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A Survey of Scheduling Problems with Setup Times or Costs
"... The first comprehensive survey paper on scheduling problems with separate setup times or costs was conducted by Allahverdi et al. (1999), who reviewed the literature since the mid1960s. Since the appearance of that survey paper, there has been an increasing interest in scheduling problems with setu ..."
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The first comprehensive survey paper on scheduling problems with separate setup times or costs was conducted by Allahverdi et al. (1999), who reviewed the literature since the mid1960s. Since the appearance of that survey paper, there has been an increasing interest in scheduling problems with setup times (costs) with an average of more than 40 papers per year being added to the literature. The objective of this paper is to provide an extensive review of the scheduling literature on models with setup times (costs) from then to date covering more than 300 papers. Given that so many papers have appeared in a short time, there are cases where different researchers addressed the same problem independently, and sometimes by using even the same technique, e.g., genetic algorithm. Throughout the paper we identify such areas where independently developed techniques need to be compared. The paper classifies scheduling problems into those with batching and nonbatching considerations, and with sequenceindependent and sequencedependent setup times. It further categorizes the literature according to shop environments, including singlemachine, parallel machines, flow shop, nowait flow shop, flexible flow shop, job shop, open shop, and others.
JobShop Scheduling Problem With Sequence Dependent Setup Times
"... Abstract — The majority of researches on scheduling assume setup times negligible or as a part of the processing time. In this paper, job shop scheduling with sequence dependent setup times is considered. After defining the problem, a mathematical model is developed. Implementing the mathematical mo ..."
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Abstract — The majority of researches on scheduling assume setup times negligible or as a part of the processing time. In this paper, job shop scheduling with sequence dependent setup times is considered. After defining the problem, a mathematical model is developed. Implementing the mathematical model in large problems presents a weak performance to find the optimum results in reasonable computational times. Although the proposed mathematical model presents a good performance to obtain feasible solutions, it is unable to reach the optimum results in larger problems. Thus, a heuristic model based on priority rules is developed. Because of the inability to find optimum solutions in reasonable computational times, 3 different innovative lower bounds are developed, which could be implemented to evaluate different heuristics and metaheuristics in large problems. The performance of the heuristic model evaluated with a wellknown example in the literature insures that the model seems to have a strong ability to solve jobshop scheduling with sequence dependent setup times problems and to obtain good solutions in reasonable computational times. Keywords: Jobshop scheduling, Heuristic model, , Priority rules, Mathematical model
SequenceDependent Setup Times in a TwoMachine JobShop with Minimizing the Schedule Length
, 2006
"... AbstractThis article addresses the jobshop problem of minimizing the schedule length (makespan) for processing n jobs on two machines with sequencedependent setup times and removal times. The processing of each job includes at most two operations that have to be nonpreemptive. Machine routes may ..."
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AbstractThis article addresses the jobshop problem of minimizing the schedule length (makespan) for processing n jobs on two machines with sequencedependent setup times and removal times. The processing of each job includes at most two operations that have to be nonpreemptive. Machine routes may differ from job to job. If all setup and removal times are equal to zero, this problem is polynomially solvable via Jackson's permutations, otherwise it is NPhard even if each of n jobs consists of one operation on the same machine. We present sufficient conditions when Jackson’s permutations may be used for solving the twomachine jobshop problem with sequencedependent setup times and removal times. For the general case of this problem, the results obtained provide polynomial lower and upper bounds for the makespan which are used in a branchandbound algorithm. Computational experiments show that an exact solution for this problem may be obtained in a suitable time for n ≤ 280. We also develop a heuristic algorithm and present a worst case analysis. KeywordsScheduling theory, Setup, Jobshop 1.
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National Academy of Sciences of Belarus,
"... Abstract: This article addresses the jobshop problem of minimizing the schedule length (makespan) for processing n jobs on two machines with sequencedependent setup and removal times. The processing of each job includes at most two operations that have to be nonpreemptive. Machine routes may diff ..."
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Abstract: This article addresses the jobshop problem of minimizing the schedule length (makespan) for processing n jobs on two machines with sequencedependent setup and removal times. The processing of each job includes at most two operations that have to be nonpreemptive. Machine routes may differ from job to job. If all setup and removal times are equal to zero, this problem is polynomially solvable via Jackson's pair of job permutations, otherwise it is NPhard even if each of n jobs consists of one operation on the same machine. We present sufficient conditions when Jackson's pair of permutations may be used for solving the twomachine jobshop problem with sequencedependent setup and removal times. For the general case of this problem, the results obtained provide polynomial lower and upper bounds for the objective function value which are used in a branchandbound algorithm. Computational experiments show that an exact solution for this problem may be obtained in a suitable time for n ≤ 280. We also develop a heuristic algorithm and present a worst case analysis for it.