A hierarchical approach to solving machine grouping and loading problems of flexible manufacturing systems. (English) Zbl 0597.90041

Stecke, Kathryn E.

Eur. J. Oper. Res. 24, 369-378 (1986).

This paper ties some previous results together by suggesting a hierarchical approach to solve actual grouping and loading problems. Both problems are first defined at an aggregated level of detail and in the context of a queueing network model. At this level, much information is suppressed. However, the robustness of the model allows the application of the application of the obtained theoretical results to a lower level in the hierarchy that considers all details of these problems. In addition, results obtained using the aggregate model can be used as input to the detailed models. Here, the grouping and loading problems are formulated in all detail as nonlinear integer programs, using all available and required information. The use of these models to solve realistic machine grouping and loading problems is then described. Finally, future research needs are suggested.

MSC:

90B30	Production models
90B22	Queues and service in operations research
90C90	Applications of mathematical programming
90C10	Integer programming
90C30	Nonlinear programming

Keywords:

planning; flexible manufacturing systems; resource allocation; grouping; loading; queueing network; nonlinear integer programs

References:

[1]	Barash, Moshe M., Computerized manufacturing systems for discrete products, (Salvendt, G., The Handbook of Industrial Engineering (1982), Wiley: Wiley New York)
[2]	Berge, Claude, Topological Spaces (1963), Macmillan: Macmillan New York
[3]	Berrada, Mohammed; Stecke, Kathryn E., A branch and bound approach for machine loading in flexible manufacturing systems, (Working paper no. 329 (1983), Graduate School of Business Administration, The University of Michigan: Graduate School of Business Administration, The University of Michigan Ann Arbor, MI) · Zbl 0604.90067
[4]	Buzen, Jeffrey P., Queueing network models of multi-programming, (Ph.D. dissertation (1971), Harvard University: Harvard University Cambridge, MA) · Zbl 0261.68031
[5]	Cavaillé, Jean-Bernard; Dubois, Didier, Heuristic methods based on mean-value analysis for flexible manufacturing systems performance evaluation, (Proceedings of the 21st IEEE Conference on Decision and Control. Proceedings of the 21st IEEE Conference on Decision and Control, Orlando, FL (1982)), 1061-1065
[6]	Cavaillé, Jean-Bernard; Forestier, J. P.; Bel, Gérard, A simulation program for analysis and design of a flexible manufacturing system, (Proceedings of the IEEE Conference on Cybernetics and Society. Proceedings of the IEEE Conference on Cybernetics and Society, Atlanta, GA (1981)), 257-259
[7]	Dubois, Didier; Stecke, Kathryn E., Using Petri nets to represent production processes, (Proceedings of the 22nd IEEE Conference on Decision and Control. Proceedings of the 22nd IEEE Conference on Decision and Control, San Antonio, TX (1983)) · Zbl 0718.90039
[8]	Giammo, T., Validation of a computer performance model of the exponential queueing network family, Acta Informatica, 17, 2, 137-152 (1976) · Zbl 0332.68048
[9]	Greenberg, Harvey J.; Pierskalla, William P., Symmetric mathematical programs, Management Science, 16, 5, 309-312 (1970) · Zbl 0191.48703
[10]	Kusiak, Andrew, Loading models in flexible manufacturing systems, (Working paper no. 05/83 (1983), Department of Industrial Engineering, Technical University of Nova Scotia: Department of Industrial Engineering, Technical University of Nova Scotia Halifax, Nova Scotia, Canada) · Zbl 0705.90039
[11]	Lipsky, L.; Church, J. D., Applications of a queueing network model for a computer system, Computing Surveys, 9, 205-221 (1977) · Zbl 0357.68071
[12]	Rose, C. A., Validation of a queueing model with classes of customers, (Proceedings of the International Symposium on Computer Performance Modeling, Measurement, and Evaluation (1976), Harvard University: Harvard University Cambridge, MA), 318-325
[13]	Shanthikumar, J. George; Stecke, Kathryn E., Reducing work-in-process inventory in certain classes of flexible manufacturing systems, European Journal of Operational Research (1986), forthcoming · Zbl 0605.90064
[14]	Solberg, James J., A mathematical model of computerized manufacturing systems, (Proceedings of the 4th International Conference on Production Research. Proceedings of the 4th International Conference on Production Research, Tokyo, Japan (1977))
[15]	Solberg, James J., CAN-Q user’s guide, (Report no. 9 (1980), School of Industrial Engineering, Purdue University: School of Industrial Engineering, Purdue University W. Lafayette, IN), (revised), NSF GRANT No. APR74 15256
[16]	Stecke, Kathryn E., Experimental investigation of a computerized manufacturing system, (Master’s thesis (1977), Purdue University: Purdue University West Lafayette, IN) · Zbl 0597.90041
[17]	Stecke, Kathryn E., Formulation and solution of nonlinear integer production planning problems for flexible manufacturing systems, Management Science, 29, 3, 273-288 (1983) · Zbl 0517.90035
[18]	Stecke, Kathryn E., On the nonconcavity of throughput in certain closed queueing networks, (Working paper no. 356 (1983), Graduate School of Business Administration, The University of Michigan: Graduate School of Business Administration, The University of Michigan Ann Arbor, MI) · Zbl 0623.90021
[19]	Stecke, Kathryn E.; Browne, Jim, Variations in flexible manufacturing systems according to the relevant types of automated materials handling, Material Flow, 2, 2, 179-185 (1985)
[20]	Stecke, Kathryn E.; Morin, Thomas L., Optimality of balancing workloads in certain types of flexible manufacturing systems, European Journal of Operational Research, 20, 1, 68-82 (1985) · Zbl 0578.90035
[21]	Stecke, Kathryn E.; Solberg, James J., The CMS loading problem, (Report no. 20, NSF Grant no. APR 74 15256 (1981), School of Industrial Engineering, Purdue University: School of Industrial Engineering, Purdue University West Lafayette, IN) · Zbl 0584.90022
[22]	Stecke, Kathryn E.; Solberg, James J., Loading and control policies for a flexible manufacturing system, International Journal of Production Research, 19, 5, 481-490 (1981)
[23]	Stecke, Kathryn E.; Solberg, James J., The optimality of unbalancing both workloads and machine group sizes in closed queueing networks of multiserver queues, Operations Research, 33, 4, 822-910 (1985) · Zbl 0584.90022
[24]	Stecke, Kathryn E.; Talbot, F. Brian, Heuristic loading algorithms for flexible manufacturing systems, (Proceedings of the Seventh International Conference on Production Research. Proceedings of the Seventh International Conference on Production Research, Windsor, Ontario, Canada, August 22-24 (1983))
[25]	Suri, Rajan, Robustness of queueing network formulas, Journal of the Association for Computing Machinery, 30, 3, 564-594 (1983) · Zbl 0628.68036
[26]	Suri, Rajan; Hildebrant, Richard R., Modeling flexible manufacturing systems using mean-value analysis, Journal of Manufacturing Systems, 3, 1, 27-38 (1984)
[27]	Whitney, Cynthia K.; Gaul, Thomas S., Sequential decision procedures for batching and balancing in FMSs, (Proceedings of the First ORSA/TIMS Special Interest Conference on Flexible Manufacturing Systems: Operations Research Models and Applications. Proceedings of the First ORSA/TIMS Special Interest Conference on Flexible Manufacturing Systems: Operations Research Models and Applications, Ann Arbor, MI, August 15-17 (1984)), 243-248