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Journal Article•DOI•

A branch and bound algorithm to minimize completion time variance on a single processor

G. Viswanathkumar1, Geetha Srinivasan1•
Indian Institute of Technology Madras1
01 Jul 2003-Computers & Operations Research (Elsevier Science Ltd.)-Vol. 30, Iss: 8, pp 1135-1150
TL;DR: A branch and bound algorithm is presented and the same algorithm is extended to generate epsilon optimal solutions for large sized problems (i.e., number of jobs > 30) and results of simulated annealing are compared.
About: This article is published in Computers & Operations Research.The article was published on 2003-07-01. It has received 37 citations till now. The article focuses on the topics: Branch and bound & Branch and cut.
Citations
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Journal Article•DOI•
Minimizing makespan subject to minimum total absolute deviation of completion time on identical parallel machines

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Ling-Huey Su1, Fuh-Der Chou, James C. Chen2•
Chung Yuan Christian University1, National Taiwan University of Science and Technology2
18 Sep 2012-Engineering Optimization
TL;DR: In this article, an identical parallel machine scheduling problem with the objective of minimizing makespan subject to minimum total absolute deviation of job completion time (TADC) is addressed, and an iterative procedure based on a polynomial binary integer programming model is proposed to minimize makespan.
Abstract: This study addresses the identical parallel machine scheduling problem with the objective of minimizing makespan subject to minimum total absolute deviation of job completion time (TADC) An optimization algorithm is first proposed to solve TADC on an identical parallel machine and an iterative procedure based on a polynomial binary integer programming model is then proposed to minimize makespan Computational experiments show that the proposed algorithm is efficient The worst case performance, which refers to the largest average execution for each scenario of the experiments, is 22910 seconds for the problem with n=200, m=30 and p j from a uniform [1, 100]

3 citations

Cites background from "A branch and bound algorithm to min..."

  • ...…such as the V-shaped property can be transferred between TADC and CTV. Recent articles that have addressed scheduling problems with CTV include Srirangacharyulu and Srinivasan (2010), Viswanathkumar and Srinivasan (2003), Ng et al. (1996), Nessah and Chu (2010), De et al. (1992) and Cai (1996)....

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Journal Article•
Batch scheduled admission control for computer and network systems

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Nong Ye1, Toni Farley1, Xueping Li1, Harish Bashettihalli1•
Arizona State University1
01 Oct 2005-Information-Knowledge-Systems Management archive
TL;DR: A Batch Scheduled Admission Control BSAC method to help provide predictability in job waiting time for high priority jobs by changing the dynamic job arriving problem into a static problem which allows the introduction of job scheduling techniques that require a static set of jobs to operate on for stabilizing their waiting time.
Abstract: An increasing number of business transactions, mission-critical operations and many other activities rely on the services of computer and network systems, and the dependability of those services. However, many computer and network systems do not currently provide adequate service dependability. Such systems place no admission control on service requests jobs, leading to variability and thus unpredictability in job waiting times which have a negative impact on service dependability. This paper presents a Batch Scheduled Admission Control BSAC method to help provide predictability in job waiting time for high priority jobs. With this method, we change the dynamic job arriving problem into a static problem which allows the introduction of job scheduling techniques that require a static set of jobs to operate on for stabilizing their waiting time. We illustrate how our method can be employed through examples and experiments that compare the performance of our method with that of no admission control. The results under our test cases show that our method improves the variance of job waiting times, and in some cases with little sacrifice to the mean of job waiting times.

3 citations

Minimizing Class-based Completion Time Variance on a Single Machine

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Xueping Li1, Yuerong Chen, Yang Sun, Rapinder Sawhney•
University of Tennessee1
01 Jan 2007
TL;DR: It is proved that a CB-CTV problem can be transformed into a series of CTV minimization problems, which allows us to apply the existing well developed properties and scheduling methods of CCTV to the problem of scheduling a set of simultaneously available jobs on a single machine.
Abstract: We consider the problem of scheduling a set of simultaneousl y available jobs on a single machine. The objective is to determine a schedule that minimizes the class-based completion time variance (CB-CTV) of the jobs while reducing the overall CTV is taken as the secondary objective. This non-regular performance measure is closely related to service stability and of practical significance in many areas. We prove that a CB-CTV problem can be transformed into a series of CTV minimization problems, which allows us to apply the existing well developed properties and scheduling methods of CTV. Computational results are presented to show the trade-off between the overall CTV and CB-CTV and indicate that it is desirable to minimize CB-CTV with regard to service stability and consistency from customers' point of view. Keywords ─Completion time variance (CTV), Class-based completion time variance (CB-CTV), Job scheduling, Optimization

2 citations

Cites methods from "A branch and bound algorithm to min..."

