Maximization of solution flexibility for robust shop scheduling

Artigues, Christian; Billaut, Jean‐Charles; Esswein, Carl

doi:10.1016/j.ejor.2004.04.004

Cited by 61 publications

(76 citation statements)

References 6 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%

“…Another class of related work in the context of flexibility generation for online scheduling is linked to the concept of groups of permutable operations [5,6], also called ordered group assignment [3,12]. A group of permutable operations is a restriction of the sequential flexibility considered here in such a way that each operation is assigned to a group and, there is a complete order between the groups of operations performed on the same machine.…”

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%

“…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. This method is based on longest path computations in a so-called worst-case graph, derived from the considered ordered group assignment.…”

Section: Literature Reviewmentioning

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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