On the Flow-Shop Sequencing Problem with No Wait in Process<sup>†</sup>

Reddi, S. S.; Ramamoorthy, C. V.

doi:10.1057/jors.1972.52

Cited by 221 publications

(39 citation statements)

References 6 publications

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“…Let , i j t be the time of processing of the job i on the machine j, Ti be the sum total of processing times corresponding of job i on m machines, ( , ) D p q be the minimum delay of the initiation of job p on the first machine after the job p is completed under no-wait constraint and can be calculated by Reddi and Ramamoorthy (1972) formula as…”

Section: Problem Formulationmentioning

confidence: 99%

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Heuristics for no-wait flow shop scheduling problem

Nailwal¹,

Gupta²,

Jeet³

2016

10.5267/j.ijiec

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No-wait flow shop scheduling refers to continuous flow of jobs through different machines. The job once started should have the continuous processing through the machines without wait. This situation occurs when there is a lack of an intermediate storage between the processing of jobs on two consecutive machines. The problem of no-wait with the objective of minimizing makespan in flow shop scheduling is NP-hard; therefore the heuristic algorithms are the key to solve the problem with optimal solution or to approach nearer to optimal solution in simple manner. The paper describes two heuristics, one constructive and an improvement heuristic algorithm obtained by modifying the constructive one for sequencing n-jobs through m-machines in a flow shop under no-wait constraint with the objective of minimizing makespan. The efficiency of the proposed heuristic algorithms is tested on 120 Taillard's benchmark problems found in the literature against the NEH under no-wait and the MNEH heuristic for no-wait flow shop problem. The improvement heuristic outperforms all heuristics on the Taillard's instances by improving the results of NEH by 27.85%, MNEH by 22.56% and that of the proposed constructive heuristic algorithm by 24.68%. To explain the computational process of the proposed algorithm, numerical illustrations are also given in the paper. Statistical tests of significance are done in order to draw the conclusions.

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Section: Problem Formulationmentioning

confidence: 99%

“…Some noteworthy theoretical works in flow shop scheduling without intermediate storage were provided by Gupta (1976), van der Veen and van Dal (1991) and Szwarc (1981). Reddi and Ramamoorthy (1972) and Wismer (1972) studied no-wait flow shop scheduling problem as an asymmetric travelling salesman problem.…”

Section: Introductionmentioning

confidence: 99%

Heuristics for no-wait flow shop scheduling problem

Nailwal¹,

Gupta²,

Jeet³

2016

10.5267/j.ijiec

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“…Reddi and Ramamoorthy (14) found that P21blockinglCmax can be formulated as a Travelling Salesman Problem with a special structure, a structure that enables one to use an O(n 2 ) algorithm.…”

Section: Imentioning

confidence: 99%

Stochastic Shop Scheduling: A Survey

Pinedo

Schrage

1982

Deterministic and Stochastic Scheduling

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In this paper a survey is made of some of the recent results in stochastic shop scheduling. The models dealt with include: Job shDps. Two objectivr: functions are considered: Minimization of the expected iz-,i-on time of the last job, the so-called makespan and cini-:iztoime of the sum of the expected completion times of all jobs, the so-called flow time. The decision-maker is not allowed to preempt. The shop models with two machines and exponentially distributed processing times usually turn out to have a very nice structure. Shop models with more than two machines are consideraIy harder..-_ INTRODUCTION AND SUkQ4AYIn this paper an attempt is made to survey the recent results in stochastic shop scheduling. Four shop models are considered; a short description of. these follows. (i)Open Shops. We have n jobs and m machines. A job requires an execution on each machine. The order in which a job passes through the machines is immaterial.(ii)Flow Shops with Infinite Intermnediate Storage. We have n jobs and m machines. The order of processing on the different machines is the same for all jobs; also the sequence in which the I. I jobs go through the first machine has to be the same as the sequence in which the jobs go through any subsequent machine, i.e. one job may not pass another while waiting for a machine. A flow shop with these restrictions is often referred to as a permutation flow shop. (iii) Flow Shops with Zero Intermediate Storage and Blocking. This shop model is similar to the previous one. The only difference is that now there is no storage space in between two successive machines. This may cause the following to happen: Job j after finishing its processing on machine i cannot leave machine i when the preceding job (job j-l) still is being processed on the next machine (machine i+l); this prevents job j+l from starting its processing on machine i. This phenomenon is called blocking. 1* (iv)Job S;;os. We have n jobs and m machines. Each job has its own machide order specified.Throughout this paper will be assumed that the decisionmaker is not allowed to preempt, i.e. interrupt the processing of a job on a machine. For results where the decision-maker is allowed to preempt, the reader should consult the references. In this paper two objectives will be considered, namely (i) minimization off the expected completion time of the last job (the so-called mak espan) and (ii) minimization of the sum of the expected comp=i ion times of all jobs (the so-called flow time).This survey is organized as follows: In Section 2 we give a short d'escription of the most important results in deterministic shz scheduling (without proofs). The purpose of this section is r: enable the reader to compare the results for the stochas-:_I versions of the different models, presented in Section 3, wiz their deterministic counterparts. For the stochastic models iz Section 3 we will not present any rigorous proofs either. However, we will provide for each model heuristic arguments that -ay rmake the results seem more intuitive. In...

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“…Other models include a method of treating manufacturing systems as continuous systems in time and controlling them using linear programming is given in van Eekelen et al (2005), and the so-called "hot ingot" problem, or continuous processing flowshop, which requires a scheduled job to move to the next machine in its route with no delay. The "hot ingot" problem is shown to be equivalent to a single machine with sequence dependent setup times in Reddi and Ramamoorthy (1972). When sequence dependent setup times are added to the flowshop, the sequencing problem is shown to be equivalent to a traveling salesman problem in Gupta (1986).…”

Section: Introductionmentioning

confidence: 99%

Model approximation for batch flow shop scheduling with fixed batch sizes

Weyerman

Rai

Warnick

2014

Discrete Event Dyn Syst

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Batch flow shops model systems that process a variety of job types using a fixed infrastructure. This model has applications in several areas including chemical manufacturing, building construction, and assembly lines. Since the throughput of such systems depends, often strongly, on the sequence in which they produce various products, scheduling these systems becomes a problem with very practical consequences. Nevertheless, optimally scheduling these systems is NP-complete. This paper demonstrates that batch flow shops can be represented as a particular kind of heap model in the max-plus algebra. These models are shown to belong to a special class of linear systems that are globally stable over finite input sequences, indicating that information about past states is forgotten in finite time. This fact motivates a new solution method to the scheduling problem by optimally solving scheduling problems on finite-memory approximations of the original system. Error in solutions for these "t-step" approximations is bounded and monotonically improving with increasing model complexity, eventually becoming zero when the complexity of the approximation reaches the complexity of the original system.

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On the Flow-Shop Sequencing Problem with No Wait in Process^†

Cited by 221 publications

References 6 publications

Heuristics for no-wait flow shop scheduling problem

Heuristics for no-wait flow shop scheduling problem

Stochastic Shop Scheduling: A Survey

Model approximation for batch flow shop scheduling with fixed batch sizes

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On the Flow-Shop Sequencing Problem with No Wait in Process†

Cited by 221 publications

References 6 publications

Heuristics for no-wait flow shop scheduling problem

Heuristics for no-wait flow shop scheduling problem

Stochastic Shop Scheduling: A Survey

Model approximation for batch flow shop scheduling with fixed batch sizes

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Product

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On the Flow-Shop Sequencing Problem with No Wait in Process^†