TY - JOUR

T1 - Scheduling under linear constraints

AU - Nip, Kameng

AU - Wang, Zhenbo

AU - Wang, Zizhuo

PY - 2016/9/1

Y1 - 2016/9/1

N2 - We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job completion time among all feasible choices. This novel problem is motivated by various real-world application scenarios. We discuss the computational complexity and algorithms for various settings of this problem. In particular, we show that if there is only one machine with an arbitrary number of linear constraints, or there is an arbitrary number of machines with no more than two linear constraints, or both the number of machines and the number of linear constraints are fixed constants, then the problem is polynomial-time solvable via solving a series of linear programming problems. If both the number of machines and the number of constraints are inputs of the problem instance, then the problem is NP-Hard. We further propose several approximation algorithms for the latter case.

AB - We introduce a parallel machine scheduling problem in which the processing times of jobs are not given in advance but are determined by a system of linear constraints. The objective is to minimize the makespan, i.e., the maximum job completion time among all feasible choices. This novel problem is motivated by various real-world application scenarios. We discuss the computational complexity and algorithms for various settings of this problem. In particular, we show that if there is only one machine with an arbitrary number of linear constraints, or there is an arbitrary number of machines with no more than two linear constraints, or both the number of machines and the number of linear constraints are fixed constants, then the problem is polynomial-time solvable via solving a series of linear programming problems. If both the number of machines and the number of constraints are inputs of the problem instance, then the problem is NP-Hard. We further propose several approximation algorithms for the latter case.

KW - Approximation algorithm

KW - Computational complexity

KW - Linear programming

KW - Parallel machine scheduling

UR - http://www.scopus.com/inward/record.url?scp=84977995902&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84977995902&partnerID=8YFLogxK

U2 - 10.1016/j.ejor.2016.02.028

DO - 10.1016/j.ejor.2016.02.028

M3 - Article

AN - SCOPUS:84977995902

VL - 253

SP - 290

EP - 297

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 2

ER -