A note on scheduling on a single processor with speed dependent on a number of executed jobs

Gawiejnowicz, Stanisław

doi:10.1016/0020-0190(96)00021-x

Cited by 78 publications

(25 citation statements)

References 7 publications

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“…Although the researchers have found a method to determine the batch sizes, they have not considered on how to schedule the resulting batches on a machine. Gaweijnowics (1996) and Biskup (1999) are pioneers who discuss job scheduling problems on a machine by considering the learning effect. They assume that job processing time is not a constant value.…”

Section: Introductionmentioning

confidence: 99%

“…Gaweijnowics (1996) discusses a single-machine scheduling problem to minimize makespan and shows that the optimal schedule should be obtained by scheduling jobs in accordance with the Shortest Processing Time (SPT) rule. In the meantime, Biskup (1999) proves the polynomial solutions for similar problems to that of Gaweijnowics (1996) for two objectives, i.e. minimizing the interval time between completion times of jobs and their common due date, and minimizing the sum of flow times.…”

Section: Introductionmentioning

confidence: 99%

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Integer batch scheduling problems for a single-machine with simultaneous effect of learning and forgetting to minimize total actual flow time

Yusriski¹,

Sukoyo²,

Samadhi³

et al. 2015

10.5267/j.ijiec

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This research discusses an integer batch scheduling problems for a single-machine with positiondependent batch processing time due to the simultaneous effect of learning and forgetting. The decision variables are the number of batches, batch sizes, and the sequence of the resulting batches. The objective is to minimize total actual flow time, defined as total interval time between the arrival times of parts in all respective batches and their common due date. There are two proposed algorithms to solve the problems. The first is developed by using the Integer Composition method, and it produces an optimal solution. Since the problems can be solved by the first algorithm in a worst-case time complexity O(n2 n-1 ), this research proposes the second algorithm. It is a heuristic algorithm based on the Lagrange Relaxation method. Numerical experiments show that the heuristic algorithm gives outstanding results.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Integer batch scheduling problems for a single-machine with simultaneous effect of learning and forgetting to minimize total actual flow time

Yusriski¹,

Sukoyo²,

Samadhi³

et al. 2015

10.5267/j.ijiec

View full text Add to dashboard Cite

show abstract

“…The matching algorithm requires O(n log n) time. This algorithm is quite well-known and has become a popular technique for solving scheduling problems in this area; see, e.g., [29], [30], [31] and [32]. Also, see a survey [2], which demonstrates that many scheduling problems can be solved by the matching algorithm, but instead less suitable approaches were used in earlier papers.…”

Section: The Solution Approachmentioning

confidence: 99%

Combining time and position dependent effects on a single machine subject to rate-modifying activities

Rustogi

Strusevich

2014

Omega

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Citation for this version held on GALA:Rustogi, Kabir and Strusevich, Vitaly (2014) Combining time and position dependent effects on a single machine subject to rate-modifying activities. London: Greenwich Academic Literature Archive. We introduce a general model for single machine scheduling problems, in which the actual processing times of jobs are subject to a combination of positional and timedependent effects, that are job-independent but additionally depend on certain activities that modify the processing rate of the machine, such as, e.g., maintenance. We focus on minimizing two classical objectives: the makespan and the sum of the completion times. The traditional classification accepted in this area of scheduling is based on the distinction between the learning and deterioration effects, on one hand, and between the positional effects and the start-time dependent effects, on the other hand. Our results show that in the framework of the introduced model such a classification is not necessary, as long as the effects are job-independent. The model introduced in this paper covers most previously known models. The solution algorithms are developed within the same general framework and their running times are no worse than those available earlier for problems with less general effects.

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“…Gawiejnowicz [10] is the first time to introduce the position dependent on a number of executed jobs on a single processor. Biskup [11] is the first to consider the learning effect in a scheduling problem.…”

Section: Introductionmentioning

confidence: 99%

Maximum Lateness Scheduling on Two-Person Cooperative Games with Variable Processing Times and Common Due Date

Liu

Wang

2017

Journal of Optimization

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A new maximum lateness scheduling model in which both cooperative games and variable processing times exist simultaneously is considered in this paper. The job variable processing time is described by an increasing or a decreasing function dependent on the position of a job in the sequence. Two persons have to cooperate in order to process a set of jobs. Each of them has a single machine and their processing cost is defined as the minimum value of maximum lateness. All jobs have a common due date. The objective is to maximize the multiplication of their rational positive cooperative profits. A division of those jobs should be negotiated to yield a reasonable cooperative profit allocation scheme acceptable to them. We propose the sufficient and necessary conditions for the problems to have positive integer solution.

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A note on scheduling on a single processor with speed dependent on a number of executed jobs

Cited by 78 publications

References 7 publications

Integer batch scheduling problems for a single-machine with simultaneous effect of learning and forgetting to minimize total actual flow time

Integer batch scheduling problems for a single-machine with simultaneous effect of learning and forgetting to minimize total actual flow time

Combining time and position dependent effects on a single machine subject to rate-modifying activities

Maximum Lateness Scheduling on Two-Person Cooperative Games with Variable Processing Times and Common Due Date

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