J. Carlier, and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35(2):164--176, 1989.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....implemented for job shop scheduling. The user can freely combine different search strategies and constraint algorithms. The performance is comparable to state of the art special purpose tools for scheduling. We show the integration of a new technique based on so called edge finding techniques [2] into constraints for job shop and multi capacitated scheduling. But also techniques coming from linear programming or graph algorithms may be integrated. The paper is structured as follows. In Section 2, constraint programming in Oz is introduced. Section 3 explains how scheduling problems can ....

....reified constraints: C 1 = A d(A) B) C 2 = B d(B) A) C 1 C 2 = 1: Here, the validity of e.g. A d(A) B is reflected into the 0 1 valued variable C 1 . But the resulting local reasoning is too weak to solve hard problems. Thus, a technique called edge finding was invented in [2]. We explain it in terms of constraint propagation. Let S be an arbitrary set of tasks to be scheduled on the same resource and T 2 S. Let S be S without T . Then, T must be last, if it cannot be scheduled before all tasks in S and not between two tasks in S . Let s(T ) c(T ) and d(T ) ....

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J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35(2):164--176, 1989.

....approach (see [39, 7] allows the user to program some new constraints. But it has no support to apply more sophisticated algorithmic techniques to implement new constraints (see also Section 8 and [28] as, for example, required for global scheduling constraints employing edge finding (refer to [2, 1]) On the other hand, combinatorial problems can be tackled in a language like C together with a dedicated library for constraint solving (see for example, Ilog [17] Although many programming abstractions are provided through C classes, it is hard for a C library to provide an adequate ....

J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35(2):164--176, 1989.

....propagator does not employ any domainspecific information other than that of a linear time scale. Global constraints, however, may also employ more elaborate propagation techniques for domain specific purposes. Applegate and Cook [1] proposed such a technique, called edge finding, see also [3]. Variants of this technique enjoy a run time which essentially grows quadratically in the number of items to be serialized. In computational terms, even these more efficient variants are yet more expensive than the global constraint described above. For certain problems, however, edge finding may ....

....tree may be reduced. The question remains which of the potential candidates for s 2 S should be considered first. For this purpose, information on the possible starting times can be exploited. In particular, it is possible to extract those items among S which may precede all others, see e.g. [3, 2, 20]. This subset of S can be computed in time O(jSj) Let F be this set of items which may precede all others in S. If F is empty, there clearly exists no serialization at all. If jF j = 1, no branching step is necessary because F s single element is the only candidate for s. If otherwise jF j 1, ....

CARLIER, J., AND PINSON, E. An algorithm for solving the job-shop problem. Management Science 35, 2 (1989), 164--176.

....overlap by reified constraints, will lead to no further propagation. On the other hand, the tasks must be scheduled between time point 1 and 18 (the latest completion time of either A, B or C) Because the overall duration is 24, this is impossible. Hence, stronger propagators were suggested in [5] (in terms of Operations Research, of course) reasoning on the whole set of tasks on a resource and, thus, are called global constraints. The principal ideas behind it are simple but very powerful. For an arbitrary set of tasks S to be scheduled on the same resource, the available time must be ....

....in S . Hence, T must be first and corresponding propagators can be imposed, narrowing the start times. Analogously, if ) d(S) c(S ) Gamma s(T ) d(S) T must be last. For this kind of reasoning, the term edgefinding was coined in [2] There are several variations of this idea in [5, 2, 6, 16] for the OR community and in [19, 7] for the constraint community; they differ in the amount of propagation and which sets S are considered for edgefinding (in principle, there are exponentially many) The resulting propagators do a lot of propagation, but are also more expensive than e.g. reified ....

[Article contains additional citation context not shown here]

J. Carlier and E. Pinson. An algorithm for solving the jobshop problem. Management Science, 35(2):164--176, 1989.

....# # # # # # # # # # # # Figure 2.2: Matching variables against values A specialized group of constraints, so called global constraints, which uses various algorithms to achieve higher level of consistency, was developed. Many of global constraints, e.g. serialize, cumulative, diffn [CP89, CP94, AB92, BE94] etc. were developed to solve complex scheduling and geometrical problems [Bel00, KCS A01] 2.2 Dynamic CSP The Constraint Satisfaction model presented in the previous section applies to the problems, i.e. problems which require a one time solution of a system representing ....

J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35(2):164-176, 1989.

....Since then, this problem has become a standard topic in scheduling textbooks (e.g. see Baker [3] Morton and Pentico [12] Rinnooy Kan [14] proved this problem to be NP Hard. One classic 10x10 job shop problem formulated by Muth and Thompson in 1963 was not solved until 1989 by Carlier and Pinson [6]. Recently however, heuristics have been very successful in solving many of the early benchmark problems. Several authors [1,2,7,8,11,18,19,22] established additional benchmark problems as the heuristic approaches improved. A listing of 159 of these benchmark problems is located on J. Beasley s ....

Carlier J., and E. Pinson, (1989). "An algorithm for solving the job shop problem," Management Science, 35, 164-176.

....feasible schedules [36] Since, each set of feasible permutations has a corresponding schedule, the objective of the JSP is to find, among the feasible permutations, the one with the smallest makespan. The JSP is NP hard [26] and has also proven to be computationally challenging. Exact methods [4, 7, 9, 10, 19] have been successful in solving small instances, including the notorious 10 10 instance of Fisher and Thompson [16] proposed in 1963 and only solved twenty years later. Problems of dimension 15 15 are still considered to be beyond the reach of today s exact methods. For such problems there ....

