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Journal ArticleDOI

Benchmarks for basic scheduling problems

22 Jan 1993-European Journal of Operational Research (North-Holland)-Vol. 64, Iss: 2, pp 278-285
TL;DR: This paper proposes 260 randomly generated scheduling problems whose size is greater than that of the rare examples published, and the objective is the minimization of the makespan.
About: This article is published in European Journal of Operational Research.The article was published on 1993-01-22 and is currently open access. It has received 2173 citations till now. The article focuses on the topics: Flow shop scheduling & Job shop scheduling.

Summary (1 min read)

Introduction

  • The authors propose 260 scheduling problems whose size is greater than that of the rare examples published.
  • The types of problems that the authors propose are : the permutation flow shop, the job shop and the open shop scheduling problems.
  • Combinatorial optimization, Scheduling, Benchmarks, also known as Keywords.
  • The authors hope that this paper will fill a gap in this domain.
  • Every operation of a job uses a different machine during a given time and may wait before being processed.

In the case of the job shop problem, any processing order of the jobs on the

  • For every job, the operations must be processed in a given order on the machines, but this order may differ according to the jobs.
  • The aim of this paper is to present unsolved problems whose size corresponds to the one of industrial problems.
  • These heuristic methods are based on taboo search techniques.
  • Then, the authors have chosen the 10 problems that seemed to be the hardest ones and they have solved them once more, allowing their heuristic method to perform a higher number of iteration.
  • The authors recall its implementation so that this paper is self contained.

A problem will be entirely defined by the initial value of the seed of the random

  • Generator and by the way of generating it.
  • Below, the authors shall denote by U(0,1) the pseudorandom number that this generator provides.
  • There are in the literature some problems of this type ; let us quote for example eight small and simple problems proposed in Carlier [2] and solved exactly in this reference.
  • The maximum number of iterations performed by taboo search (long resolution).
  • Then the authors give ten instances for every size of problem with the following information (Table 2) :.

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Citations
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Journal ArticleDOI
TL;DR: A hybrid particle swarm optimization (PSO) for the job shop problem (JSP) is proposed and the computational results show that the modified PSO performs better than the original design, and that the hybrid PSO is better than other traditional metaheuristics.

307 citations


Cites background or methods from "Benchmarks for basic scheduling pro..."

  • ...In Section 4, we test the hybrid PSO on Fisher and Thompson (1963) and Lawrence (1984) and Taillard (1993) test problems....

    [...]

  • ...The PSOs were tested on Fisher and Thompson (1963) (FT06, FT10, and FT20), Lawrence (1984) (LA01 to LA40) and Taillard (1993) (TA01 to TA80) test problems....

    [...]

  • ...Keywords: Job shop problem; Scheduling; Particle swarm optimization...

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  • ...We further tested HPSO on TA test problems (Taillard, 1993)....

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Journal ArticleDOI
TL;DR: This paper deals with a classic flow-shop scheduling problem with makespan criterion and proposes a new very fast local search procedure based on a tabu search approach.

295 citations


Cites background or methods from "Benchmarks for basic scheduling pro..."

  • ...So far the best approximation algorithms for a permutation 'ow-shop problem with Cmax criterion were presented in papers by Ishubuchi et al. [2], Grabowski and Pempera [1], Nowicki and Smutnicki [3], Ogbu and Smith [4], Osman and Potts [5], Reeves and Yamada [6], Taillard [7,8], Werner [9], Widmer and Hertz [10]....

    [...]

  • ...[2], Grabowski and Pempera [1], Nowicki and Smutnicki [3], Ogbu and Smith [4], Osman and Potts [5], Reeves and Yamada [6], Taillard [7,8], Werner [9], Widmer and Hertz [10]....

    [...]

  • ...Having these values we deGne the following measures of the algorithm quality: • PRD(A) = 100(CA − CT )=CT—the value (average) of the percentage relative diLerence between makespan CA and the reference makespan CT given by algorithm T [8]....

    [...]

