Parallel machine scheduling problem to minimize the earliness/tardiness costs with learning effect and deteriorating jobs

TOKSARI M. D. , Guner E.

JOURNAL OF INTELLIGENT MANUFACTURING, cilt.21, sa.6, ss.843-851, 2010 (SCI İndekslerine Giren Dergi) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Konu: 6
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1007/s10845-009-0260-3
  • Sayfa Sayıları: ss.843-851


The focus of this work is to analyze parallel machine earliness/tardiness (ET) scheduling problem with simultaneous effects of learning and linear deterioration, sequence-dependent setups, and a common due-date for all jobs. By the effects of learning and linear deterioration, we mean that the processing time of a job is defined by an increasing function of its starting time and a decreasing function of the position in the sequence. We develop a mixed integer programming formulation for the problem and show that the optimal sequence is V-shaped: all jobs scheduled before the shortest jobs and all jobs scheduled after the shortest job are in a non-increasing and non-decreasing order of processing times, respectively. The developed model allows sequence-dependent setups and sequence-dependent early/tardy penalties. The illustrative example with 11 jobs for 2 machines and 3 machines shows that the model can easily provide the optimal solution, which is V-shaped, for problem.