scholarly journals Multitasking Scheduling Problems with Deterioration Effect

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Zhanguo Zhu ◽  
Jinlin Li ◽  
Chengbin Chu
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Joint Effect ◽  
Optimal Algorithms ◽  
Scheduling Problems ◽  
Processing Times ◽  
Special Cases ◽  
Deterioration Effect ◽  
Task Processing ◽  
Human Operators

Multitasking scheduling problems with a deterioration effect incurred by coexisting behavioral phenomena in human-related scheduling systems including deteriorating task processing times and deteriorating rate-modifying activity (DRMA) of human operators are addressed. Under the assumption of this problem, the processing of a selected task suffers from the joint effect of available but unfinished waiting tasks, the position-dependent deterioration of task processing time, and the DRMA of human operators. Traditionally, these issues have been considered separately; herein, we address their integration. We propose optimal algorithms to solve the problems to minimize makespan and the total absolute differences in completion time, respectively. Based on the analysis, some special cases and extensions are also discussed.

scholarly journals Parallel-machine scheduling of jobs with mixed job-, machine- and position-dependent processing times

2021 ◽  
Author(s):  
Bartłomiej Przybylski
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Positive Function ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Scheduling Problems ◽  
Processing Times ◽  
Maximum Completion Time ◽  
Machine Scheduling Problems

AbstractWe consider a number of parallel-machine scheduling problems in which jobs have variable processing times. The actual processing time of each job is described by an arbitrary positive function of the position it holds on a machine. However, the function itself may additionally depend on the job or a machine this job was assigned to. Our aim is to find a schedule that minimizes the objectives of maximum completion time or the total completion time. We present a full set of polynomial solutions for the cases of jobs with no precedence constraints. We also show that the case of single-chained jobs may be not easier in general, but some polynomial results can be obtained, too.

SCHEDULING PROBLEMS WITH THE EFFECTS OF DETERIORATION AND LEARNING

2007 ◽  
Vol 24 (02) ◽  
pp. 245-261 ◽  
Author(s):  
JI-BO WANG ◽  
T. C. EDWIN CHENG
Keyword(s):  
Performance Measures ◽  
Single Machine ◽  
Completion Time ◽  
Flow Shop ◽  
Machine Scheduling ◽  
Total Weighted Completion Time ◽  
Scheduling Problems ◽  
Processing Times ◽  
Weighted Completion Time ◽  
Machine Scheduling Problems

This paper deals with the machine scheduling problems with the effects of deterioration and learning. In this model the processing times of jobs are defined as functions of their starting times and positions in a sequence. We introduce polynomial solutions for some single machine problems and flow shop problems. The performance measures include makespan, total completion time, total weighted completion time, and maximum lateness.

scholarly journals Minimizing Total Completion Time For Preemptive Scheduling With Release Dates And Deadline Constraints

2014 ◽  
Vol 39 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Cheng He ◽  
Hao Lin ◽  
Yixun Lin ◽  
Junmei Dou
Keyword(s):  
Completion Time ◽  
Total Completion Time ◽  
Release Dates ◽  
Preemptive Scheduling ◽  
Release Date ◽  
Enumeration Algorithm ◽  
Processing Times ◽  
Special Cases ◽  
Deadline Constraints ◽  
Special Case

Abstract It is known that the single machine preemptive scheduling problem of minimizing total completion time with release date and deadline constraints is NP- hard. Du and Leung solved some special cases by the generalized Baker's algorithm and the generalized Smith's algorithm in O(n2) time. In this paper we give an O(n2) algorithm for the special case where the processing times and deadlines are agreeable. Moreover, for the case where the processing times and deadlines are disagreeable, we present two properties which could enable us to reduce the range of the enumeration algorithm

USING ANT COLONY OPTIMIZATION TO MINIMIZE THE FUZZY MAKESPAN AND TOTAL WEIGHTED FUZZY COMPLETION TIME IN FLOW SHOP SCHEDULING PROBLEMS

2009 ◽  
Vol 17 (04) ◽  
pp. 559-584 ◽  
Author(s):  
PENG-JEN LAI ◽  
HSIEN-CHUNG WU
Keyword(s):  
Completion Time ◽  
Ant Colony Algorithm ◽  
Fuzzy Numbers ◽  
Flow Shop ◽  
Computational Procedure ◽  
Ant Colony ◽  
Flow Shop Scheduling ◽  
Scheduling Problems ◽  
Shop Scheduling ◽  
Processing Times

The flow shop scheduling problems with fuzzy processing times are investigated in this paper. For some special kinds of fuzzy numbers, the analytic formulas of the fuzzy compltion time can be obtained. For the general bell-shaped fuzzy numbers, we present a computational procedure to obtain the approximated membership function of the fuzzy completion time. We define a defuzzification function to rank the fuzzy numbers. Under this ranking concept among fuzzy numbers, we plan to minimize the fuzzy makespan and total weighted fuzzy completion time. Because the ant colony algorithm has been successfully used to solve the scheduling problems with real-valued processing times, we shall also apply the ant colony algorithm to search for the best schedules when the processing times are assumed as fuzzy numbers. Numerical examples are also provided and solved by using the commercial software MATLAB.

