Two competitive agents to minimize the weighted total late work and the total completion time

Xingong Zhang

Applied Mathematics and Computation, 2021, vol. 406, issue C

Abstract: This paper studies deterministic constraint optimization problem with two competitive agents in which the following objective functions on a single machine: the total weighted late work and the total completion time. We show that the constraint optimization problem is the binary NP-hard by Knapsack problem reduction. Furthermore, we present a pseudo-polynomial time algorithm by early due date maximum not-late sequence, and an approximation Pareto curve by dynamic programming algorithm and two eliminated states, which time complexity of the two approximation algorithms are O(nA2nBQ∑(pjA+pjB)) and O(n4θ2logUBAlogUBB), where pj,θare processing time of job Jj, a given positive constant, and UBx an upper bound of the objective function of agent x,x∈{A,B}. Finally, we present a simple approximation algorithm by the earliest due date (EDD) rule, which jobs of agent B are assigned an dummy due date.

Keywords: Two competitive agent; Single-machine scheduling; Total late work; Approximation algorithm (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003751

DOI: 10.1016/j.amc.2021.126286

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