An Algorithm for Solving the Job-Shop Problem

Carlier, Jacques; Pinson, Éric

doi:10.1287/mnsc.35.2.164

Cited by 645 publications

(244 citation statements)

References 13 publications

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“…One of the most popular filtering techniques for the unary resource constraint is known as Edge-Finding (Carlier and Pinson (1989), Nuijten (1994)). Let T denote a set of tasks sharing a unary resource, Ω denote a subset of T , and let t i Ω (respectively t i Ω)…”

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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“…With D = d 3 = 24 we get the tails q 1 = 19, q 2 = 14, q 3 = 0, q 4 = 12, q 5 = 8. Let us assume that on the production machine the jobs are processed in the sequence (1,2,4,3,5); in the transportation stage the batch sequence is ({1}, {2, 4}, {3}, {5}). A corresponding feasible schedule with C q max = 24 and L max = 0 (i.e.…”

Section: Problem Formulationmentioning

confidence: 99%

Tabu search and lower bounds for a combined production–transportation problem

Condotta

Knust

Meier

et al. 2013

Computers & Operations Research

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In this paper we consider a combined production-transportation problem, where n jobs have to be processed on a single machine at a production site before they are delivered to a customer. At the production stage, for each job a release date is given; at the transportation stage, job delivery should be completed not later than a given due date. The transportation is done by m identical vehicles with limited capacity. It takes a constant time to deliver a batch of jobs to the customer. The objective is to find a feasible schedule minimizing the maximum lateness.After formulating the considered problem as a mixed integer linear program, we propose different methods to calculate lower bounds. Then we describe a tabu search algorithm which enumerates promising partial solutions for the production stage. Each partial solution is complemented with an optimal transportation schedule (calculated in polynomial time) achieving a coordinated solution to the combined productiontransportation problem. Finally, we present results of computational experiments on randomly generated data.

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“…an upper bound computed by a fast queuing algorithm, or greedy algorithm (Carlier and Pinson, 1989). The TBON graph remains applicable if this bound can still be assumed as an absolute "limit" (any lateness is forbidden).…”

Section: The Tbon Graphmentioning

confidence: 99%

Modelling and managing disjunctions in scheduling problems

1995

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__________________________________________________________________________In this paper we present a method for modeling and managing various constraints encountered in task scheduling problems. Our approach aims at characterizing feasible schedules through the analysis of the set of constraints and their interaction, regardless to any optimization criteria. This analysis is achieved by a constraint propagation process on a constraint graph and produces both restricted domains for the decision variables and an updated formulation of the initial constraints. The graphs usually used to model temporal constraints seem to be limited because they only allow the representation of strict precedence relations between two tasks. In order to model a larger variety of temporal constraints, particularly any constraint that connects two events (start-or finish-time of a task), we propose a model called a Time-Bound-On-Node graph in which each task is featured by two nodes. Then it becomes possible to handle constraints on task durations, due for example to flexibilities in resource utilization. This kind of graph is not new and has already been investigated in related works on project planning and constraint satisfaction problems. But its processing and interpretation deserved to be developed, particularly for our purpose, which is the search for the necessary conditions of feasibility. With respect to conjunctive temporal constraints, the analysis is achieved with a polynomial algorithm based on the longest path search on a conjunctive TBON graph, yielding the necessary and sufficient conditions of feasibility. Taking account of resource constraints leads to defining disjunctive constraints. To this end, disjunctive sets of arcs are introduced, making the TBON graph non conjunctive. In this case, a complete characterization of feasibility cannot reasonably be faced, due to the combinatorial feature. Nevertheless, a polynomial algorithm that applies reduction and deletion rules on the non conjunctive part of the graph is proposed to restart new propagations on the conjunctive part until all deductions have been made.

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An Algorithm for Solving the Job-Shop Problem

Cited by 645 publications

References 13 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

Tabu search and lower bounds for a combined production–transportation problem

Modelling and managing disjunctions in scheduling problems

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