ONLINE SCHEDULING OF MIXED CPU-GPU JOBS

2014 ◽  
Vol 25 (06) ◽  
pp. 745-761 ◽  
Author(s):  
LIN CHEN ◽  
DESHI YE ◽  
GUOCHUAN ZHANG
Keyword(s):  
Competitive Ratio ◽  
Completion Time ◽  
Online Algorithm ◽  
Online Scheduling ◽  
Scheduling Problem ◽  
Competitive Algorithm ◽  
Processing Times ◽  
Special Cases ◽  
Identical Machines ◽  
The One

We consider the online scheduling problem in a CPU-GPU cluster. In this problem there are two sets of processors, the CPU processors and the GPU processors. Each job has two distinct processing times, one for the CPU processor and the other for the GPU processor. Once a job is released, a decision should be made immediately about which processor it should be assigned to. The goal is to minimize the makespan, i.e., the largest completion time among all the processors. Such a problem could be seen as an intermediate model between the scheduling problem on identical machines and unrelated machines. We provide a 3.85-competitive online algorithm for this problem and show that no online algorithm exists with competitive ratio strictly less than 2. We also consider two special cases of this problem, the balanced case where the number of CPU processors equals to that of GPU processors, and the one-sided case where there is only one CPU or GPU processor. For the balanced case, we first provide a simple 3-competitive algorithm, and then a better algorithm with competitive ratio of 2.732 is derived. For the one-sided case, a 3-competitive algorithm is given.

STOCHASTIC BATCH SCHEDULING AND THE “SMALLEST VARIANCE FIRST” RULE

2007 ◽  
Vol 21 (4) ◽  
pp. 579-595 ◽  
Author(s):  
Michael Pinedo
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Random Variable ◽  
Combinatorial Problems ◽  
Set Partitioning ◽  
Batch Scheduling ◽  
Matching Problem ◽  
Batch Mode ◽  
Processing Times ◽  
Expected Makespan

Consider a single machine that can process multiple jobs in batch mode. We havenjobs and the processing time of jobjis a random variableXjwith distributionFj. Up tobjobs can be processed simultaneously by the machine. The jobs in a batch all have to start at the same time and the batch is completed when all jobs have finished their processing (i.e., at the maximum of the processing times of the jobs in that batch). We are interested in two objective functions, namely the minimization of the expected makespan and the minimization of the total expected completion time. We first show that under certain fairly general conditions, the minimization of the expected makespan is equivalent to specific deterministic combinatorial problems, namely the Weighted Matching problem and the Set Partitioning problem. We then consider the case when all jobs have the same mean processing time but different variances. We show that for certain special classes of processing time distributions theSmallest Variance Firstrule minimizes the expected makespan as well as the total expected completion time. In our conclusions we present various general rules that are suitable for the minimization of the expected makespan and the total expected completion time in batch scheduling.

scholarly journals Due Date Single Machine Scheduling Problems with Nonlinear Deterioration and Learning Effects and Past Sequence Dependent Setup Times

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Hüseyin Ceylan
Keyword(s):  
Processing Time ◽  
Single Machine Scheduling ◽  
Setup Times ◽  
Scheduling Problems ◽  
Due Dates ◽  
Sequence Dependent ◽  
Special Cases ◽  
Sequence Dependent Setup ◽  
Dependent Setup Times ◽  
Sequence Dependent Setup Times

We present some problems against due dates with nonlinear learning and deterioration effects and past sequence dependent setup times. In this study, two effects (learning and deterioration) are used for the same processing time. The processing time of a job is shorter if it is scheduled later, rather than in the sequence. This phenomenon is known in the literature as a “learning effect.” On the other hand, in many realistic scheduling settings, a job processed later consumes more time than the same job processed earlier—this is known as scheduling with deteriorating jobs. In the past sequence dependent setup times approach, the setup time of a job is proportionate to the sum of processing times of the jobs already scheduled. In this study, we demonstrated that some problems with due dates remain polynomially solvable. However, for some other problems, we concentrated on finding polynomially solves under their special cases.

A Note on Scheduling Jobs with Extended Sum-of-Processing-Times-Based and Position-Based Learning Effect

2015 ◽  
Vol 32 (02) ◽  
pp. 1550001 ◽  
Author(s):  
Yu-Ping Niu ◽  
Long Wan ◽  
Ji-Bo Wang
Keyword(s):  
Learning Effect ◽  
Flow Shop ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Flow Shop Scheduling ◽  
Scheduling Problems ◽  
Processing Times ◽  
Effect Model ◽  
Special Cases ◽  
Machine Scheduling Problems

The note deals with machine scheduling problems with a more general learning effect model, i.e., the actual job processing time is a function of the sum of the function of the processing times of the jobs already processed and job position. We show that some single machine scheduling problems are still polynomially solvable under the proposed model. We also show that some special cases of the flow shop scheduling problems can be solved in polynomial time.

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.

scholarly journals Single-Machine Scheduling Problems with the General Sum-of-Processing-Time and Position-Dependent Effect Function

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Kunping Shen ◽  
Yuke Chen ◽  
Shangchia Liu
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Objective Functions ◽  
Dependent Effect ◽  
Effect Function ◽  
Processing Times ◽  
Time Problem ◽  
Normal Processing

This paper considers the combination of the general sum-of-processing-time effect and position-dependent effect on a single machine. The actual processing time of a job is defined by functions of the sum of the normal processing times of the jobs processed and its position and control parameter in the sequence. We consider two monotonic effect functions: the nondecreasing function and the nonincreasing function. Our focus is the following objective functions, including the makespan, the sum of the completion time, the sum of the weighted completion time, and the maximum lateness. For the nonincreasing effect function, polynomial algorithm is presented for the makespan problem and the sum of completion time problem, respectively. The latter two objective functions can also be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the nondecreasing effect function, assume that the given parameter is zero. We also show that the makespan problem can remain polynomially solvable. For the sum of the total completion time problem and a 1 is the deteriorating rate of the jobs, there exists an optimal solution for a 1 ≥ M ; a V-shaped property with respect to the normal processing times is obtained for 0 < a 1 ≤ 1 . Finally, we show that the sum of the weighted completion problem and the maximum lateness problem have polynomial-time solutions for a 1 > M under some agreeable conditions, respectively.

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