Journal ArticleDOI
TL;DR: A Genetic Algorithm is presented which solves the job shop scheduling problem and a highly efficient decoding procedure is proposed which strongly improves the quality of schedules.
Abstract: A general model for job shop scheduling is described which applies to static, dynamic and non-deterministic production environments. Next, a Genetic Algorithm is presented which solves the job shop scheduling problem. This algorithm is tested in a dynamic environment under different workload situations. Thereby, a highly efficient decoding procedure is proposed which strongly improves the quality of schedules. Finally, this technique is tested for scheduling and rescheduling in a non-deterministic environment. It is shown by experiment that conventional methods of production control are clearly outperformed atreasonable runtime costs.

289 citations


Cites background from "Benchmarks for basic scheduling pro..."

  • ...This finding is verified in Mattfeld (1996) by a comprehensive study on large-scale benchmarks for static job shop scheduling proposed by Taillard (1993)....

    [...]

Journal ArticleDOI
TL;DR: A new approximate algorithm is provided that is based on the big valley phenomenon, and uses some elements of so-called path relinking technique as well as new theoretical properties of neighbourhoods.
Abstract: The job shop scheduling problem with the makespan criterion is a certain NP-hard case from OR theory having excellent practical applications. This problem, having been examined for years, is also regarded as an indicator of the quality of advanced scheduling algorithms. In this paper we provide a new approximate algorithm that is based on the big valley phenomenon, and uses some elements of so-called path relinking technique as well as new theoretical properties of neighbourhoods. The proposed algorithm owns, unprecedented up to now, accuracy, obtainable in a quick time on a PC, which has been confirmed after wide computer tests.

289 citations


Cites methods from "Benchmarks for basic scheduling pro..."

  • ...…FT6, 10, 20 (Fisher and Thompson, 1963), LA01-40 (Lawrence, 1984), ABZ5-9 (Adams, Balas, and Zawack, 1988), ORB01-10 (Applegate and Cook, 1991), YN1-4 (Yamada and Nakano, 1992), SWV01-20 (Storer, Wu, and Vaccari, 1992), TA01-80 (Taillard, 1993) and DMU01-80 (Demirkol, Mehta, and Uzsloy, 1998)....

    [...]

  • ...For the sake of limited length of the paper, we show here results for three hard benchmarks YN1-4, SWV01-20, TA01-80....

    [...]

  • ...We have tested benefits from Theorem 1 using algorithm TSAB, on instances from Taillard (1993), having o j = m, j = 1, . . . , n, mk = n, k = 1, . . . , m, n ≥ m....

    [...]

  • ...COMPARISON OF i -TSAB WITH OTHER ALGORITHMS Algorithm i -TSAB has been tested on the following benchmarks: FT6, 10, 20 (Fisher and Thompson, 1963), LA01-40 (Lawrence, 1984), ABZ5-9 (Adams, Balas, and Zawack, 1988), ORB01-10 (Applegate and Cook, 1991), YN1-4 (Yamada and Nakano, 1992), SWV01-20 (Storer, Wu, and Vaccari, 1992), TA01-80 (Taillard, 1993) and DMU01-80 (Demirkol, Mehta, and Uzsloy, 1998)....

    [...]

References
More filters
Journal ArticleDOI
TL;DR: The elements of staged search and structured move sets are characterized, which bear on the issue of finiteness, and new dynamic strategies for managing tabu lists are introduced, allowing fuller exploitation of underlying evaluation functions.
Abstract: This is the second half of a two part series devoted to the tabu search metastrategy for optimization problems. Part I introduced the fundamental ideas of tabu search as an approach for guiding other heuristics to overcome the limitations of local optimality, both in a deterministic and a probabilistic framework. Part I also reported successful applications from a wide range of settings, in which tabu search frequently made it possible to obtain higher quality solutions than previously obtained with competing strategies, generally with less computational effort. Part II, in this issue, examines refinements and more advanced aspects of tabu search. Following a brief review of notation, Part II introduces new dynamic strategies for managing tabu lists, allowing fuller exploitation of underlying evaluation functions. In turn, the elements of staged search and structured move sets are characterized, which bear on the issue of finiteness. Three ways of applying tabu search to the solution of integer programmin...

