Concurrent open shop scheduling to minimize the weighted number of tardy jobs

  • Authors:

  • C. T. Ng;T. C. E. Cheng;J. J. Yuan

  • Affiliations:

  • Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People's Republic of China;Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People's Republic of China;Department of Management, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, People's Republic of China and Department of Mathematics, Zhengzhou, Henan 450052, People's Republic o ...

  • Venue:
  • Journal of Scheduling
  • Year:
  • 2003

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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-ε)ln m-approximation algorithm for any ε 0 if NP is not a subset of DTIME(nlog log n), and has no c ċ 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.