Mixed graph colouring for unit-time scheduling

We consider the job shop scheduling problem with unit-time operations and the makespan criterion. This problem is reduced to finding an optimal colouring of a special class of mixed graph, where its partial graph without edges represents the union of maximal directed paths and its partial graph with...

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Bibliographic Details
Published in:International journal of production research 2017-03, Vol.55 (6), p.1720-1729
Main Authors: Kouider, Ahmed, Ait Haddadène, Hacène, Ourari, Samia, Oulamara, Ammar
Format: Article
Language:English
Subjects:
Computational efficiency
Computer Science
Computing time
Criteria
Graph coloring
Graphs
Job shop scheduling
Job shops
Linear programming
lower and upper bounds
Mathematical models
mixed graph colouring
mixed integer linear programming
Operations Research
Production scheduling
Scheduling
tabu search
Unions
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Summary:We consider the job shop scheduling problem with unit-time operations and the makespan criterion. This problem is reduced to finding an optimal colouring of a special class of mixed graph, where its partial graph without edges represents the union of maximal directed paths and its partial graph without arcs represents the union of maximal cliques. As the problem is known to be NP-hard, both exact and heuristic methods are proposed to solve it. This study is carried out in three steps. First, a new lower and upper bounds for the mixed chromatic number are proposed. Afterwards, a colour-indexed mathematical model using the proposed bounds is developed. Then, a tabu search using a dynamic neighbourhood structure is adapted for solving large instances. Computational experiments conducted on several modified benchmarks show the efficiency and effectiveness of the proposed resolution methods.
ISSN:0020-7543
1366-588X
DOI:10.1080/00207543.2016.1224950