Strong NP-hardness of the single machine multi-operation jobs total completion time scheduling problem

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

  • Venue:
  • Information Processing Letters
  • Year:
  • 2002

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Abstract

We consider the single machine multi-operation jobs total completion time scheduling problem. 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 set-up time. A job completes when all of its operations have been processed. The objective is to minimize the sum of the job completion times. In the literature, the computational complexity of this problem is posed as open. We show that the problem is strongly NP-hard even when the set-up times are common and the processing time of each operation is 0 or 1.