Abstract
We consider the problem of minimizing the makespan on a batch processing machine, in which jobs are not all compatible. Only compatible jobs can be included into the same batch. This relation of compatibility is represented by a split graph. All jobs are available at the same date. The capacity of the batch processing machine is finite or infinite. The processing time of a batch is given by the processing time of the longest job in the batch. We establish the NP-hardness of the general problem and present polynomial algorithms for several special cases.
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Boudhar, M.: Static scheduling on a single batch processing machine with split compatibility graphs, Cahiers du Laboratoire Leibniz-IMA Grenoble (France) 28, 2001.
Boudhar, M.: Dynamic scheduling on a single batch processing machine with split compatibility graphs, J. Math. Modelling Algorithms 2 (2003), 17???35.
Boudhar, M.: Scheduling a batch processing machine with bipartite compatibility graphs, Math. Methods Oper. Res. 57 (2003), 513???527.
Boudhar, M.: Ordonnancement sur machines ?? traitement par batch sous contraintes de compatibilit?? de t??ches: Complexit?? et approches algorithmiques, Th??se de doctorat d'??tat, Universit?? USTHB-Alger, 2004.
Boudhar, M. and Finke, G.: Scheduling on batch processing machines with constraints of compatibility between jobs, in Proceedings Second IFAC/IFIP/IEEE Conference on Management and Control of Production and Logistics (MCPL'2000) 2 (Grenoble, France, 2000), pp. 703???708.
Boudhar, M. and Finke, G.: Scheduling on a batch machine with job compatibilities, Belgian J. Oper. Res., Statist. Comput. Sci. (JORBEL) 40 (2000), 69???80.
Boudhar, M. and Finke, G.: Probl??me d'ordonnancement de t??ches sur une machine ?? traitement par batch, Maghreb Math. Review 10 (2001), 161???178.
Boudhar, M. and Khelladi, A.: Ordonnancement par batchs sous contraintes de compatibilit?? de t??ches, Maghreb Math. Review (2004), in press.
Brauner, N., Dhaenens-Flipo, C., Espinouse, M. L., Finke, G. and Gavranovic H.: Decomposition into parallel work phases with application to the sheet metal industry, in Proceedings International Conference on Industrial Engineering and Production Management (IEPM'99) 1, 1999, pp. 389???396.
Brucker, P., Gladky, A., Hoogeveen, H., Kovalyov, M. Y., Potts, C., Tautenhahn, T. and Van De Velde, S.: Scheduling a batching machine, J. Scheduling 1 (1998), 31???54.
Chandru, V., Lee, C. Y. and Uzsoy, R.: Minimizing total completion time on batch processing machines, Internat. J. Production Res. 31 (1993), 2097???2121.
Demange, M., Werra, D., Monnot, J. and Paschos, V. T.: Weighted node coloring: When stable sets are expensive (extended abstract), in L. Kucera (ed.), WG 2002, LNCS 2573, Springer-Verlag, Berlin, 2002, pp. 114???125.
Dobson, G. and Nambinadom, R. S.: The batch loading and scheduling problem, Research Report, Simon School of Business Administration, University of Rochester, NY, 1992.
Finke, G. and Gavranovic, H.: Graph partitioning and set covering for the optimal design of a production system in the metal industry, in Proceedings Second Conference IFAC/IFIP/IEEE on Management and Control of Production and Logistics (MCPL'2000) 2 (Grenoble, France, 2000), pp. 603???608.
Garey, M. R. and Johnson, D. S.: Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Company, San Francisco, 1979.
Hochbaum, D. S. and Landy, D.: Algorithms and heuristics for scheduling semiconductor burn-in operations, Research Report ESRC 94-8, University of California, Berkeley, USA, 1994.
Ikura, Y. and Gimple, M.: Efficient scheduling algorithms for a single batch processing machine, Oper. Res. Lett. 5 (1986), 61???65.
Kubiak, W. and Jolai Ghazvini, F.: Minimizing earliness/tardiness criteria on a batch processing machine with job families, in Proceedings Second Annual International Conference on Industrial Engineering 2, 1997, pp. 785???790.
Lee, C. Y. and Uzsoy, R.: Minimizing makespan on a single batch processing machine with dynamic job arrivals, Internat. J. Production Res. 17 (1999), 219???236.
Lee, C. L., Uzsoy, R. and Martin-Vega, L. A.: Efficient algorithms for scheduling semiconductor burn-in operations, Oper. Res. 40 (1992), 764???775.
Li, C. L. and Lee, C. Y.: Scheduling with agreeable release and due dates on a batch processing machine, Europ. J. Oper. Res. 96 (1997), 564???569.
Mehta, S. V. and Uzsoy, R.: Minimizing total tardiness on a batch processing machine with incompatible job families, IIE Trans. Scheduling and Logistics 31 (1998), 165???178.
Potts, C. N. and Kovalyov, Y. K.: Scheduling with batching: A review, Europ. J. Oper. Res. 120 (2000), 228???249.
Tarjan, R. E.: Data Structures and Networks Algorithms, SIAM, 1983.
Uzsoy, R.: Scheduling batch processing machines with incompatible job families, Internat. J. Production Res. 33 (1995), 2685???2708.
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Mathematics Subject Classifications (2000)
90B35, 90C15, 90C90, 65K05.
Mourad Boudhar: Partially supported by CMEP, project: 96MDU375 IMAG(UJF, Grenoble)???FM(USTHB, Alger).
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Boudhar, M. Scheduling on a Batch Processing Machine with Split Compatibility Graphs. J Math Model Algor 4, 391–407 (2005). https://doi.org/10.1007/s10852-005-3083-z
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DOI: https://doi.org/10.1007/s10852-005-3083-z