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.

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 A LEARNING EFFECT AND A RATE-MODIFYING ACTIVITY

2011 ◽  
Vol 28 (04) ◽  
pp. 511-521 ◽  
Author(s):  
CHUANLI ZHAO ◽  
HENGYONG TANG
Keyword(s):  
Single Machine ◽  
Processing Time ◽  
Learning Effect ◽  
Window Size ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Polynomial Time Algorithms ◽  
Due Window ◽  
Machine Scheduling Problems

In the paper, single machine scheduling problems with a learning effect and a rate-modifying activity are considered. Under the learning effect, the processing time of a job is a decreasing function of its position in the sequence. The rate-modifying activity is an event that can change the speed of the machine, and hence the processing time of jobs after the activity. The following objective functions are considered: the makespan, the total earliness, tardiness and completion time penalty, and the total earliness, tardiness, due-window starting time and due-window size penalty. Polynomial time algorithms are proposed to optimally solve the problems.

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.

Scheduling Problems with Human and Machine Effects

2013 ◽  
Vol 423-426 ◽  
pp. 2206-2210
Author(s):  
Na Yin ◽  
Tian Chuan Sun
Keyword(s):  
Cost Function ◽  
Waiting Times ◽  
Single Machine Scheduling ◽  
Learning Effects ◽  
Scheduling Problems ◽  
Objective Functions ◽  
Optimal Sequence ◽  
Removal Time ◽  
Machine Scheduling Problems ◽  
Completion Times

We discuss single machine scheduling problems with learning effects of setup and removal times and deterioration effects of processing time, i.e., the processing (setup or removal) time of a job is a function of its position . The objective functions are finding the optimal sequence of jobs to minimize a cost function containing makespan, total completion time and total absolute differences in completion times and to minimize a cost function containing makespan, total waiting time and total absolute differences in waiting times. The problems are modeled as an assignment problem respectively, and thus can be solved in polynomial time.

scholarly journals A Genetic Algorithm-Based Approach for Single-Machine Scheduling with Learning Effect and Release Time

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Der-Chiang Li ◽  
Peng-Hsiang Hsu ◽  
Chih-Chieh Chang
Keyword(s):  
Genetic Algorithm ◽  
Single Machine ◽  
Learning Effect ◽  
Unit Cost ◽  
Single Machine Scheduling ◽  
Release Time ◽  
Scheduling Problems ◽  
Release Times ◽  
Completion Times ◽  
Machine Problem

The way to gain knowledge and experience of producing a product in a firm can be seen as new solution for reducing the unit cost in scheduling problems, which is known as “learning effects.” In the scheduling of batch processing machines, it is sometimes advantageous to form a nonfull batch, while in other situations it is a better strategy to wait for future job arrivals in order to increase the fullness of the batch. However, research with learning effect and release times is relatively unexplored. Motivated by this observation, we consider a single-machine problem with learning effect and release times where the objective is to minimize the total completion times. We develop a branch-and-bound algorithm and a genetic algorithm-based heuristic for this problem. The performances of the proposed algorithms are evaluated and compared via computational experiments, which showed that our approach has superior ability in this scenario.

scholarly journals Single-Machine Scheduling Problems with a Sum-of-Processing-Time-Based Learning Function

2009 ◽  
Vol 2009 ◽  
pp. 1-8
Author(s):  
Xingong Zhang ◽  
Guangle Yan
Keyword(s):  
Single Machine ◽  
Minimization Problem ◽  
Completion Time ◽  
Processing Time ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Proposed Model ◽  
Time Minimization ◽  
Polynomially Solvable

Recently, learning scheduling problems have received increasing attention. However, the majority of the research assume that the actual job processing time is a function of its position. This paper deals with the single-machine scheduling problem with a sum-of-processing-time-based learning effect. By the effect of sum-of-processing-time-based learning, we mean that the processing time of a job is defined by total normal processing time of jobs in front of it in the sequence. We show that the single-machine makespan problem remains polynomially solvable under the proposed model. We show that the total completion time minimization problem for a≥1 remains polynomially solvable under the proposed model. For the case of 0<a<1, we show that an optimal schedule of the total completion time minimization problem is V-shaped with respect to normal job processing times.

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