scholarly journals A Note on a Fully Polynomial-Time Approximation Scheme for Minimizing Makespan of Deteriorating Jobs

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Long Wan
Keyword(s):  
Polynomial Time ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Polynomial Time Approximation

scholarly journals Scheduling Simple Linear Deteriorating Jobs with Rejection

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Juan Zou ◽  
Yuzhong Zhang
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Release Dates ◽  
Polynomial Time Approximation Scheme ◽  
Machine Model ◽  
Time Approximation ◽  
Total Penalty ◽  
Polynomial Time Approximation

We consider the problems of scheduling deteriorating jobs with release dates on a single machine (parallel machines) and jobs can be rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. For a single machine model, the objective is to minimize the maximum lateness of the accepted jobs plus the total penalty of the rejected jobs. We show that the problem is NP-hard in the strong sense and presents a fully polynomial time approximation scheme to solve it when all jobs have agreeable release dates and due dates. For parallel-machine model, the objective is to minimize the maximum delivery completion time of the accepted jobs plus the total penalty of the rejected jobs. When the jobs have identical release dates, we first propose a fully polynomial time approximation scheme to solve it. Then, we present a heuristic algorithm for the case where all jobs have to be accepted and evaluate its efficiency by computational experiments.

SCHEDULING PROPORTIONALLY DETERIORATING JOBS IN TWO-MACHINE OPEN SHOP WITH A NON-BOTTLENECK MACHINE

2011 ◽  
Vol 28 (05) ◽  
pp. 623-631 ◽  
Author(s):  
SHISHENG LI
Keyword(s):  
Polynomial Time ◽  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Open Shop ◽  
Ordinary Sense ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Decision Version ◽  
Bottleneck Machine ◽  
Polynomial Time Approximation

We address the problem of scheduling proportionally deteriorating jobs in two-machine open shop in which one of the machines is non-bottleneck. The objective is to minimize the makespan. We show that the decision version of the problem is [Formula: see text]-complete in the ordinary sense, and present for it a fully polynomial-time approximation scheme.

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