The complexity of two supply chain scheduling problems

  • Authors:

  • Jianfeng Ren;Donglei Du;Dachuan Xu

  • Affiliations:

  • Department of Management Sciences, Qufu Normal University, Rizhao 276826, Shandong Province, PR China and Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, PR Ch ...;Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, PR China and Faculty of Business Administration, University of New Brunswick, Fredericton, NB, Canada E3B 5A3;Department of Applied Mathematics, Beijing University of Technology, Beijing 100124, PR China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2013

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Abstract

We consider an assembling manufacture system where several suppliers provide component parts to a manufacturer, who assembles products from all the supplied component parts. The delivery time of any product is the maximum of the suppliers@? delivery time of the parts needed for that product. We assume that the final stage is non-bottleneck. Chen and Hall (2007) show that the suppliers@? problem of minimizing the total weighted number of tardy parts is binary (i.e., weakly) NP-hard and left open whether it is unary (i.e., strongly) NP-hard. In this paper we resolve this open problem by showing that it is unary NP-hard. Moreover we show that the suppliers@? problem of minimizing the total late work of parts is also unary NP-hard.