A job-shop problem with one additional resource type
We consider a job-shop scheduling problem with n jobs and the constraint that at most p<n jobs can be processed simultaneously. This model arises in several manufacturing processes, where each operation has to be assisted by one human operator and there are p (versatile) operators. The problem is binary NP-hard even with n=3 and p=2. When the number of jobs is fixed, we give a pseudopolynomial dynamic programming algorithm and a fully polynomial time approximation scheme (FPTAS). We also propose an enumeration scheme based on a generalized disjunctive graph, and a dynamic programming-based heuristic algorithm. The results of an extensive computational study for the case with n=3 and p=2 are presented.
KeywordsJob shop Scheduling with resource constraints Disjunctive graph Dynamic programming
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- Carlier, J., & Pinson, E. (1990). A practical use of Jackson’s preemptive schedule for solving the job shop problem. Annals of Operations Research, 26, 269–287. Google Scholar
- Garey, M. R., & Johnson, D. S. (1979). Computers and intractability. New York: Freeman. Google Scholar
- Roy, B., & Sussmann, B. (1964). Les problemes d’ordonnancement avec constraintes disjonctives. SEMA, Note D.S., No. 9, Paris. Google Scholar
- Wang, M. Y., Sethi, S. P., Sriskandarajah, C., & van de Velde, S. L. (1997). Minimizing makespan in a flowshop with pallet requirements: computational complexity. INFOR (Information Systems and Operational Research), 35, 277–285. Google Scholar
- Wei, V. K. (1981). A lower bound on the stability number of a simple graph. Technical Memorandum No. 81-11217-9. Bell Laboratories. Google Scholar