scholarly journals Heuristic for Stochastic Online Flowshop Problem with Preemption Penalties

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Mohammad Bayat ◽  
Mehdi Heydari ◽  
Mohammad Mahdavi Mazdeh
Keyword(s):  
Standard Deviation ◽  
Processing Time ◽  
Heuristic Method ◽  
Heuristic Procedure ◽  
Release Date ◽  
Numerical Examples ◽  
Processing Times ◽  
Flowshop Problem ◽  
Expected Makespan ◽  
Actual Processing Time

The deterministic flowshop model is one of the most widely studied problems; whereas its stochastic equivalent has remained a challenge. Furthermore, the preemptive online stochastic flowshop problem has received much less attention, and most of the previous researches have considered a nonpreemptive version. Moreover, little attention has been devoted to the problems where a certain time penalty is incurred when preemption is allowed. This paper examines the preemptive stochastic online flowshop with the objective of minimizing the expected makespan. All the jobs arrive overtime, which means that the existence and the parameters of each job are unknown until its release date. The processing time of the jobs is stochastic and actual processing time is unknown until completion of the job. A heuristic procedure for this problem is presented, which is applicable whenever the job processing times are characterized by their means and standard deviation. The performance of the proposed heuristic method is explored using some numerical examples.

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 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.

Inequalities and bounds for the scheduling of stochastic jobs on parallel machines

1985 ◽  
Vol 22 (3) ◽  
pp. 739-744 ◽  
Author(s):  
Michael Pinedo ◽  
Zvi Schechner
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Random Variable ◽  
Expected Time ◽  
Processing Times ◽  
Set Up ◽  
Expected Makespan

Consider n jobs and m machines. The m machines are identical and set up in parallel. All n jobs are available at t = 0 and each job has to be processed on one of the machines; any one can do. The processing time of job j is Xj, a random variable with distribution Fj. The sequence in which the jobs start with their processing is predetermined and preemptions are not allowed. We investigate the effect of the variability of the processing times on the expected makespan and the expected time to first idleness. Bounds are presented for these quantities in case the distributions of the processing times of the jobs are new better (worse) than used.

scholarly journals A Novel Heuristic to Minimize the Bottlenecks Presence in Batch Generation. Case of Study.

2021 ◽  
Author(s):  
Pedro Henoc Ireta-Sánchez ◽  
Elías Gabriel Carrum-Siller ◽  
David Salvador González-González ◽  
Ricardo Martínez-López
Keyword(s):  
Simulated Annealing ◽  
Processing Time ◽  
Heuristic Method ◽  
The Other ◽  
Dispatching Rule ◽  
Processing Times ◽  
Real Process ◽  
Random Instances ◽  
The One ◽  
First In First Out

Abstract This paper presents a new heuristic method capable of minimizing the presence of bottlenecks generated when production batches have a distinct makespan. The proposed heuristic groups the jobs into items, where the one with the longest processing time in the batch determines the makespan. To test the heuristic, information was collected from a real paint process with two stations: one with a single cabin and the other with two parallel cabins. The capacity of processing jobs is limited by the cabin dimensions where jobs have different sizes and processing times. A makespan comparison between the heuristic proposed versus the First in First out (FIFO) dispatching rule that the case of study uses. Additionally, ten random instances based on data taken from the real process were created with the purpose to compare the new heuristic method versus Genetic Algorithm (GA) and Simulated Annealing (SA). The result of the comparison to FIFO, GA and SA showed that the proposed heuristic minimizes the bottleneck in a and creating batches almost with the same makespan. Results indicated a bottleneck time reduction of 96% when new heuristic method were compared to FIFO rule, while compared to Generic Algorithm and Simulated Annealing the bottleneck reduction were around 89% in both cases.

scholarly journals Minimizing Makespan in A Two-Machine Flowshop Problem with Processing Time Linearly Dependent on Job Waiting Time

2019 ◽  
Vol 11 (24) ◽  
pp. 6885 ◽  
Author(s):  
Dar-Li Yang ◽  
Wen-Hung Kuo
Keyword(s):  
Integer Programming ◽  
Waiting Time ◽  
Environmental Sustainability ◽  
Computational Experiment ◽  
Processing Time ◽  
Waiting Times ◽  
Mixed Integer ◽  
Flowshop Scheduling ◽  
Processing Times ◽  
Flowshop Problem

This paper is aimed at studying a two-machine flowshop scheduling where the processing times are linearly dependent on the waiting times of the jobs prior to processing on the second machine. That is, when a job is processed completely on the first machine, a certain delay time is required before its processing on the second machine. If we would like to reduce the actual waiting time, the processing time of the job on the second machine increases. The objective is to minimize the makespan. When the processing time is reduced, it implies that the consumption of energy is reduced. It is beneficial to environmental sustainability. We show that the proposed problem is NP-hard in the strong sense. A 0-1 mixed integer programming and a heuristic algorithm with computational experiment are proposed. Some cases solved in polynomial time are also provided.

