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
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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 -