A polynomial-time approximation scheme for the two-machine flow shop scheduling problem with an availability constraint

2006 ◽  
Vol 33 (8) ◽  
pp. 2143-2153 ◽  
Author(s):  
Joachim Breit
Keyword(s):  
Polynomial Time ◽  
Approximation Scheme ◽  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Scheduling Problem ◽  
Polynomial Time Approximation Scheme ◽  
Availability Constraint ◽  
Time Approximation ◽  
Shop Scheduling ◽  
Polynomial Time Approximation

TWO-MACHINE FLOW SHOP SCHEDULING WITH INDIVIDUAL OPERATION'S REJECTION

2014 ◽  
Vol 31 (01) ◽  
pp. 1450002 ◽  
Author(s):  
QIANG GAO ◽  
XIWEN LU
Keyword(s):  
Approximation Scheme ◽  
Flow Shop ◽  
Dynamic Programming Algorithm ◽  
Flow Shop Scheduling ◽  
Programming Algorithm ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Shop Scheduling ◽  
Processing Times ◽  
Total Penalty

A two-machine flow shop scheduling problem with rejection is considered in this paper. The objective is to minimize the sum of makespan of accepted operations and total penalty of rejected operations. Each job has two operations that could be rejected, respectively. Operations on the first machine have penalties α1 times of their processing times and operations on the second machine have penalties α2 times of their processing times. A [Formula: see text]-approximation algorithm is presented for the case where min{α1, α2} < 1 and max{α1, α2} ≥ 1. A dynamic programming algorithm is provided for general α1 and α2. A fully polynomial-time approximation scheme (FPTAS) is designed for all NP-hard cases.

scholarly journals Strongly Fully Polynomial Time Approximation Scheme for the weighted completion time minimization problem on two-parallel capacitated machines

2017 ◽  
Vol 51 (4) ◽  
pp. 1177-1188 ◽  
Author(s):  
Imed Kacem ◽  
Myriam Sahnoune ◽  
Günter Schmidt
Keyword(s):  
Polynomial Time ◽  
Completion Time ◽  
Approximation Scheme ◽  
Dynamic Programming Algorithm ◽  
Scheduling Problem ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Time Minimization ◽  
Weighted Completion Time ◽  
Polynomial Time Approximation

We consider the total weighted completion time minimization for the two-parallel capacitated machines scheduling problem. In this problem, one of the machines can process jobs until a certain time T1 after which it is no longer available. The other machine is continuously available for performing jobs at any time. We prove the existence of a strongly Fully Polynomial Time Approximation Scheme (FPTAS) for the studied problem, which extends the results for the unweighted version (see [I. Kacem, Y. Lanuel and M. Sahnoune, Strongly Fully Polynomial Time Approximation Scheme for the two-parallel capacitated machines scheduling problem, Int. J. Plann. Sched. 1 (2011) 32–41]). Our FPTAS is based on the simplification of a dynamic programming algorithm. Moreover, we present a set of numerical experiments and we discuss the results.

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