  • ...…(De et al., 1992), a genetic algorithm (Gupta et al., 1993), a simulated annealing method (Mittenthal et al., 1993), a tabu search method (Al-Turki et al., 2001), a branch and bound method (Viswanathkumar and Srinivasan, 2003), and an ant-colony optimization algorithm (Gajpal and Rajendran, 2006)....

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Journal Article•DOI•
A branch and price algorithm for single-machine completion time variance

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Shijin Wang1, Ying Lu1•
Tongji University1
01 Sep 2019-Computers & Operations Research
TL;DR: A new time-indexed quadratic programming formulation is proposed, in which the Quadratic terms are further linearized into a mixed integer programming with non-negative continuous variables with Lagrangian relaxation with clusters.

2 citations

Posted Content•
A lower bound for weighted completion time variance

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Rabia Nessah1, Chengbin Chu2•
Lille Catholic University1, École Centrale Paris2
01 Jan 2010-Research Papers in Economics
TL;DR: In this article, a heuristic and a lower bound based on job splitting and the Viswanathkumar and Srinivasan procedure were proposed to minimize the weighted completion time variance.
Abstract: We consider a single machine scheduling problem to minimize the weighted completion time variance. This problem is known to be NP-hard. We propose a heuristic and a lower bound based on job splitting and the Viswanathkumar and Srinivasan procedure. The test on more than 2000 instances shows that this lower bound is very tight and the heuristic yields solutions very close to optimal ones since the gap between the solution given by the heuristic and the lower bound is very small. (This abstract was borrowed from another version of this item.)

2 citations

References
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Journal Article•DOI•
Minimizing Variation of Flow Time in Single Machine Systems

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John J. Kanet1•
University of Georgia1
01 Dec 1981-Management Science
TL;DR: This paper addresses the problem of n jobs to be scheduled on a single machine in such a way that flow time variation is minimized and a heuristic method for scheduling is proposed.
Abstract: This paper addresses the problem of n jobs to be scheduled on a single machine in such a way that flow time variation is minimized. When the measure of variation is total absolute difference of completion times TADC the problem is shown to be quite simple. Sufficient conditions are shown for minimal TADC and a simple method for generating an optimal solution is provided. When the measure of variation is variance of flow time the problem is much more difficult. For this case a heuristic method for scheduling is proposed. The heuristic is simple and provides solutions which compare favorably with others found in the literature.

199 citations

"A branch and bound algorithm to min..." refers background in this paper

  • ...For further references and applications in various contexts, see Kanet [5], Vani and Ragavachari [6], Bagchi et al....

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  • ...For further references and applications in various contexts, see Kanet [5], Vani and Ragavachari [6], Bagchi et al. [7], Gupta et al. [8], Mittenthal et al. [9], Gupta et al. [10], Ventura and Weng [11], Manna and Prasad [12]....

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Journal Article•DOI•
Minimising Waiting Time Variance in the Single Machine Problem

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Samuel Eilon1, I. G. Chowdhury1•
Imperial College London1
01 Feb 1977-Management Science
TL;DR: A heuristic method is proposed for solving the problem where n is large; this method requires very little computing and was found to produce very good results for a sample of problems of varying size.
Abstract: The paper considers the problem of n given jobs to be processed on a single machine where it is desirable to minimise the variance of job waiting times. A theorem is presented to the effect that the optimal sequence must be V-shaped i.e., the jobs must be arranged in descending order of processing times if they are placed before the shortest job, but in ascending order of processing times if placed after it, and an algorithm for determining the optimal solution is given. A heuristic method is proposed for solving the problem where n is large; this method requires very little computing and was found to produce very good results for a sample of problems of varying size. The concept of the “efficient set” is examined and heuristic methods for generating this set are given.

