scholarly journals Polynomial Time Approximation Scheme for Two Parallel Machines Scheduling with a Common Due Date to Maximize Early Work

2017 ◽  
Vol 174 (3) ◽  
pp. 927-944 ◽  
Author(s):  
Malgorzata Sterna ◽  
Kateryna Czerniachowska
Keyword(s):  
Polynomial Time ◽  
Parallel Machines ◽  
Approximation Scheme ◽  
Polynomial Time Approximation Scheme ◽  
Due Date ◽  
Common Due Date ◽  
Time Approximation ◽  
Parallel Machines Scheduling ◽  
Polynomial Time Approximation

TWO APPROXIMATION SCHEMES FOR SCHEDULING ON PARALLEL MACHINES UNDER A GRADE OF SERVICE PROVISION

2012 ◽  
Vol 29 (05) ◽  
pp. 1250029 ◽  
Author(s):  
WEIDONG LI ◽  
JIANPING LI ◽  
TONGQUAN ZHANG
Keyword(s):  
Polynomial Time ◽  
Parallel Machines ◽  
Approximation Scheme ◽  
Approximation Schemes ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Running Time ◽  
Grade Of Service ◽  
Special Case ◽  
Polynomial Time Approximation

We consider the offline scheduling problem to minimize the makespan on m parallel and identical machines with certain features. Each job and machine are labeled with the grade of service (GoS) levels, and each job can only be executed on the machine whose GoS level is no more than that of the job. In this paper, we present an efficient polynomial-time approximation scheme (EPTAS) with running time O(n log n) for the special case where the GoS level is either 1 or 2. This partially solves an open problem posed in (Ou et al., 2008). We also present a simpler full polynomial-time approximation scheme (FPTAS) with running time O(n) for the case where the number of machines is fixed.

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