TY - JOUR

T1 - Two-machine flow-shop scheduling with rejection

AU - Shabtay, Dvir

AU - Gasper, Nufar

N1 - Funding Information:
This research was supported by THE ISRAEL SCIENCE FOUNDATION (Grant No. 633/08). Partial support by the Paul Ivanier Center for Robotics and Production Management, Ben-Gurion University of the Negev is also gratefully acknowledged.

PY - 2012/5/1

Y1 - 2012/5/1

N2 - We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1ε)R and a makespan value of at most (1ε)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them.

AB - We study a scheduling problem with rejection on a set of two machines in a flow-shop scheduling system. We evaluate the quality of a solution by two criteria: the first is the makespan and the second is the total rejection cost. We show that the problem of minimizing the makespan plus total rejection cost is NP-hard and for its solution we provide two different approximation algorithms, a pseudo-polynomial time optimization algorithm and a fully polynomial time approximation scheme (FPTAS). We also study the problem of finding the entire set of Pareto-optimal points (this problem is NP-hard due to the NP-hardness of the same problem variation on a single machine [20]). We show that this problem can be solved in pseudo-polynomial time. Moreover, we show how we can provide an FPTAS that, given that there exists a Pareto optimal schedule with a total rejection cost of at most R and a makespan of at most K, finds a solution with a total rejection cost of at most (1ε)R and a makespan value of at most (1ε)K. This is done by defining a set of auxiliary problems and providing an FPTAS algorithm to each one of them.

KW - Approximation algorithm

KW - Bicriteria optimization

KW - FPTAS

KW - Flow-shop scheduling

KW - NP - hard

KW - Pseudo-polynomial time algorithm

KW - Scheduling with rejection

UR - http://www.scopus.com/inward/record.url?scp=80052263693&partnerID=8YFLogxK

U2 - 10.1016/j.cor.2011.05.023

DO - 10.1016/j.cor.2011.05.023

M3 - Article

AN - SCOPUS:80052263693

VL - 39

SP - 1087

EP - 1096

JO - Computers and Operations Research

JF - Computers and Operations Research

SN - 0305-0548

IS - 5

ER -