Two-machine shop scheduling: Compromise between flexibility and makespan value

Esswein, Carl; Billaut, Jean‐Charles; Strusevich, Vitaly A.

doi:10.1016/j.ejor.2004.01.029

Cited by 21 publications

(18 citation statements)

References 15 publications

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“…We show that the problem of computing the worse completion time of an operation in all feasible semi-active schedules can be done by finding an elementary longest path in the disjunctive graph representing the problem with additional constraints. This gives a general framework integrating previous studies [1,3,5,6,7,12].…”

Section: Introductionmentioning

confidence: 99%

“…All objective functions are the completion times of the activities. Let us consider additional precedence constraints {(1, 3), (1,5), (1, 7), (3,7), (2,4), (2,6), (6,8)}. We obtain the disjunctive graph G displayed in Figure 1.…”

Section: Problem Settingmentioning

confidence: 99%

“…We obtain the 6 schedules displayed in Figure 2. Note that such restriction cannot be modeled by the group of permutable operation representation used in [1,5,6,7,12]. The solution of problem SP is 20 which is the worst-case makespan value of the 6 semi-active schedules.…”

Section: Problem Settingmentioning

confidence: 99%

“…There are no precedence constraints between the operations of the same group. Heuristics have been designed to generate groups of permutable operations for general disjunctive problems [5,6] and multiobjective methods have been designed to find a compromise between flexibility and performance in the two-machine flowshop [7]. Artigues et al [3] propose a polynomial algorithm to perform the exact worst-case evaluation of an ordered group assignment.…”

Section: Literature Reviewmentioning

confidence: 99%

“…This paper addresses the problem of providing more flexibility than the classical temporal one in disjunctive scheduling problems where the objective is to minimize a regular minmax objective function. As already considered in previous studies [2,3,5,6,7,12], this can be achieved by defining only a partial order of the operations on each machine, leaving to the end-user the possibility to make the remaining sequencing decisions. This is the principle of the groups of permutable operations model that has been studied by several authors [3,5,6,7,12].…”

Section: Introductionmentioning

confidence: 99%

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Computational Science and Its Applications – ICCSA 2007

2007

Lecture Notes in Computer Science

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Abstract. In this paper, we consider the problem of evaluating the worst case performance of flexible solutions in non-preemptive disjunctive scheduling. A flexible solution represents a set of semi-active schedules and is characterized by a partial order on each machine. A flexible solution can be used on-line to absorb the impact of some data disturbances related for example to job arrival, tool availability and machine breakdowns. Providing a flexible solution is useful in practice only if it can be assorted with an evaluation of the complete schedules that can be obtained by extension. For this purpose, we suggest to use only the best case and the worst case performance. The best case performance is an ideal performance that can be achieved only if the on-line conditions allow to implement the best schedule among the set of schedules characterized by the flexible solution. In contrast, the worst case performance indicates how poorly the flexible solution may perform. These performances can be obtained by solving corresponding minimization and maximization problems. We focus here on maximization problems when a regular minmax objective function is considered. In this case, the worse objective function value can be determined by computing the worse completion time of each operation separately. We show that this problem can be solved by finding an elementary longest path in the disjunctive graph representing the problem with additional constraints. In the special case of the flow-shop problem with release dates and additional precedence constraints, we give a polynomial algorithm that determines the worst case performance of a flexible solution.

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Section: Introductionmentioning

confidence: 99%

Section: Problem Settingmentioning

confidence: 99%

Section: Problem Settingmentioning

confidence: 99%

Section: Literature Reviewmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Computational Science and Its Applications – ICCSA 2007

2007

Lecture Notes in Computer Science

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Scheduling Operation Groups: A Multicriteria Approach to Provide Sequential Flexibility

Esswein¹,

Billaut²,

Artigues³

2008

Flexibility and Robustness in Scheduling

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Robust Machine Scheduling Based on Group of Permutable Jobs

Artigues

Billaut

Cheref

et al. 2016

International Series in Operations Research &Amp; Management Science

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This chapter presents the "group of permutable jobs" structure to represent set of solutions to disjunctive scheduling problems. Traditionally, solutions to disjunctive scheduling problems are represented by assigning sequence of jobs to each machine. The group of permutable jobs structure assigns an ordered partition of jobs to each machine, i.e. a group sequence. The permutation of jobs inside a group must be all feasible with respect to the problem constraints. Such a structure provides more flexibility to the end user and, in particular, allows a better reaction to unexpected events. The chapter considers the robust scheduling framework where uncertainty is modeled via a discrete set of scenarios, each scenario specifying the problem parameters values. The chapter reviews the models and algorithms that have been proposed in the literature for evaluating a group sequence with respect to scheduling objectives for a fixed scenario as well as the recoverable robust optimization methods that have been proposed for generating robust group sequence5) M 2 (4) 7 0 2 4 Fig. 9.9: Gantt representation of a group sequence for the single machine problem Example 2: Job Shop EnvironmentIn Fig. 9.10, two groups of permutable operations are proposed. The first one is composed by the operations of J 1 and J 3 performed on the first machine. The second is composed of the operations of the same jobs on the third machine. One can see that whatever the order of the operations inside each group, the sequence remains feasible. Of course, this flexibility has a price since the makespan is now equal to 32.

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Two-machine shop scheduling: Compromise between flexibility and makespan value

Cited by 21 publications

References 15 publications

Computational Science and Its Applications – ICCSA 2007

Computational Science and Its Applications – ICCSA 2007

Scheduling Operation Groups: A Multicriteria Approach to Provide Sequential Flexibility

Robust Machine Scheduling Based on Group of Permutable Jobs

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