Variance Minimization in Single Machine Sequencing Problems
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.
Citations
More filters
TL;DR: A unified framework of the common due date assignment and scheduling problems in the deterministic case is provided by surveying the literature concerning the models involving single machine and parallel machines by finding an optimal value of thecommon due date and the related optimal schedule.
436 citations
TL;DR: In this article, a single-machine scheduling problem in which penalities occur when a job is completed early or late is considered, where the objective is to minimize the total penalty subject to restrictive assumptions on the due dates and penalty functions.
Abstract: This paper considers a single-machine scheduling problem in which penalities occur when a job is completed early or late. The objective is to minimize the total penalty subject to restrictive assumptions on the due dates and penalty functions for jobs. A procedure is presented for finding an optimal schedule.
331 citations
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
Cites background from "Variance Minimization in Single Mac..."
...As Merton and Muller [3] indicate, in computer systems with large data sets the response time to a user's request is often strongly dependent on the file-access time....
[...]
...In the earliest paper on this topic, Merton and Muller [3] analyze the relation between flow time variance and waiting time variance....
[...]
..., [1], [3], and [4]) and no theoretical breakthrough is claimed here....
[...]
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
TL;DR: In this paper, the authors consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date and present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold.
Abstract: We consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold. We also establish the similarity of this problem to the two parallel machines mean flow time problem.
165 citations
References
More filters
Book•
01 Jan 1973
4,243 citations
Book•
[...]
01 Jan 1967
TL;DR: Reading theory of scheduling as one of the reading material to finish quickly to increase the knowledge and happiness in your lonely time.
Abstract: Feel lonely? What about reading books? Book is one of the greatest friends to accompany while in your lonely time. When you have no friends and activities somewhere and sometimes, reading book can be a great choice. This is not only for spending the time, it will increase the knowledge. Of course the b=benefits to take will relate to what kind of book that you are reading. And now, we will concern you to try reading theory of scheduling as one of the reading material to finish quickly.
2,356 citations
1,854 citations
TL;DR: In this article, a functional equation similar to that formulated for the knapsack problem is applied to the solution of a problem of resource allocation in critical path scheduling, and to a variety of single-machine sequencing problems with deadlines and loss functions.
Abstract: A functional equation, similar to that formulated for the knapsack problem, is applied to the solution of a problem of resource allocation in critical path scheduling, and to a variety of single-machine sequencing problems with deadlines and loss functions. Among these are: minimization of the weighted number of tardy jobs, maximization of weighted earliness, minimization of tardiness with respect to common relative and absolute deadlines, and minimization of weighted tardiness with respect to a common deadline. Extensions to multiple-machine sequencing problems are discussed, and the sequencing of two machines in series is treated in detail.
417 citations
"Variance Minimization in Single Mac..." refers background in this paper
...The initial investigations of various performance measures are due to Smith [81 and Riesel [7], and, recently, Lawler and 1\'Ioore [4] investigated a special class of performance measures....
[...]