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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.
Flowshop Scheduling with Random and Bounded Setup Times
, 2002
"... The twomachine permutation flowshop scheduling problem to minimize makespan or total completion time criterion is addressed where setup times are considered to be separate from processing times. Setup times are relaxed to be random variables as opposed to the common assumption in the literature ..."
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The twomachine permutation flowshop scheduling problem to minimize makespan or total completion time criterion is addressed where setup times are considered to be separate from processing times. Setup times are relaxed to be random variables as opposed to the common assumption in the literature that setup times are exactly known (deterministic) in advance. The probability distributions of setup times are unknown, and only the lower and upper bounds of setup times are given. In such cases, there may not exist a unique schedule that remains optimal for all possible realizations of setup times, and therefore, a set of schedules has to be considered which dominates all other schedules for the given makespan or total completion time criterion. Some sufficient conditions are obtained when transposition of jobs minimizes makespan or total completion time criterion.
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.
The M × N Flowshop Problem with Separable, Sequenceindependent Setup Times
, 2006
"... AbstractThis paper presents an MILP model for the permutation flowshop wherein the setup times are both separable from the job processing times and independent of a job’s position in the processing sequence. Two experiments were conducted to estimate the computer times necessary to solve problems wi ..."
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AbstractThis paper presents an MILP model for the permutation flowshop wherein the setup times are both separable from the job processing times and independent of a job’s position in the processing sequence. Two experiments were conducted to estimate the computer times necessary to solve problems with up to 9 machines and 15 jobs, and to then compare these solution time requirements to those required to solve the same sets of problems solved as regular (NSIST) flowshop problems. The resultant data were then used to assess the impact on two optimal sequence performance measures, makespan and mean flowtime when setup times were separated from their jobs and allowed to begin as soon as the machine was free from the preceding job. This impact of separated setup times was found to increase with increasing numbers of machines, but to decrease slightly with increasing numbers of jobs for a given number of machines. Lastly, the data were used to analyze the impact on mean flowtime when makespan is minimized, and the impact on makespan when mean flowtime is minimized.
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.
Minimizing the sum of flow times with batching and delivery in a Supply Chain
, 2005
"... I have to indicate my best thankfulness to Professor Khalil Hindi with whose supervision I started my PhD. Although he left the UK but, always felt responsible about my work and I used his ideas and comments throughout this work. I also have to indicate my best thankfulness to Professor Mansoor Sarh ..."
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I have to indicate my best thankfulness to Professor Khalil Hindi with whose supervision I started my PhD. Although he left the UK but, always felt responsible about my work and I used his ideas and comments throughout this work. I also have to indicate my best thankfulness to Professor Mansoor Sarhadi, who kindly accepted the supervision of this project after Professor Hindi left. He supported and encouraged me in the all aspects of my work. In addition, I would like to thank Professor Malcolm Irving, my second supervisor for his support and kindness. I would finally like to appreciate Mr. Habib Nehzati who did a great deal of help in coding of the algorithms and was always there for me. I The aim of this thesis is to study one of the classical scheduling objectives that is of minimizing the sum of flow times, in the context of a supply chain network. We consider the situation that a supplier schedules a set of jobs for delivery in batches to