troy, New York, May 20–22, 1992.
Hu, J. and Caramanis, M. (1995), “Dynamic Set-up Scheduling of Flexible Manufacturing Systems: Design and Stability of Near Optimal General Round Robin Policies,” To appear in Discrete Event Systems, IMA Volumes in Mathematics and its Applications Series, 1995.
Jones, P. and Inman, R. (1989), “When Is the Economic Lot Scheduling Problem Easy?,” IIE Transactions 21, 11–20.
Kimemia, J. and Gershwin, S. B. (1983), “An Algorithm for the Computer Control of a Flexible Manufacturing System,” IIE Transactions 15(4), 353–362.
Kumar, P. R., and Seidman, T. I. (1990), “Dynamic Instabilities and Stabilization Methods in Distributed Real-Time Scheduling of Manufacturing Systems,” IEEE Transactions on Automatic Control 35, 289–338.
Kushner, H. J. and Dupuis, P. G. (1992), Numerical Methods for Stochastic Control Problems in Continuous Time. Springer-Verlag.
Moon, I., Gallego, G., and Simchi-Levi, D. (1991), “Controllable Production Rates in a Family Context,” International Journal of Production Research 29, 2459–2470.
Olsder, G. J. and Suri, R. (1980), “The Optimal Control of Part Routing in a Manufacturing System with Failure Prone Machines,” Proceedings of the 19th IEEE Conference on Decision and Control.
Perkins, J. and Kumar, P.R. (1989), “Stable, Distributed, Real-Time Scheduling of Flexible Manufacturing/Assembly/Disassembly Systems,” IEEE Transactions on Automatic Control 34, 139–148.
Roundy, R. (1985), “98%-Effective Integer-Ratio Lot Sizing for One-Warehouse Multi-Retailer Systems,” Management Science 31, 1416–1430.
Sharifnia, A., Caramanis, M., and Gershwin, S. B. (1991), “Dynamic Setup Scheduling and Flow Control in Manufacturing Systems,” Discrete Event Dynamic Systems: Theory and Applications, 1, 149–175.
Silver, E. (1990), “Deliberately Slowing Down Output in a Family Production Context,” International Journal of Production Research 28, 17–27.
Srivatsan, N., and Gershwin, S. B. (1990), “Selection of Setup Times in a Hierarchically Controlled Manufacturing System,” Proceedings of the 29th IEEE Conference on Decision and Control, Hawaii, December 1990.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Elhafsi, M., Bai, S.X. Optimal production control of a dynamic two-product manufacturing system with setup costs and setup times. J Glob Optim 9, 183–216 (1996). https://doi.org/10.1007/BF00121663
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00121663