Abstract
Loading problems in flexible manufacturing systems involve assigning operations for selected part types and their associated tools to machines or machine groups. One of the objectives might be to maximize the expected production rate (throughput) of the system. Because of the difficulty in dealing with this objective directly, a commonly used surrogate objective is the closeness of the actual workload allocation to the continuous workload allocation that maximizes throughput. We test several measures of closeness and discuss correlations between these measures and throughput. Using the best measure, we show how to modify an existing branch and bound algorithm which was developed for the case of equal target workloads for all machine groups to accommodate unequal target workloads. We also develop a new branch and bound algorithm which can be used for both types of problems. The efficiency of the algorithm in finding optimal solutions is achieved through the application of better branching rules and improved dominance results. Computational results on randomly generated test problems indicate that the new algorithm performs well.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ammons, J.C., Lofgren, C.B., and McGinnis, L.F., “A Large Scale Machine Loading Problem in Flexible Assembly,”Annals of Operations Research, Vol. 3, pp. 319–322 (1985).
Berrada, M. and Stecke, K.E., “A Branch and Bound Approach for Machine Load Balancing in Flexible Manufacturing Sytems,”Management Science, Vol. 32, No. 10, pp. 1316–1335 (October 1986).
Carrie, A.S. and Perera, D.T.S., “Work Scheduling in FMS under Tool Availability Constraints,”International Journal of Production Research, Vol. 24, No. 6, pp. 1299–1308 (June 1986).
Dallery, Y. and Stecke, K.E., “On the Optimal Allocation of Servers and Workloads in Closed Queuing Networks,”Operations Research, Vol. 37, No. 4, pp. 694–703 (July–August 1990).
Greene, T.J. and Sadowski, R.P. “A Mixed Integer Program for Loading and Scheduling Multiple Flexible Manufacturing Cells,”European Journal of Operational Research, Vol. 24, No. 3, pp. 379–386 (March 1986).
Kim, Y.-D. and Yano, C.A., “A New Branch and Bound Approach for Loading Problems in Flexible Manufacturing Systems,” Technical Report 89-5, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbor, MI (February 1989).
Kim, Y.-D. and Yano, C.A., “A Heuristic Approach for Loading Problems in Flexible Manufacturing Systems,”IIE Transactions, Vol. 25, No. 1, pp. 26–39 (February 1993).
Kiran, A.S. and Tansel, B. C. “The System Setup in FMS: Concepts and Formulation,”Proceedings of the 2nd ORSA/TIMS Conference on Flexible Manufacturing Systems, Ann Arbor, MI, K.E. Stecke and R. Suri (Eds.), Elsevier Science Publishers B.V., Amsterdam, pp. 321–332 (August 1986).
Kusiak, A., “Loading Models in Flexible Manufacturing Systems,” inFlexible Manufacturing: Recent Development on FMS, Robotics, CAD/CAM, CIM, A. Raouf and S.I. Ahmad (Eds.), Elsevier Science Publishers B. V., Amsterdam, pp. 119–132 (1985).
Lashkari, R.S., Dutta, S.P., and Padhye, A.M., “A New Formulation of Operation Allocation Problem in Flexible Manufacturing Systems: Mathematic Modeling and Computational Experience,”International Journal of Production Research, Vol. 25, No. 9, pp. 1267–1283 (September 1987).
Montgomery, D.C.,Design and Analysis of Experiments, John Wiley & Sons, Inc., New York, NY (1984).
Rajagopalan, S., “Formulation and Heuristic Solutions for Parts Grouping and Tool Loading in Flexible Manufacturing Systems,”Proceedings of the 2nd ORSA/TIMS Conference on Flexible Manufacturing Systems, Ann Arbor, MI, K.E. Stecke and R. Suri (Eds.), Elsevier Science Publishers B.V., Amsterdam, pp. 312–314 (August 1986).
Sarin, S.C. and Chen, C.S., “The Machine Loading and Tool Allocation Problem in a Flexible Manufacturing System,”International Journal of Production Research, Vol. 25, No. 7, pp. 1081–1094 (July 1987).
Shanker, K. and Tzen, Y.-J. J., “A Loading and Dispatching Problem in a Random Flexible Manufacturing System,”International Journal of Production Research, Vol. 23, No. 3, pp. 579–595 (May–June 1985).
Shanthikumar, J.G. and Stecke, K.E., “Reducing Work-in-Process Inventory in Certain Classes of Flexible Manufacturing Systems,”European Journal of Operational Research, Vol. 26, No. 2, pp. 266–271 (August 1986).
Shanthikumar, J.G. and Yao, D.D., “Optimal Server Allocation in a System of Multi-Server Stations,”Management Science, Vol. 33, No. 9, pp. 1173–1180 (September 1987).
Shanthikumar, J.G. and Yao, D.D. “On Server Allocation in Multiple Center Manufacturing Systems,”Operations Research, Vol. 36, No. 2, pp. 333–342 (March–April 1988).
Stecke, K.E., “Formulation and Solution of Nonlinear Integer Production Planning Problems for Flexible Manufacturing Systems,”Management Science, Vol. 29, No. 3, pp. 273–288 (March 1983).
Stecke, K.E., “A Hierarchical Approach to Solving Machine Grouping and Loading Problems of Flexible Manufacturing Systems,”European Journal of Operational Research, Vol. 24, No. 3, pp. 369–378 (March 1986).
Stecke, K.E. and Morin, T.L., “The Optimality of Balancing Workloads in Certain Types of Flexible Manufacturing Systems,”European Journal of Operational Research, Vol. 20, No. 1, pp. 68–82 (April 1985).
Stecke, K.E. and Solberg, J.J., “Loading and Control Policies for a Flexible Manufacturing System,”International Journal of Production Research, Vol. 19, No. 5, pp.. 481–490 (May 1981).
Stecke, K.E. and Solberg, J.J., “The Optimality of Unbalancing Both Workloads and Machine Group Sizes in Closed Queuing Networks of Multi-Server Queues,”Operations Research, Vol. 33, No. 4, pp. 882–910 (July–August 1985).
Stecek, K.E., and Talbot, F.B., “Heuristics for Loading Flexible Manufacturing Systems,”Flexible Manufacturing: Recent Developments in FMS, Robotics, CAD/CAM, CIM, A. Raouf, and S.I. Ahmad (Eds.), Elsevier Science Publishers B.V., Amsterdam (1985), pp. 73–85.
Yao, D.D., “Some Properties of the Throughput Function of Closed Networks of Queues,”Operations Research Letters, Vol. 3, No. 6, pp. 313–317 (April 1985).
Yao, D.D. and Kim, S.C., “Reducing the Congestion in a Class of Job Shops,”Management Science, Vol. 33, No. 9, pp. 1165–1172 (September 1987a).
Yao, D.D. and Kim, S.C., “Some Order Relations in Closed Networks of Queues with Multiserver Stations,”Naval Research Logistics, Vol. 34, No. 1, pp. 53–66 (February 1987b).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Kim, YD., Yano, C.A. A new branch and bound algorithm for loading problems in flexible manufacturing systems. Int J Flex Manuf Syst 6, 361–381 (1994). https://doi.org/10.1007/BF01324801
Issue Date:
DOI: https://doi.org/10.1007/BF01324801