scholarly journals Schedule Execution for Two-Machine Job-Shop to Minimize Makespan with Uncertain Processing Times

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1314 ◽  
Author(s):  
Yuri N. Sotskov ◽  
Natalja M. Matsveichuk ◽  
Vadzim D. Hatsura
Keyword(s):  
Job Shop ◽  
Job Shop Scheduling ◽  
Optimal Schedule ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Processing Times ◽  
On Line ◽  
Asymptotic Complexity ◽  
The Stability

This study addresses a two-machine job-shop scheduling problem with fixed lower and upper bounds on the job processing times. An exact value of the job duration remains unknown until completing the job. The objective is to minimize a schedule length (makespan). It is investigated how to best execute a schedule, if the job processing time may be equal to any real number from the given (closed) interval. Scheduling decisions consist of the off-line phase and the on-line phase of scheduling. Using the fixed lower and upper bounds on the job processing times available at the off-line phase, a scheduler may determine a minimal dominant set of schedules (minimal DS), which is based on the proven sufficient conditions for a schedule dominance. The DS optimally covers all possible realizations of the uncertain (interval) processing times, i.e., for each feasible scenario, there exists at least one optimal schedule in the minimal DS. The DS enables a scheduler to make the on-line scheduling decision, if a local information on completing some jobs becomes known. The stability approach enables a scheduler to choose optimal schedules for most feasible scenarios. The on-line scheduling algorithms have been developed with the asymptotic complexity O(n2) for n given jobs. The computational experiment shows the effectiveness of these algorithms.

scholarly journals Two-Machine Job-Shop Scheduling Problem to Minimize the Makespan with Uncertain Job Durations

Algorithms ◽  
2019 ◽  
Vol 13 (1) ◽  
pp. 4 ◽  
Author(s):  
Yuri N. Sotskov ◽  
Natalja M. Matsveichuk ◽  
Vadzim D. Hatsura
Keyword(s):  
Relative Error ◽  
Job Shop ◽  
Sufficient Conditions ◽  
Upper Bounds ◽  
Maximum Relative Error ◽  
Scheduling Problems ◽  
Lower And Upper Bounds ◽  
Shop Scheduling ◽  
Job Duration ◽  
On Line

We study two-machine shop-scheduling problems provided that lower and upper bounds on durations of n jobs are given before scheduling. An exact value of the job duration remains unknown until completing the job. The objective is to minimize the makespan (schedule length). We address the issue of how to best execute a schedule if the job duration may take any real value from the given segment. Scheduling decisions may consist of two phases: an off-line phase and an on-line phase. Using information on the lower and upper bounds for each job duration available at the off-line phase, a scheduler can determine a minimal dominant set of schedules (DS) based on sufficient conditions for schedule domination. The DS optimally covers all possible realizations (scenarios) of the uncertain job durations in the sense that, for each possible scenario, there exists at least one schedule in the DS which is optimal. The DS enables a scheduler to quickly make an on-line scheduling decision whenever additional information on completing jobs is available. A scheduler can choose a schedule which is optimal for the most possible scenarios. We developed algorithms for testing a set of conditions for a schedule dominance. These algorithms are polynomial in the number of jobs. Their time complexity does not exceed O ( n 2 ) . Computational experiments have shown the effectiveness of the developed algorithms. If there were no more than 600 jobs, then all 1000 instances in each tested series were solved in one second at most. An instance with 10,000 jobs was solved in 0.4 s on average. The most instances from nine tested classes were optimally solved. If the maximum relative error of the job duration was not greater than 20 % , then more than 80 % of the tested instances were optimally solved. If the maximum relative error was equal to 50 % , then 45 % of the tested instances from the nine classes were optimally solved.

scholarly journals ON-LINE JOB-SHOP SCHEDULING OF A MANUFACTURING SYSTEM BASED ON A VIRTUAL SUPERVISOR CONCEPT

2005 ◽  
Vol 38 (1) ◽  
pp. 183-188
Author(s):  
Jesús Trujillo ◽  
Zbigniew J. Pasek ◽  
Enrique Baeyens
Keyword(s):  
Manufacturing System ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Shop Scheduling ◽  
On Line

Theoretical Analysis on Powers-of-Two Applied to JSP

2011 ◽  
Vol 2 (2) ◽  
pp. 1-20
Author(s):  
V. Mahesh ◽  
L. Siva Rama Krishna ◽  
Sandeep Dulluri ◽  
C. S. P. Rao
Keyword(s):  
Job Shop ◽  
Job Shop Scheduling ◽  
Optimal Schedule ◽  
Optimal Solution ◽  
Mathematical Induction ◽  
Release Dates ◽  
Scheduling Problems ◽  
Job Shop Scheduling Problem ◽  
Shop Scheduling ◽  
Optimal Value

This paper discusses the scheduling of precedence-related jobs non-preemptively in a job shop environment with an objective of minimizing the makespan. Due to the NP-hard nature of the scheduling problems, it is usually difficult to find an exact optimal schedule and hence one should rely on finding a near to optimal solution. This paper proposes a computationally effective powers-of-two heuristic for solving job shop scheduling problem. The authors prove that the makespan obtained through powers-of-two release dates lies within 6% of the optimal value. The authors also prove the efficacy of powers-of-two approach through mathematical induction.

scholarly journals Two-Machine Job-Shop Scheduling with Equal Processing Times on Each Machine

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 301 ◽  
Author(s):  
Evgeny Gafarov ◽  
Frank Werner
Keyword(s):  
Dynamic Programming ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Single Track ◽  
Shop Scheduling ◽  
Processing Times ◽  
Equal Processing Times

In this paper, we consider a two-machine job-shop scheduling problem of minimizing total completion time subject to n jobs with two operations and equal processing times on each machine. This problem occurs e.g., as a single-track railway scheduling problem with three stations and constant travel times between any two adjacent stations. We present a polynomial dynamic programming algorithm of the complexity O ( n 5 ) and a heuristic procedure of the complexity O ( n 3 ) . This settles the complexity status of the problem under consideration which was open before and extends earlier work for the two-station single-track railway scheduling problem. We also present computational results of the comparison of both algorithms. For the 30,000 instances with up to 30 jobs considered, the average relative error of the heuristic is less than 1 % . In our tests, the practical running time of the dynamic programming algorithm was even bounded by O ( n 4 ) .

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