Minimizing makespan in hybrid flowshops

  • Authors:

  • Chung-Yee Lee;George L. Vairaktarakis

  • Affiliations:

  • Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA;Department of Industrial and Systems Engineering, University of Florida, Gainesville, FL 32611, USA

  • Venue:
  • Operations Research Letters
  • Year:
  • 1994

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Abstract

We consider flowshop environments that consist of multiple stages and multiple machines in each stage. The flowshops are flexible in the sense that a task within a stage can be processed by any of the machines in the stage. We refer to this design as the hybrid flowshop. Our objective is to schedule a set of n jobs so as to minimize makespan. The problem is N P-complete even in the case of a single stage. We develop a heuristic H for the 2-stage hybrid flowshop that has complexity O (n log n) (where n is the number of jobs) and an error bound of 2 -1/max {m"1, m"2} (where m"i is the number of machines at stage i, i = 1, 2). This bound extends a recent bound for the case m"1 = 1, m"2 = m and significantly improves all other results that have been developed for some special cases of the 2-stage hybrid flowshop. We develop five new lower bounds which are used in a computational experiment to show that the relative gap of H from optimality is small. We extend H to the case of more than two stages. We perform error bound analysis on the resulting heuristic H' whose complexity is O (kn log n) (where k is the number of stages). This is the first error bound analysis for the general hybrid flowshop problem and extends the current best error bound for the traditional k-machine flowshop problem.