Scheduling with Time-Changing Effects and Rate-Modifying Activities

Strusevich, Vitaly A.; Rustogi, Kabir

doi:10.1007/978-3-319-39574-6

Cited by 37 publications

(26 citation statements)

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“…Time-changing effects are represented by explicit formulae for how the actual processing time of a job is affected. There are three main types of so-called pure effects studied in the literature, which in accordance with the recent monograph Strusevich and Rustogi (2017) can be informally classified as follows:…”

Section: Introductionmentioning

confidence: 92%

“…We start with a brief review of the results on problem 1| p j (r ) = p j g(r )| . A systematic exposition of the relevant material is contained in Chapter 7 of the monograph Strusevich and Rustogi (2017). Then, we focus on problem 1| p j (r ) = p j g(r )| C j , which under an arbitrary deterioration effect does not admit solution by a priority rule.…”

Section: Pure Positional Effects: Algorithms and V-shapenessmentioning

confidence: 99%

“…C j under an exponential positional deterioration effect (15) is solvable by the LPT rule if γ ≥ 2, while no priority rule solution exists for this problem if 1 < γ < 2. For problem 1| p j (r ) = p j g(r )| C j under a polynomial deterioration effect given by (14), the conditions on A that guarantee that the problem can be solved either by the SPT rule or by the LPT rule are given in Chapter 7.2.2 of the monograph Strusevich and Rustogi (2017).…”

Section: Algorithm Matchmentioning

confidence: 99%

“…The results presented in Strusevich and Rustogi (2017) are summarized in Table 3, including their implication for a polynomial cumulative effect (26). Here, in the second column, we use symbols and to indicate whether the sequence g(r ), 1 ≤ r ≤ n, is non-decreasing or non-increasing, respectively.…”

Section: Pure and Combined Cumulative Effects: Review And V-shapenessmentioning

confidence: 99%

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Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

Soper

Strusevich

2019

J Sched

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We address single-machine scheduling problems for which the actual processing times of jobs are subject to various effects, including a positional effect, a cumulative effect and their combination. We review the known results on the problems to minimize the makespan, the sum of the completion times and their combinations and identify the problems for which an optimal sequence cannot be found by simple priority rules such as Shortest Processing Time (SPT) and/or Longest Processing Time (LPT). Typically, these are problems to minimize the sum of the completion times under a deterioration effect, and we verify under which conditions for these problems an optimal permutation is V-shaped (an LPT subsequence followed by an SPT subsequence). We demonstrate that previously used techniques for proving that an optimal sequence is V-shaped are not properly justified. We use the corrected method to describe a wide range of problems with a pure positional effect and a combination of a cumulative effect with a positional effect for which an optimal sequence is V-shaped. On the other hand, we show that even the refined approach has its limitations.

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Section: Introductionmentioning

confidence: 92%

Section: Pure Positional Effects: Algorithms and V-shapenessmentioning

confidence: 99%

Section: Algorithm Matchmentioning

confidence: 99%

Section: Pure and Combined Cumulative Effects: Review And V-shapenessmentioning

confidence: 99%

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Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

Soper

Strusevich

2019

J Sched

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“…Gawiejnowicz and Kononov [10] considered the general properties of scheduling with fixed job processing time and scheduling with job processing time as proportional linear functions of the job starting time. The relevant research includes [11][12][13][14][15][16][17][18], among many others. Recently, some works have been published about online algorithms for linear deteriorating jobs [19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families

Wang

Chai

et al. 2020

Mathematics

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We considered the online scheduling problem of simple linear deteriorating job families on m parallel batch machines to minimize the makespan, where the batch capacity is unbounded. In this paper, simple linear deteriorating jobs mean that the actual processing time p j of job J j is assumed to be a linear function of its starting time s j , i.e., p j = α j s j , where α j > 0 is the deterioration rate. Job families mean that one job must belong to some job family, and jobs of different families cannot be processed in the same batch. When m = 1 , we provide the best possible online algorithm with the competitive ratio of ( 1 + α max ) f , where f is the number of job families and α max is the maximum deterioration rate of all jobs. When m ≥ 1 and m = f , we provide the best possible online algorithm with the competitive ratio of 1 + α max .

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Preemptive Scheduling of Jobs with a Learning Effect on Two Parallel Machines

Żurowski

2018

Operations Research Proceedings

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Scheduling with Time-Changing Effects and Rate-Modifying Activities

Cited by 37 publications

References 0 publications

Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

Refined conditions for V-shaped optimal sequencing on a single machine to minimize total completion time under combined effects

Online Batch Scheduling of Simple Linear Deteriorating Jobs with Incompatible Families

Preemptive Scheduling of Jobs with a Learning Effect on Two Parallel Machines

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