Abstract
We consider a relaxed version of the open shop scheduling problem–the “concurrent open shop” scheduling problem, in which any two operations of the same job on distinct machines are allowed to be processed concurrently. The completion time of a job is the maximum completion time of its operations. The objective is to schedule the jobs so as to minimize the weighted number of tardy jobs, with 0–1 operation processing times and a common due date d. We show that, even when the weights are identical, the problem has no (1 − ∈)ln m-approximation algorithm for any ε > 0 if NP is not a subset of DTIME(n loglogn), and has no c·ln m-approximation algorithm for some constant c > 0 if P ≠ NP, where m is the number of machines. This also implies that the problem is strongly NP-hard. We also give a (1 + d)-approximation algorithm for the problem.
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REFERENCES
Cheng, T. C. E. and G. Wang, “Customer order scheduling on multiple facilities,” Working Paper No. 11/98-9, Faculty of Business and Information Systems, The Hong Kong Polytechnic University, Hong Kong, 1999.
Feige, U., “A threshold of ln n for approximating set cover,” J. ACM, 45, 634-652 (1998).
Garey, M. R., D. S. Johnson, and L. Stockmeyer, “Some simplified NP-complete graph problem,” Theor. Comput. Sci., 1, 237-267 (1976).
Garey, M. R., and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, Freeman, San Francisco, 1979.
Papadimitriou, C. H., Computational Complexity, Addison-Wesley, NY, 1994.
Raz, R. and S. Safra, “A sub-constant error-probability low-degree test, and sub-constant error-probability PCP characterization of NP,” Proc. 29th ACM Symp. Theory Comput., ACM, 1997, pp. 475-484.
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Ng, C.T., Cheng, T.C.E. & Yuan, J.J. Concurrent Open Shop Scheduling to Minimize the Weighted Number of Tardy Jobs. Journal of Scheduling 6, 405–412 (2003). https://doi.org/10.1023/A:1024284828374
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DOI: https://doi.org/10.1023/A:1024284828374