A Stronger Complexity Result for the Single Machine Multi-Operation Jobs Scheduling Problem to Minimize the Number of Tardy Jobs

  • Authors:

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

  • Affiliations:

  • Department of Logistics, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Logistics, Faculty of Business, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong;Department of Mathematics, Zhengzhou University, 450052, Henan, Zhengzhou, People's Republic of China

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

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Abstract

We consider the single machine multi-operation jobs scheduling problem to minimize the number of tardy jobs. Each job consists of several operations that belong to different families. In a schedule, each family of job operations may be processed in batches with each batch incurring a setup time. A job completes when all of its operations have been processed. The objective is to minimize the number of tardy jobs. In the literature, this problem has been proved to be strongly NP-hard for arbitrary due-dates. We show in this paper that the problem remains strongly NP-hard even when the due-dates are common and all jobs have the same processing time.