A branch and price algorithm for single-machine completion time variance

2019 ◽  
Vol 109 ◽  
pp. 188-199
Author(s):  
Shijin Wang ◽  
Ying Lu
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Branch And Price ◽  
Time Variance ◽  
Price Algorithm

scholarly journals Column generation for minimizing total completion time in a parallel-batching environment

2021 ◽  
Author(s):  
A. Alfieri ◽  
A. Druetto ◽  
A. Grosso ◽  
F. Salassa
Keyword(s):  
Lower Bound ◽  
Column Generation ◽  
Single Machine ◽  
Completion Time ◽  
Computation Time ◽  
Total Completion Time ◽  
Branch And Price ◽  
Total Size ◽  
Parallel Batching ◽  
Price Algorithm

AbstractThis paper deals with the $$1|{p-\text {batch}, s_j\le b}|\sum C_j$$ 1 | p - batch , s j ≤ b | ∑ C j scheduling problem, where jobs are scheduled in batches on a single machine in order to minimize the total completion time. A size is given for each job, such that the total size of each batch cannot exceed a fixed capacity b. A graph-based model is proposed for computing a very effective lower bound based on linear programming; the model, with an exponential number of variables, is solved by column generation and embedded into both a heuristic price and branch algorithm and an exact branch and price algorithm. The same model is able to handle parallel-machine problems like $$Pm|{p-\text {batch}, s_j\le b}|\sum C_j$$ P m | p - batch , s j ≤ b | ∑ C j very efficiently. Computational results show that the new lower bound strongly dominates the bounds currently available in the literature, and the proposed heuristic algorithm is able to achieve high-quality solutions on large problems in a reasonable computation time. For the single-machine case, the exact branch and price algorithm is able to solve all the tested instances with 30 jobs and a good amount of 40-job examples.

Minimizing Single-Machine Completion Time Variance

1995 ◽  
Vol 41 (9) ◽  
pp. 1448-1455 ◽  
Author(s):  
Jose A. Ventura ◽  
Michael X. Weng
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Time Variance

A SINGLE-MACHINE DETERIORATING JOB SCHEDULING PROBLEM WITH A NON-REGULAR CRITERION

2011 ◽  
Vol 28 (03) ◽  
pp. 349-359 ◽  
Author(s):  
CHIN-CHIA WU ◽  
WEN-CHIUNG LEE ◽  
YAU-REN SHIAU
Keyword(s):  
Heuristic Algorithm ◽  
Single Machine ◽  
Completion Time ◽  
Job Scheduling ◽  
Optimal Schedule ◽  
Scheduling Problems ◽  
Time Variance ◽  
Time Minimization ◽  
Deteriorating Job ◽  
Job Scheduling Problem

In scheduling environments with deterioration, a job processed later consumes more time than that same job when processed earlier. The deteriorating job scheduling problems have been widely studied in the last two decades. However, no result of the completion time variance has been reported. In this study, we consider the variance of job completion time minimization problem on a single machine. It is assumed that the job processing time is a simple linear function of its starting time. We show that an optimal schedule is V-shaped with respect to the job deteriorating rates. A heuristic algorithm utilized the V-shaped property is then proposed, and a computational experiment shows that the proposed heuristic algorithm is quite accurate.

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