A new approach to computing optimal schedules for the job-shop scheduling problem

Martin, Paul; Shmoys, David B.

doi:10.1007/3-540-61310-2_29

Cited by 114 publications

(64 citation statements)

References 15 publications

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“…The Shaving filtering technique (Carlier and Pinson (1994), Martin and Shmoys (1996)) updates the task time windows by assessing the earliest and latest start times. For each unassigned task t i , at each node, it temporarily assigns t i a starting time (either est i or lst i ) and propagates the assignment using the filtering algorithms (Edge-Finding, etc.).…”

Section: Traditional Constraint Programming Approach ("Heavy Model")mentioning

confidence: 99%

Solving Variants of the Job Shop Scheduling Problem Through Conflict-Directed Search

Grimes

Hébrard

2015

INFORMS Journal on Computing

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We introduce a simple technique for disjunctive machine scheduling problems and show that this method can match or even outperform state of the art algorithms on a number of problem types. Our approach combines a number of generic search techniques such as restarts, adaptive heuristics and solution guided branching on a simple model based on a decomposition of disjunctive constraints and on the reification of these disjuncts. This paper describes the method and its application to variants of the job shop scheduling problem (JSP ).We show that our method can easily be adapted to handle additional side constraints and different objective functions, often outperforming the state of the art and closing a number of open problems.* Moreover, we perform in-depth analysis of the various factors that makes this approach efficient. We show that, while most of the factors give moderate benefits, the variable and value ordering components are key.

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Section: Traditional Constraint Programming Approach ("Heavy Model")mentioning

confidence: 99%

Solving Variants of the Job Shop Scheduling Problem Through Conflict-Directed Search

Grimes

Hébrard

2015

INFORMS Journal on Computing

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“…Due to the complexity of constraints relating the decision variables to variables representing probabilities, there was little constraint propagation, and, essentially, search was required to explore the entire branch-and-bound tree. As a consequence, in the following two sections we examine dominance rules (Beck & Prestwich, 2004;Smith, 2005) and shaving (Caseau & Laburthe, 1996;Martin & Shmoys, 1996), two stronger inference forms used in CP. In Section 8, we investigate why the models without dominance rules and shaving need to search the whole tree in order to prove optimality, and also discuss differences in the performance of the models based on our experimental results.…”

Section: Discussionmentioning

confidence: 99%

“…In a more general case, both the temporary constraint and the inferences made based on it can be more complex. Shaving has been particularly useful in the job-shop scheduling domain, where it is used to reduce the domains of start and end times of operations (Caseau & Laburthe, 1996;Martin & Shmoys, 1996). For such problems, shaving is used either as a domain reduction technique before search, or is incorporated into branch-and-bound search so that variable domains are shaved after each decision (Caseau & Laburthe, 1996).…”

Section: Shavingmentioning

confidence: 99%

A Constraint Programming Approach for Solving a Queueing Design and Control Problem

Terekhov

Beck

Brown

2009

INFORMS Journal on Computing

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In a facility with front room and back room operations, it is useful to switch workers between the rooms in order to cope with changing customer demand. Assuming stochastic customer arrival and service times, we seek a policy for switching workers such that the expected customer waiting time is minimized while the expected back room staffing is sufficient to perform all work. Three novel constraint programming models and several shaving procedures for these models are presented. Experimental results show that a model based on closed-form expressions together with a combination of shaving procedures is the most efficient. This model is able to find and prove optimal solutions for many problem instances within a reasonable run-time. Previously, the only available approach was a heuristic algorithm. Furthermore, a hybrid method combining the heuristic and the best constraint programming method is shown to perform as well as the heuristic in terms of solution quality over time, while achieving the same performance in terms of proving optimality as the pure constraint programming model. This is the first work of which we are aware that solves such queueing-based problems with constraint programming.

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“…The edge-finding algorithm [7], [8], [14] is one of the most well known OR algorithm integrated in CP. This global constraint propagation algorithm for disjunctive scheduling is a key ingredient for solving complex scheduling problems such as the Job-Shop Scheduling problem…”

Section: Edge-findingmentioning

confidence: 99%

Inter-distance Constraint: An Extension of the All-Different Constraint for Scheduling Equal Length Jobs

Artiouchine

Baptiste

2005

Principles and Practice of Constraint Programming - CP 2005

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Abstract. We study a global constraint, the "inter-distance constraint" that ensures that the distance between any pair of variables is at least equal to a given value. When this value is 1, the inter-distance constraint reduces to the all-different constraint. We introduce an algorithm to propagate this constraint and we show that, when domains of the variables are intervals, our algorithm achieves arc-B-consistency. It provides tighter bounds than generic scheduling constraint propagation algorithms (like edge-finding) that could be used to capture this constraint. The worst case complexity of the algorithm is cubic but it behaves well in practice and it drastically reduces the search space. Experiments on special Job-Shop problems and on an industrial problem are reported.

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A new approach to computing optimal schedules for the job-shop scheduling problem

Cited by 114 publications

References 15 publications

Solving Variants of the Job Shop Scheduling Problem Through Conflict-Directed Search

Solving Variants of the Job Shop Scheduling Problem Through Conflict-Directed Search

A Constraint Programming Approach for Solving a Queueing Design and Control Problem

Inter-distance Constraint: An Extension of the All-Different Constraint for Scheduling Equal Length Jobs

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