Total completion time scheduling problem with temperature considerations

Bu çalışmanın odağı tek makineli çizelgeleme problemlerinde iş ortam sıcaklığının analiz edilmesidir. Klasik çizelgeleme problemlerinde çoğunlukla işlem zamanları iş ortamının sıcaklık etkisi olmadan düşünülür. Fakat birçok gerçek çizelgeleme ortamında, iş ortamı sıcaklığı işin doğasından dolayı işlem zamanını etkileyebilir. Bu makalede toplam tamamlanma zamanı (ve tamamlanma zamanlarının karesi toplamı) problemleri için iş ortamı sıcaklığına bağlı işlerin işlem zamanları sunulmuştur. Her iki amaç için de polinom zamanlı çözümler elde edilmiştir.The focus of this work is to analyze working environment temperature in single-machine scheduling problems. In classical scheduling problems, the processing times are considered usually without the effect of working environment temperature. However, in many real scheduling environments, working environment temperature may affect processing time due to the nature of work. In this paper, we present job processing times based on the working environment temperature for total completion time (square) problem. We derive solutions with polynomial-time for both objectives

A branch and bound algorithm for minimizing makespan on a single machine with unequal release times under learning effect and deteriorating jobs

We present a single-machine problem with the unequal release times under learning effect and deteriorating jobs when the objective is minimizing the makespan. In this study, we introduced a scheduling model with unequal release times in which both job deterioration and learning exist simultaneously. By the effects of learning and deterioration, we mean that the processing time of a job is defined by increasing function of its execution start time and position in the sequence. A branch-and-bound algorithm incorporating with several dominance properties and lower bounds is developed to derive the optimal solution. A heuristic algorithm is proposed to obtain a near-optimal solution. The computational experiments show that the branch-and-bound algorithm can solve instances up to 30 jobs, and the average error percentage of the proposed heuristic is less than 0.16%. (C) 2010 Elsevier Ltd. All rights reserved