scholarly journals Optimal Rules for Single Machine Scheduling with Stochastic Breakdowns

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Jinwei Gu ◽  
Manzhan Gu ◽  
Xingsheng Gu
Keyword(s):  
Single Machine ◽  
Large Scale ◽  
Processing Time ◽  
Single Machine Scheduling ◽  
Scale Problem ◽  
Processing Times ◽  
Spt Rule ◽  
Lpt Rule ◽  
Completion Times ◽  
Stochastic Breakdowns

This paper studies the problem of scheduling a set of jobs on a single machine subject to stochastic breakdowns, where jobs have to be restarted if preemptions occur because of breakdowns. The breakdown process of the machine is independent of the jobs processed on the machine. The processing times required to complete the jobs are constants if no breakdown occurs. The machine uptimes are independently and identically distributed (i.i.d.) and are subject to a uniform distribution. It is proved that theLongest Processing Time first(LPT) rule minimizes the expected makespan. For the large-scale problem, it is also showed that theShortest Processing Time first(SPT) rule is optimal to minimize the expected total completion times of all jobs.

scholarly journals Two-Agent Single-Machine Scheduling of Jobs with Time-Dependent Processing Times and Ready Times

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Jan-Yee Kung ◽  
Yuan-Po Chao ◽  
Kuei-I Lee ◽  
Chao-Chung Kang ◽  
Win-Chin Lin
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Time Dependent ◽  
Research Attention ◽  
Processing Times ◽  
Ready Time ◽  
Increasing Function ◽  
Actual Processing Time

Scheduling involving jobs with time-dependent processing times has recently attracted much research attention. However, multiagent scheduling with simultaneous considerations of jobs with time-dependent processing times and ready times is relatively unexplored. Inspired by this observation, we study a two-agent single-machine scheduling problem in which the jobs have both time-dependent processing times and ready times. We consider the model in which the actual processing time of a job of the first agent is a decreasing function of its scheduled position while the actual processing time of a job of the second agent is an increasing function of its scheduled position. In addition, each job has a different ready time. The objective is to minimize the total completion time of the jobs of the first agent with the restriction that no tardy job is allowed for the second agent. We propose a branch-and-bound and several genetic algorithms to obtain optimal and near-optimal solutions for the problem, respectively. We also conduct extensive computational results to test the proposed algorithms and examine the impacts of different problem parameters on their performance.

Robust Single Machine Scheduling with Stochastic Processing Times Based on Event Point

2014 ◽  
Vol 668-669 ◽  
pp. 1641-1645
Author(s):  
Xiao Xia He ◽  
Chun Yao ◽  
Qiu Hua Tang
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Model Base ◽  
Processing Times ◽  
Robust Model ◽  
Stochastic Processing ◽  
Stochastic Processing Times

The scheduling of the single machine is of major importance in applications. The focus of this work is to analyze the scheduling problems in single-machine scheduling in the presence of uncertain parameters. By assuming that the processing time is represented by the nominal value plus a perturbation, we propose a robust model base on event point, and we obtain the feasible job sequence with some probability confidence level.

Single Machine Scheduling with Discretely Compressible Processing Times

2013 ◽  
Vol 787 ◽  
pp. 1020-1024
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Release Times

In this paper, we address the single machine scheduling problem with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost. Jobs may have different release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

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

2019 ◽  
Vol 23 (6) ◽  
pp. 665-680
Author(s):  
Alan J. Soper ◽  
Vitaly A. Strusevich
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Cumulative Effect ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Priority Rules ◽  
Optimal Sequence ◽  
Positional Effect ◽  
Wide Range ◽  
Completion Times

AbstractWe 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.

An Optimal Algorithm for Scheduling with Variable Job Processing Times and Rejection

2015 ◽  
Vol 775 ◽  
pp. 449-452
Author(s):  
Ji Bo Wang ◽  
Chou Jung Hsu
Keyword(s):  
Objective Function ◽  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Optimal Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Rejection Penalty

This paper studies a single machine scheduling problem with rejection. Each job has a variable processing time and a rejection penalty. The objective function is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem can be solved in polynomial time.

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