Inequalities and bounds for the scheduling of stochastic jobs on parallel machines

1985 ◽  
Vol 22 (03) ◽  
pp. 739-744
Author(s):  
Michael Pinedo ◽  
Zvi Schechner
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Random Variable ◽  
Expected Time ◽  
Processing Times ◽  
Set Up ◽  
Expected Makespan

Consider n jobs and m machines. The m machines are identical and set up in parallel. All n jobs are available at t = 0 and each job has to be processed on one of the machines; any one can do. The processing time of job j is Xj , a random variable with distribution Fj. The sequence in which the jobs start with their processing is predetermined and preemptions are not allowed. We investigate the effect of the variability of the processing times on the expected makespan and the expected time to first idleness. Bounds are presented for these quantities in case the distributions of the processing times of the jobs are new better (worse) than used.

A new tool for rapid development of electron microscopy negatives and micrographs: Initial impressions of the MOHR/PRO-8 processor

1992 ◽  
Vol 50 (2) ◽  
pp. 972-973
Author(s):  
James C. Long
Keyword(s):  
Electron Microscopy ◽  
Processing Time ◽  
Rapid Development ◽  
Processing Times ◽  
Initial Impressions ◽  
Transport Method

Over the years, many techniques and products have been developed to reduce the amount of time spent in a darkroom processing electron microscopy negatives and micrographs. One of the latest tools, effective in this effort, is the Mohr/Pro-8 film and rc paper processor.At the time of writing, a unit has been recently installed in the photographic facilities of the Electron Microscopy Center at Texas A&M University. It is being evaluated for use with TEM sheet film, SEM sheet film, 35mm roll film (B&W), and rc paper.Originally designed for use in the phototypesetting industry, this processor has only recently been introduced to the field of electron microscopy.The unit is a tabletop model, approximately 1.5 × 1.5 × 2.0 ft, and uses a roller transport method of processing. It has an adjustable processing time of 2 to 6.5 minutes, dry-to-dry. The installed unit has an extended processing switch, enabling processing times of 8 to 14 minutes to be selected.

Unrelated Parallel-Machine Scheduling with Controllable Processing Times and Impact of Deteriorating Maintenance Activities under Consideration

2016 ◽  
Vol 33 (01) ◽  
pp. 1650001 ◽  
Author(s):  
Chun-Lai Liu ◽  
Jian-Jun Wang
Keyword(s):  
Processing Time ◽  
Machine Scheduling ◽  
Parallel Machine Scheduling ◽  
Parallel Machine ◽  
Controllable Processing Times ◽  
Maintenance Activity ◽  
Processing Times ◽  
Unrelated Parallel Machine Scheduling ◽  
Deteriorating Maintenance ◽  
Maintenance Activities

In this paper, we study the problem of unrelated parallel machine scheduling with controllable processing times and deteriorating maintenance activity. The jobs are nonresumable. The processing time of each job is a linear function of the amount of a continuously divisible resource allocated to the job. During the planning horizon, there is at most one maintenance activity scheduled on each machine. Additionally, if the starting time of maintenance activity is delayed, the length of the maintenance activity required to perform will increase. Considering the total completion times of all jobs, the impact of maintenance activity in the form of the variation in machine load and the amounts of compression, we need to determine the job sequence on each machine, the location of maintenance activities and processing time compression of each job simultaneously. Accordingly, a polynomial time solution to the problem is provided.

The Research of Heuristic Algorithm for Flow Shop Scheduling Problem

2012 ◽  
Vol 605-607 ◽  
pp. 528-531
Author(s):  
Dan Tang ◽  
Hong Ping Shu
Keyword(s):  
Heuristic Algorithm ◽  
Processing Time ◽  
Flow Shop ◽  
Heuristic Method ◽  
Flow Shop Scheduling ◽  
Scheduling Problem ◽  
Average Quality ◽  
Simulation Experiments ◽  
Shop Scheduling ◽  
Better Than

For the flow shop scheduling problem which aims to minimize makespan, this paper gives a new derivation about its mathematical definition, and mining characteristics of the problem itself further. By which analysis, the new heuristic method proposed in the paper shorten the waiting time of each job as much as possible on the basis of reduce the processing time of the first machine and last job. The result of simulation experiments shows that, our new heuristic algorithm has good performance, and the average quality and stability of scheduling sequences generated by new method is significantly better than other heuristic algorithm which has the same complexity.

scholarly journals Scheduling jobs with stochastically ordered processing times on parallel machines to minimize expected flowtime

1986 ◽  
Vol 23 (03) ◽  
pp. 841-847 ◽  
Author(s):  
R. R. Weber ◽  
P. Varaiya ◽  
J. Walrand
Keyword(s):  
Processing Time ◽  
Parallel Machines ◽  
Preemptive Scheduling ◽  
Total Reward ◽  
Processing Times ◽  
Identical Machines ◽  
Scheduling Strategies

A number of jobs are to be processed using a number of identical machines which operate in parallel. The processing times of the jobs are stochastic, but have known distributions which are stochastically ordered. A reward r(t) is acquired when a job is completed at time t. The function r(t) is assumed to be convex and decreasing in t. It is shown that within the class of non-preemptive scheduling strategies the strategy SEPT maximizes the expected total reward. This strategy is one which whenever a machine becomes available starts processing the remaining job with the shortest expected processing time. In particular, for r(t) = – t, this strategy minimizes the expected flowtime.

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