A bi-objective branch-and-bound algorithm for the unit-time job shop scheduling : A mixed graph coloring approach

•A bi-objective unit-time job shop scheduling is modeled as a mixed graph coloring.•A new branch-and-bound and an epsilon-constraint algorithms address bi-objective mixed graph coloring.•A new lower bound is proposed for the sum of path-endpoints coloring.•The lower bound improves considerably upon...

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Bibliographic Details
Published in:Computers & operations research Vol. 132; p. 105319
Main Authors: KOUIDER, Ahmed, AIT HADDADÈNE, Hacène
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.08.2021
Pergamon Press Inc
Subjects:
[formula omitted]-constraint
Algorithms
Benchmarks
Bi-objective branch-and-bound
Completion time
Graph coloring
Job shop scheduling
Job shops
Lower bounds
Mixed graph coloring
Multiobjective optimization
Operations research
Optimization
Performance measurement
Scheduling
constraint
Scheduling
Bi-objective branch-and-bound
Multiobjective optimization
Mixed graph coloring
ISSN:0305-0548, 0305-0548
Online Access:Get full text
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Summary:•A bi-objective unit-time job shop scheduling is modeled as a mixed graph coloring.•A new branch-and-bound and an epsilon-constraint algorithms address bi-objective mixed graph coloring.•A new lower bound is proposed for the sum of path-endpoints coloring.•The lower bound improves considerably upon the known lower bound from the literature.•The branch-and-bound method is faster and more efficient than the epsilon-constraint method. A bi-objective branch-and-bound and an ∊-constraint algorithms are proposed for the unit-time job shop scheduling problem. These two objectives are the minimization of the makespan and the total completion time. We model this problem as a bi-objective mixed graph coloring using both the chromatic number and the sum of path-endpoints coloring (i.e. sum of the colors assigned to the endpoints of maximal paths) to determine the optimal set of the non-dominated solutions. A new lower bound is also constructed for the sum of path-endpoints coloring which is used alongside an existing lower bound from the literature on two bounding procedures. Computational experiments on benchmark data sets show that the proposed lower bound improves considerably upon the known lower bound from the literature. Besides, our algorithms are found to find an optimal set of non-dominated solutions for most of the tested benchmarks within a reasonable amount of CPU time. In addition, two interesting performance metrics are introduced to compare and assess the effectiveness and the efficiency of our algorithms.
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ISSN:0305-0548
0305-0548
DOI:10.1016/j.cor.2021.105319