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

TOKSARI M. D., GÜNER E.

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

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 21 Sayı: 6
  • Basım Tarihi: 2010
  • Doi Numarası: 10.1007/s10845-009-0260-3
  • Dergi Adı: JOURNAL OF INTELLIGENT MANUFACTURING
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.843-851
  • Anahtar Kelimeler: Earliness/tardiness, Learning effect, Deterioration jobs, V-shaped property, Parallel machine, Sequence-dependent setup time, Common due date, DEPENDENT PROCESSING TIMES, EARLINESS-TARDINESS COSTS, TOTAL COMPLETION-TIME, COMMON DUE-DATE, SINGLE-MACHINE, FLOW-SHOP, LINEAR DETERIORATION, SHAPED POLICIES, PENALTIES, IMPACT
  • Gazi Üniversitesi Adresli: Evet

Özet

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.