A two-stage flow shop scheduling problem on a batching machine and a discrete machine with blocking and shared setup times

  • Authors:

  • Hua Gong;Lixin Tang;C. W. Duin

  • Affiliations:

  • Liaoning Key Laboratory of Manufacturing System and Logistics, The Logistics Institute, Northeastern University, Shenyang 110004, China;Liaoning Key Laboratory of Manufacturing System and Logistics, The Logistics Institute, Northeastern University, Shenyang 110004, China;Faculty of Economics and Econometrics, University of Amsterdam, Roetersstraat 11, 1018 WB Amsterdam, The Netherlands

  • Venue:
  • Computers and Operations Research
  • Year:
  • 2010

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Abstract

Motivated by applications in iron and steel industry, we consider a two-stage flow shop scheduling problem where the first machine is a batching machine subject to the blocking constraint and the second machine is a discrete machine with shared setup times. We show that the problem is strongly NP-hard when the objective is to minimize the makespan. When solved with a heuristic priority rule, the worst case ratio with the minimum makespan is 2. For a more general objective, the minimization of a linear combination of the makespan and the total blocking time, a quadratic mixed integer program is presented first. Then we pinpoint two cases with polynomial time algorithms: the case without blocking constraint and the case with a given job sequence. Also for the general objective, we analyze an approximation algorithm. Finally, we evaluate the algorithms, giving experimental results on randomly generated test problems.