J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35:164--176, 1989.

....scheduling. Define a job shop instance to be acyclic if no job has two or more operations that need to run on any given machine. A single instance of acyclic job shop scheduling with 10 jobs, 10 machines and 100 operations resisted attempts at exact solution for 22 years until its resolution [17]. See also Applegate Cook [6] We will show here that good approximation algorithms do exist for job shop scheduling. There are two natural lower bounds on the makespan of any job shop instance: P max , the maximum total processing time needed for any job, and Pi max , the maximum total amount ....

J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35:164--176, 1989.

....each job passes once through each machine) which was randomly generated as an example in an early scheduling textbook [28] was taken up by the combinatorial optimization community as a challenge and bench mark. Named the 10 10 scheduling problem, it took 12 years of continuous e#ort to solve [8]. Currently some heuristic methods will reach the optimal solution for this problem, with a value of 930, in about 20 seconds of computing [1, 26] but this is without an optimality proof, and the heuristics do not provide performance guarantees. The optimal solution of job shop problems with 20 ....

Carlier, J. and Pinson, E, (1988). An algorithm for solving the job-shop problem. Management Science 35, 164--176.

....the one hand, Balas [3] was the first author to extensively exploit the properties of the DG for solving machine sequencing problems. In particular, he already proved the theoretical results leading to the compatibility of the DG with meta heuristic optimization approach [24] Carlier and Pinson s [9] results on well known benchmarks rely on the DG model. On the other hand, it deserves to read [19, 25] which survey natural extension of the basic DG to catch additional characteristics of the jobs (namely, dates and ready times, sequence dependent set up times and scheduled maintenance ....

J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35:164--176, 1989.

....problem is a classical NP hard problem notoriously difficult to solve even relatively small instances. As an example, a specific instance involving 10 machines and 10 jobs posed in a book by Muth and Thompson [11] in 1963 remained unsolved for over 20 years until solved by Carlier and Pinson [2] in 1985. The packet routing problem in a communication network (V; A) is the problem of routing a collection of packets from a source node to a destination node. It takes one time unit for a packet to traverse an edge in A, and only one packet can traverse a given edge at a time. As in the job ....

J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35:164--176, 1985.

....and DMS 9505155 and ONR grant N00014 96 1 0050O. The job shop scheduling problem is NP hard [12] and has proven to be very difficult even for relatively small instances. An instance with 10 jobs and 10 machines posed in a 1963 book by Muth Thompson [10] remained unsolved until Carlier Pinson [7] finally solved it in 1986, and there is a 20 job and 10 machine instance of Lawrence [15] that remains unsolved despite a great amount of effort that has been devoted to improving optimization codes for this problem. The most effective optimization techniques to date have been branch andbound ....

....problem. The decision variables in this formulation indicate the order in which operations are processed on each machine. Once these variables are set, the time at which each operation starts processing can be easily computed. Algorithms of this type have been proposed by Carlier Pinson [7], Brucker, Jurisch Sievers [6] and Applegate Cook [2] Although solving job shop scheduling problems to optimality is difficult, recently there has been progress developing heuristics that find good schedules. Adams, Balas Zawack [1] proposed the shifting bottleneck procedure, which uses a ....

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J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Sci., 35:164--176, 1989.

....problem is NP hard ( Garey and Johnson, 1979] So it is difficult to find an optimal solution. In order to give an example solving the moderate sized classical problem with 10 jobs to be processed on 10 machines (c.f. Muth and Thompson, 1963] optimally took over 25 years in development (c.f. [Carlier and Pinson, 1989]) Due to the fact that even the best known exact algorithms (c.f. Brucker et al. 1994] or ( Applegate and Cook, 1991] are not able to solve problems with 15 jobs and 15 machines in acceptable time, a long list of heuristics were developed in the last 25 years. In 1988 ( Balas et al. 1988] ....

Carlier, J. and Pinson, E. (1989). An algorithm for solving the job shop problem. Management Science, 35:164--176.

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Jacques Carlier and Eric Pinson [1989]. An Algorithm for Solving the Job-Shop Problem. Management Science, 35(2):164-176, 1989.

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J. Carlier, and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35(2):164--176, 1989.

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] Jacques Carlier and E. Pinson. "An algorithm for solving the job-shop problem." Management Science, 35:164-176, 1989.

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Carlier, J. and E. Pinson. 1989. An Algorithm for Solving the Job-Shop Problem. Management Science 35, 164--176.

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Carlier J., Pinson E., 1989. An algorithm for solving the job-shop problem. Management Science 35, 164-176.

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J. Carlier and E. Pinson. An Algorithm for Solving the Job Shop Problem. Management Science, 35:164-176, 1989.

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J. Carlier and E. Pinson (1989). An algorithm for solving the job shop problem. Management Science 35, 164-176.

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J. Carlier and E. Pinson. An algorithm for solving the job-shop problem. Management Science, 35(2):164--176, 1989.

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J. Carlier & E. Pinson, "An algorithm for solving the job-shop problem", Management Science, Vol 35 No 2, 164-176, 1989.

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J. Carlier and E. Pinson, An algorithm for solving the job-shop problem, Management Science, 35 (1989), pp. 164-176.

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Jacques Carlier and Eric Pinson. An Algorithm for Solving the Job-Shop Problem. Management Science, 35(2):164-176, 1989.

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Carlier, J., and Pinson, E. 1989. An algorithm for solving the job-shop problem. Management Science 35:165--176.

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