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Zbl 1193.90105
Mazdeh, Mohammad Mahdavi; Zaerpour, Farzad; Zareei, Abalfazl; Hajinezhad, Ali
Parallel machines scheduling to minimize job tardiness and machine deteriorating cost with deteriorating jobs. (English)
[J] Appl. Math. Modelling 34, No. 6, 1498-1510 (2010). ISSN 0307-904X

Summary: This paper studies the parallel machines bi-criteria scheduling problem (PMBSP) in a deteriorating system. Sequencing and scheduling problems (SSP) have seldom considered the two phenomena concurrently. This paper discusses the parallel machines scheduling problem with the effects of machine and job deterioration. By the machine deterioration effect, we mean that each machine deteriorates at a different rate. This deterioration is considered in terms of cost which depends on the production rate, the machine's operating characteristics and the kind of work done by each machine. Moreover, job processing times are increasing functions of their starting times and follow a simple linear deterioration. The objective functions are minimizing total tardiness and machine deteriorating cost. The problem of total tardiness on identical parallel machines is NP-hard, thus the problem with machine deteriorating cost as an additional term is also NP-hard. We propose the LP-metric method to show the importance of our proposed multi-objective problem. A metaheuristic algorithm is developed to locate optimal or near optimal solutions based on a Tabu search mechanism. Numerical examples are presented to show the efficiency of this model.

MSC 2000:: *90B35 Scheduling theory
90C60 Abstract computational complexity for math. programming problems
90C11 Mixed integer programming
90C29 Multi-objective programming, etc.

Keywords: scheduling and sequencing; parallel machines; machine deterioration; job deterioration; multi-objectives integer programming

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Zentralblatt MATH Berlin [Germany]