TY - JOUR

T1 - Coordinating scheduling and rejection decisions in a two-machine flow shop scheduling problem

AU - Shabtay, Dvir

AU - Gerstl, Enrique

N1 - Publisher Copyright:
© 2024 Elsevier B.V.

PY - 2024/8/1

Y1 - 2024/8/1

N2 - We study a two-machine flow shop scheduling problem where any operation can be rejected at a certain cost. A solution for such a problem requires two sets of decisions. The first involves the partition of the set of operations into two subsets: the set of operations that are accepted for scheduling in the shop, and the set of rejected operations. The second decision involves scheduling the set of accepted operations in the shop. The objective is to find a solution that minimizes the sum of the makespan and the total rejection cost. We prove that the problem is NP-hard even if all processing operations have identical processing times and identical rejection costs on either one of the two machines. We show, however, that the problem is fixed parameterized tractable with respect to a parameter that combine the number of different processing times on both machines with the number of different rejection costs on one out of the two machines. We also provide a pseudo-polynomial time algorithm for the problem, which we then convert into a fully polynomial time approximation scheme. This is achieved by dividing the problem into a set of subproblems and deriving a fully polynomial time approximation scheme for each one of them, separately. Finally, we present an integer linear programming formulation of the problem and two simple 2-approximation algorithms.

AB - We study a two-machine flow shop scheduling problem where any operation can be rejected at a certain cost. A solution for such a problem requires two sets of decisions. The first involves the partition of the set of operations into two subsets: the set of operations that are accepted for scheduling in the shop, and the set of rejected operations. The second decision involves scheduling the set of accepted operations in the shop. The objective is to find a solution that minimizes the sum of the makespan and the total rejection cost. We prove that the problem is NP-hard even if all processing operations have identical processing times and identical rejection costs on either one of the two machines. We show, however, that the problem is fixed parameterized tractable with respect to a parameter that combine the number of different processing times on both machines with the number of different rejection costs on one out of the two machines. We also provide a pseudo-polynomial time algorithm for the problem, which we then convert into a fully polynomial time approximation scheme. This is achieved by dividing the problem into a set of subproblems and deriving a fully polynomial time approximation scheme for each one of them, separately. Finally, we present an integer linear programming formulation of the problem and two simple 2-approximation algorithms.

KW - Approximation algorithms

KW - Flow shop

KW - Integer linear programming

KW - Rejection

KW - Scheduling

UR - http://www.scopus.com/inward/record.url?scp=85188698771&partnerID=8YFLogxK

U2 - 10.1016/j.ejor.2024.03.021

DO - 10.1016/j.ejor.2024.03.021

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85188698771

SN - 0377-2217

VL - 316

SP - 887

EP - 898

JO - European Journal of Operational Research

JF - European Journal of Operational Research

IS - 3

ER -