Machine scheduling with an availability constraint

Lee, Chung Yee

doi:10.1007/bf00121681

Cited by 358 publications

(232 citation statements)

References 14 publications

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“…Lee [2] also showed that if the Moore and Hodgson algorithm was used for solving the problem 1, ℎ 1 || ∑ , the inequality ( ) ≤ * ( ) + 1 would always be true, in which ( ) denotes the number of tardy jobs obtained by the Moore and Hodgson algorithm and * ( ) denotes the optimal number of tardy jobs.…”

Section: Theorems Of the Problemmentioning

confidence: 99%

“…Go to Step 2. It is necessary to note that Lee [2] did not propose any procedure to solve the problem optimally. From the above considerations, we can conclude the following corollary.…”

Section: Theorems Of the Problemmentioning

confidence: 99%

“…On the other hand, it can be assumed that the ready times for all the jobs in 2 are equal to 2 , which entails that determining the optimal job sequence in this set is similar to minimizing the number of tardy jobs in a single machine with ready times equal to 2 for all jobs. Therefore, the number of tardy jobs in 2 Proof. Clearly, in the problem 1, ℎ 1 || ∑ , the total completion time of all jobs is not less than ∑ =1 + ( 2 − 1 ).…”

Section: Theorems Of the Problemmentioning

confidence: 99%

“…Lee [2] showed that the SPT rule, the EDD rule, and the Moore and Hodgson algorithm [3] minimize the targets of sum of completion times, maximum lateness, and the number of tardy jobs, respectively, in the single machine problem with a fixed nonavailability interval and resumable jobs. He also proved that the problem 1, ℎ 1 |pmtn| ∑ =1…”

Section: Introductionmentioning

confidence: 99%

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Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

Molaee

Moslehi

2014

Journal of Industrial Engineering

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Most scheduling problems are based on the assumption that machines work continuously during the planning horizon. This assumption is not true in many production environments because the machine may not be available during one or more periods such as during breakdowns or maintenance operations. In this paper, the problem of the single machine scheduling with one unavailability period and nonresumable jobs with the aim of minimizing the number of tardy jobs is studied. A number of theorems are proved and a heuristic procedure is developed to solve the problem. A branch-and-bound approach is also presented which includes upper and lower bounds and efficient dominance rules. Computational results for 2680 problem instances show that the branch-and-bound approach is capable of solving 98.7% of the instances optimally, bearing witness to the efficiency of the proposed procedure. Our results also indicate that the proposed approaches are more efficient when compared to other methods.

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Section: Theorems Of the Problemmentioning

confidence: 99%

“…Go to Step 2. It is necessary to note that Lee [2] did not propose any procedure to solve the problem optimally. From the above considerations, we can conclude the following corollary.…”

Section: Theorems Of the Problemmentioning

confidence: 99%

Section: Theorems Of the Problemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

Molaee

Moslehi

2014

Journal of Industrial Engineering

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“…Lee [12] studies the deterministic machine availability constraint problem with di erent performance measures, including makespan, total weighted completion time, maximum lateness and number of tardy jobs, for single machine and parallel machines situations. In each case, he either provides a polynomial exact algorithm to solve the problem, or proves that the problem is NP-hard.…”

Section: Problem Statementmentioning

confidence: 99%

Match-up scheduling under a machine breakdown

Aktürk

Gorgulu

1999

European Journal of Operational Research

115

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When a machine breakdown forces a modi®ed¯ow shop (MFS) out of the prescribed state, the proposed strategy reschedules part of the initial schedule to match up with the preschedule at some point. The objective is to create a new schedule that is consistent with the other production planning decisions like material¯ow, tooling and purchasing by utilizing the time critical decision making concept. We propose a new rescheduling strategy and a match-up point determination procedure through a feedback mechanism to increase both the schedule quality and stability. The proposed approach is compared with alternative reactive scheduling methods under di erent experimental settings. Ó

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A new tabu search procedure for an audit‐scheduling problem

Brucker

Schumacher

1999

J. Sched.

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We consider the following version of the auditing problem. A set of jobs must be processed by auditors A , . . . , A K . Each job consists of several tasks and there may be precedence constraints between these tasks. There is a due date associated with each job. Each auditor is available during disjoint time periods. Furthermore, s/he has a minimal and maximal working time. If task i is assigned to an auditor A H , the processing time is p GH and the processing costs are c GH . A task assigned to auditor A H can be preempted only at the end of one of the working periods of A H . In this case it must be continued at the beginning of the next period.One has to assign the tasks to the auditors and "nd a feasible schedule for the assigned tasks for each auditor such that the sum of the assignment costs and a weighted sum of tardiness values is minimized.A tabu search procedure for this problem is described and computational results are presented.KEY WORDS: audit scheduling; tabu search; time windows 4. the precedence constraints are not violated, and 5. tasks of J J do not start before r J .Given a schedule (for all auditors), the "nishing time C J of J J is the latest "nishing time of all tasks of J J . Our objective is to assign each task i to an auditor A ? G and to construct a feasible schedule such that the sum of mismatching costs and weighted sum of tardiness ¹ J "max +0, C J !d J ,, i.e.

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Machine scheduling with an availability constraint

Cited by 358 publications

References 14 publications

Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

Minimizing the Number of Tardy Jobs on a Single Machine with an Availability Constraint

Match-up scheduling under a machine breakdown

A new tabu search procedure for an audit‐scheduling problem

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