MAKESPAN MINIMIZATION ON THREE-MACHINE FLOW SHOP WITH DETERIORATING JOBS

2013 ◽  
Vol 30 (06) ◽  
pp. 1350022 ◽  
Author(s):  
JI-BO WANG ◽  
MING-ZHENG WANG
Keyword(s):  
Branch And Bound ◽  
Flow Shop ◽  
Deteriorating Jobs ◽  
Flow Shop Scheduling ◽  
Makespan Minimization ◽  
Permutation Flow Shop Scheduling ◽  
Special Cases ◽  
Deteriorating Job ◽  
Job Deterioration ◽  
Increasing Function

In this study, we consider a permutation flow shop scheduling problem on a three-machine with deteriorating jobs (a deteriorating job means that the job's processing time is an increasing function of its starting time) so as to minimize the makespan. We model job deterioration as a function that is proportional to a linear function of time. For some special cases, we prove that the problem can be solved in polynomial time. We develop branch-and-bound and heuristic procedures for the general case. Computational experiments for the branch-and-bound algorithm and heuristic algorithm are presented.

Minimizing Makespan in Permutation Flow Shop Scheduling with Proportional Deterioration

2015 ◽  
Vol 32 (06) ◽  
pp. 1550050 ◽  
Author(s):  
Na Yin ◽  
Liying Kang
Keyword(s):  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Shop Scheduling ◽  
Permutation Flow Shop Scheduling ◽  
Special Cases ◽  
Permutation Flow Shop ◽  
Maximum Completion Time ◽  
Permutation Schedule ◽  
Job Deterioration ◽  
Increasing Function

The [Formula: see text]-job and [Formula: see text]-machine permutation flow shop scheduling problem with a proportional deterioration is considered in which all machines process the jobs in the same order, i.e., a permutation schedule. A proportional deterioration means that the job deterioration as an increasing function that is proportional to a linear function of time. The objective is to minimize the makespan, i.e., the maximum completion time. When some dominant relationships between [Formula: see text] machines can be satisfied, we show that some special cases of the problem can be polynomial solvable. For the general case, we also propose a heuristic algorithm and give the computational experiments.

Permutation Flow Shop Problem with Shortening Job Processing Times

2016 ◽  
Vol 33 (04) ◽  
pp. 1650032 ◽  
Author(s):  
Zhenyou Wang ◽  
Cai-Min Wei ◽  
Yuan-Yuan Lu
Keyword(s):  
Branch And Bound ◽  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Nonincreasing Function ◽  
Start Time ◽  
Processing Times ◽  
Special Cases ◽  
Permutation Flow Shop ◽  
Time Optimal ◽  
Dominance Properties

In this paper, we consider a three-machine makespan minimization permutation flow shop scheduling problem with shortening job processing times. Shortening job processing times means that its processing time is a nonincreasing function of its execution start time. Optimal solutions are obtained for some special cases. For the general case, several dominance properties and two lower bounds are developed to construct a branch-and-bound (B&B) algorithm. Furthermore, we propose a heuristic algorithm to overcome the inefficiency of the branch-and-bound algorithm.

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