5,883 citations

Journal ArticleDOI
TL;DR: A system (OR-Library) that distributes test problems by electronic mail (e-mail) that has available test problems drawn from a number of different areas of operational research.
Abstract: In this note we present a system (OR-Library) that distributes test problems by electronic mail (e-mail). This system currently has available test problems drawn from a number of different areas of...

1,939 citations

Journal ArticleDOI
TL;DR: Despite the brevity of the book, its mathematical notation, and the problems which it poses without solutions, the textbook is imbued with a feeling for theitty-gritty practical aspects of simulation.
Abstract: Bratley, Fox, and Schrage’s A Guide to Simulation provides practical recommendations for both the novice and the experienced simulationist, without insulting the reader’s intelligence. It does this with a text that is readable, mathematically precise, and comprehensive enough so that it touches on the majority of concerns which arise in a simulation project. Despite the brevity of the book (only 287 pages of text), its mathematical notation, and the problems which it poses without solutions, the textbook is imbued with a feeling for the &dquo;nitty-gritty&dquo; practical aspects of simulation. The authors generously present many helpful hints, suggestions, recommendations, and caveats gleaned from practical experience.

1,276 citations

Book
01 Jan 1983

1,061 citations

Journal ArticleDOI
TL;DR: The optimization procedure, combining the heuristic method and the combinatorial branch and bound algorithm, solved the well-known 10×10 problem of J. F. Thomson in under 7 minutes of computation time on a Sun Sparcstation 1.
Abstract: The job-shop scheduling problem is a notoriously difficult problem in combinatorial optimization. Although even modest sized instances remain computationally intractable, a number of important algorithmic advances have been made in recent years by J. Adams, E. Balas and D. Zawack; J. Carlier and E. Pinson; B. J. Lageweg, J. K. Lenstra and A. H. G. Rinnooy Kan; and others. Making use of a number of these advances, we have designed and implemented a new heuristic procedure for finding schedules, a cutting-plane method for obtaining lower bounds, and a combinatorial branch and bound algorithm. Our optimization procedure, combining the heuristic method and the combinatorial branch and bound algorithm, solved the well-known 10×10 problem of J. F. Muth and G. L. Thomson in under 7 minutes of computation time on a Sun Sparcstation 1. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

849 citations

Frequently Asked Questions (7)
Q1. What have the authors contributed in "Basic scheduling problems" ?

In this paper, the authors propose 260 scheduling problems whose size is greater than that of the rare examples published. The types of problems that the authors propose are: the permutation flow shop, the job shop and the open shop scheduling problems. 

let us mention5 that an iteration of taboo search needs about 4.10-6.n2.m seconds on a “Silicon Graphics” personal workstation (10 Mips). 

The machine Mij on which the jth operation of job i has to be performed is given by the following procedure :0) Mij := j (1 L Q M P 1) For i = 1 to nFor j = 1 to m Swap Mij and MiU[j,m]Let us note the use of another initial seed for the choice of the machines : Machine seed. 

The proportion of problems for which the authors found a solution for which the makespan was equal to the lower bound (or equal to the lower bound augmented by 2% for the 500-job 20-machine problems). 

This implementation uses only 32-bit integers and provides a uniformly distributed sequence of numbers between 0 and 1 (not contained) :3 0) Initial seed and X0 (0 < X0 < 231- 1) constants : a = 16 807, b = 127 773, c = 2 836, m = 231 - 11) Modification of k := Xi/b the seed : Xi+1 := a(Xi mod b) - kcIf Xi+1 < 0 then let Xi+1 := Xi+1 + m2) New value of the seed : Xi+1 Current value of the generator : Xi+1/mBelow, the authors shall denote by U(0,1) the pseudorandom number that this generator provides. 

The random number generator Let us recall the implementation of the linear congruential generator the authors have used which is based on the recursive formula Xi+1 = (16 807 Xi) mod (231 - 1). 

In order to implement the integer random procedure only with 32-bit integers, the problems have been chosen in such a way that one never has to deal with a seed X such that :a + P DE; )1( +−⋅ ≠ a + )1( +−