Maximization Problems in Single Machine Scheduling

Aloulou, Mohamed Ali; Kovalyov, Mikhail Y.; Portmann, Marie-Claude

doi:10.1023/b:anor.0000030679.25466.02

Cited by 13 publications

(23 citation statements)

References 14 publications

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“…These results generalize some results previously established for the single machine version of this problem [1].…”

Section: Introductionsupporting

confidence: 90%

“…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: 68%

“…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%

“…Several works have aleady been proposed in this domain. In particular, Aloulou, Kovalyov and Portmann [1] adapt the traditional three-field notation α|β|γ to this class of problems.…”

Section: Literature Reviewmentioning

confidence: 99%

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Worst-Case Evaluation of Flexible Solutions in Disjunctive Scheduling Problems

Aloulou

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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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“…These results generalize some results previously established for the single machine version of this problem [1].…”

Section: Introductionsupporting

confidence: 90%

Section: Introductionmentioning

confidence: 68%

Section: Problem Settingmentioning

confidence: 99%

Section: Problem Settingmentioning

confidence: 99%

“…Several works have aleady been proposed in this domain. In particular, Aloulou, Kovalyov and Portmann [1] adapt the traditional three-field notation α|β|γ to this class of problems.…”

Section: Literature Reviewmentioning

confidence: 99%

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