Scheduling a maintenance activity and due-window assignment on a single machine

Mosheiov, Gur; Sarig, Assaf

doi:10.1016/j.cor.2008.10.007

Cited by 75 publications

(34 citation statements)

References 8 publications

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“…Under the condition 0 < λ j ≤ 1, Gordon and Tarasevich (2009) consider several properties of problem 1|RMA, CON| n j =1 (αE j + βT j + γ d) which in some cases can reduce the complexity of the problem to either O(n 2 ) or O(n 3 l), where l ≤ n − n(β − γ )/(α + β) . Mosheiov and Sarig (2009) extend the results on common due date assignment to the case where all the jobs have to be assigned a common due window with the starting time d and size D. The objective is to determine the job schedule, the time to schedule the rate modifying activity, the starting time and the length of the due window such that the following objective function is minimized: n j =1 (αE j + βT j + γ d + δD). It is shown that an optimal schedule exists in which d coincides with the completion time of the job in position k = n(δ − γ )/α , the due window finishing time coincides with the completion time of the job in position k + m = n(β − γ )/β and one of the following cases holds: (i) the maintenance activity starts at time zero, (ii) the maintenance activity is not performed at all, or (iii) the maintenance activity is scheduled after the finishing time of the due window and immediately prior to the starting time of one of the jobs, say, the job in position l > k + m. Thus, the relevant values of l are l = k + m + 1, .…”

Section: Maintenance Activitymentioning

confidence: 99%

Scheduling with due date assignment under special conditions on job processing

Gordon¹,

Strusevich

Dolgui

2011

J Sched

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International audienceWe review the results on scheduling with due date assignment under such conditions on job processing as given precedence constraints, maintenance activity or various scenarios of processing time changing. The due date assignment and scheduling problems arise in production planning when the management is faced with setting realistic due dates for a number of jobs. Most research on scheduling with due date assignment is focused on optimal sequencing of independent jobs. However, it is often found in practice that some products are manufactured in a certain order implied, for example, by technological, marketing or assembly requirements and this can be modeled by imposing precedence constraints on the set of jobs. In classical deterministic scheduling models, the processing conditions, including job processing times, are usually viewed as given constants. In many real-life situations, however, the processing conditions may vary over time, thereby affecting actual durations of jobs. In the models with controllable processing times, the scheduler can speed up job execution times by allocating some additional resources to the jobs. In the models with deterioration or learning, the actual processing time can depend either on the position or on the start time of a job in the schedule. In scheduling with deterioration, the later a job starts, the longer it takes to process, while in scheduling with learning, the actual processing time of a job gets shorter, provided that the job is scheduled later. We consider also scheduling models with optional maintenance activity. In manufacturing processing, production scheduling with preventive maintenance planning is one of the most significant methods in preventing the machinery from failure or wear

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Section: Maintenance Activitymentioning

confidence: 99%

Scheduling with due date assignment under special conditions on job processing

Gordon¹,

Strusevich

Dolgui

2011

J Sched

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“…However, after the activity, the machine becomes more efficient, which is reflected in the new shortened job processing times. Mosheiov and Sarig (2009b) …”

Section: Other Modelsmentioning

confidence: 99%

“…One part is a decreasing start-time dependent function and the other part is an increasing position-dependent function. The maintenance activity (ma) is defined as in the work of Mosheiov and Sarig (2009b). An O(n 2 log n) time optimal solution algorithm was provided.…”

Section: Other Modelsmentioning

confidence: 99%

“…They showed that the problem is polynomially solvable by an O(n log n) time algorithm. Mosheiov and Sarig (2009b) introduced some maintenance activities to scheduling problems with a common due window assignment. A maintenance activity is an optional activity that requires a fixed time interval during which the production is stopped, as the machine is turned off.…”

Section: Other Modelsmentioning

confidence: 99%

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Scheduling problems with a common due window assignment: A survey

Janiak¹,

Kwiatkowski²,

Lichtenstein³

2013

International Journal of Applied Mathematics and Computer Science

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In this article a survey of studies on scheduling problems with a common due window assignment and earliness/tardiness penalty functions is presented. A due window is a generalization of the classical due date and describes a time interval in which a job should be finished. If a job is completed before or after the due window, it incurs an earliness or a tardiness penalty, respectively. In this survey we separately analyse the classical models with job-independent and job-dependent earliness/tardiness penalty functions and some other more complicated models. We describe the computational complexity of the problems and the main features of the approaches developed to solve them. Particular attention is paid to practical applications of the analysed models. As turns out, some complicated models combining classical scheduling problems with, e.g., learning and aging effects have no reasonable practical justification in the literature.

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“…Contrarily, a job will get a tardiness penalty when it is finished after its due date because it violates the contractual obligation with the customer. For extensive surveys related to scheduling problems with the job completion time due window, reader can refer to the papers [15][16][17][18][19]. In this paper, we set the upper bound for the actual processing time of each job.…”

Section: Introductionmentioning

confidence: 99%

Single-Machine Scheduling with Upper Bounded Maintenance Time under the Deteriorating Effect

Xue

Zhang

2013

Discrete Dynamics in Nature and Society

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We consider a single-machine scheduling problem with upper bounded actual processing time and upper bounded maintenance time under deteriorating effect. The actual processing time of a job is a position-dependent power function. If the actual processing time of a job exceeds the upper bound, tardiness penalty of the job should be paid. And if the maintenance time exceeds the corresponding upper bound, tardiness penalty of the maintenance should also be paid. The maintenance duration studied in the paper is a position-dependent exponential function. The objective is to find jointly the optimal maintenance frequency and the optimal job sequence to minimize the total cost, which is a linear function of the makespan and the total tardiness. We show that the studied scheduling problem can be transformed as a classic assignment problem to solve. There is also shown that a special case of the scheduling problem can be optimally solved by a lower order algorithm.

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Scheduling a maintenance activity and due-window assignment on a single machine

Cited by 75 publications

References 8 publications

Scheduling with due date assignment under special conditions on job processing

Scheduling with due date assignment under special conditions on job processing

Scheduling problems with a common due window assignment: A survey

Single-Machine Scheduling with Upper Bounded Maintenance Time under the Deteriorating Effect

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