187 citations

Journal Article•DOI•
Variance Minimization in Single Machine Sequencing Problems

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Alan G. Merten, Mervin E. Muller
01 May 1972-Management Science
TL;DR: While the two mean performance measures attain their minimums at the same job sequence, it is shown that the sequence that minimizes the variance of flow-time is antithetical to the sequenceThat minimizesThe variance of waiting-time, and the minimum values of the two variance measures are equal.
Abstract: The variance of flow-time and variance of waiting-time performance measures are analyzed for the single machine sequencing problem. These measures are compared and contrasted to the performance measures of mean flow-time and mean waiting-time. In particular, while the two mean performance measures attain their minimums at the same job sequence, it is shown that the sequence that minimizes the variance of flow-time is antithetical to the sequence that minimizes the variance of waiting-time. However, the minimum values of the two variance measures are equal. Relationships are also derived for the special problems where either all the job processing-times are equal or all the job weights are equal.

169 citations

"A branch and bound algorithm to min..." refers background or methods in this paper

  • ...It can be observed from expressions (3) and (14) that (C[1] − Pa1)(2) + (C[2] − Pa1)(2) + (C[n−1] − Pa1)(2) + (C[n] − Pa1)(2)¿V; (15) where V represents the sum of squared deviations of four completion times from their average Pa and hence it is smaller than the squared deviations about Pa1....

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  • ...where, C[1]; C[2]; C[3]; : : : ; C[n] are the completion times of jobs scheduled in positions 1; 2; 3; : : : ; n in a given partial sequence....

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  • ...Let C∗ [1]; C∗ [2]; C∗ [3]; : : : ; C∗ [n] be the completion times of jobs in positions 1; 2; 3; : : : ; n in the optimal sequence (S∗), and MCT ∗ and CTV ∗ be the mean completion time and completion time variance of the jobs, respectively, in the optimal sequence....

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  • ...The sum of squares of deviations of the six completion times from the average Pa1 is given by V1 = (C[1] − Pa1)(2) + (C[2] − Pa1)(2) + (C[3] − Pa1)(2) + (C[n−2] − Pa1)(2) + (C[n−1] − Pa1)(2) + (C[n] − Pa1)(2); (14)...

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  • ...The objective of variance minimization was introduced by Merten and Muller [1] in 7le organization problems....

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Journal Article•DOI•
On the minimization of completion time variance with a bicriteria extension

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Prabuddha De, Jay B. Ghosh, Charles E. Wells
01 Nov 1992-Operations Research
TL;DR: It is shown that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time and a fully polynomial approximation scheme is proposed.
Abstract: We discuss a single-machine scheduling problem where the objective is to minimize the variance of job completion times. To date, the problem has not been solved in polynomial time. This paper presents a dynamic programming algorithm that is pseudopolynomial in complexity. We also propose a fully polynomial approximation scheme and derive a lower bound that is useful in its implementation. Furthermore, we show that the dynamic programming solution is easy to extend to a bicriteria version of the problem in which it is desired to simultaneously minimize the mean completion time.

122 citations

"A branch and bound algorithm to min..." refers background or methods in this paper

  • ...[13] in terms of the number of solutions evaluated for various problem sizes....

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  • ...[13] presented a dynamic programming algorithm that is pseudo-polynomial in complexity to minimize the variance of job completion times with bi-criteria extension and derived a lower bound that is useful in its implementation....

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  • ...[13], which has a pseudo-polynomial complexity....

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  • ...[13] using a simple proof and tested the bound on randomly generated problems....

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Journal Article•DOI•
Minimizing the Time-in-System Variance for a Finite Jobset

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Linus Schrage
01 Jan 1975-Management Science
TL;DR: In this article, a finite number of jobs are scheduled on a single machine and the objective is to sequence the jobs so that the time-in-system (or equivalently, the completion time) variance is minimized.
Abstract: There are a finite number of jobs to be scheduled on a single machine. All jobs are available from the start and the objective is to sequence the jobs so that the time-in-system (or equivalently, the completion time) variance is minimized. A number of necessary conditions for an optimal sequencing (which for small jobsets turn out to be sufficient) are presented.

113 citations

Related Papers (5)
Variance Minimization in Single Machine Sequencing Problems

[...]

01 May 1972-Management Science
Alan G. Merten, Mervin E. Muller
Completion time variance minimization on a single machine is difficult

[...]

01 Aug 1993-Operations Research Letters
Wieslaw Kubiak
Minimising Waiting Time Variance in the Single Machine Problem

[...]

01 Feb 1977-Management Science
Samuel Eilon, I. G. Chowdhury
Minimizing Variation of Flow Time in Single Machine Systems

[...]

01 Dec 1981-Management Science
John J. Kanet
Minimizing the Time-in-System Variance for a Finite Jobset

[...]

01 Jan 1975-Management Science
Linus Schrage