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

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  • Zhang, Xingong

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.

Suggested Citation

  • Zhang, Xingong, 2021. "Two competitive agents to minimize the weighted total late work and the total completion time," Applied Mathematics and Computation, Elsevier, vol. 406(C).
    • Handle: RePEc:eee:apmaco:v:406:y:2021:i:c:s0096300321003751
    DOI: 10.1016/j.amc.2021.126286
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    Cited by:

    1. Sterna, Małgorzata, 2021. "Late and early work scheduling: A survey," Omega, Elsevier, vol. 104(C).
    2. Chen, Rubing & Geng, Zhichao & Lu, Lingfa & Yuan, Jinjiang & Zhang, Yuan, 2022. "Pareto-scheduling of two competing agents with their own equal processing times," European Journal of Operational Research, Elsevier, vol. 301(2), pages 414-431.
    3. Shi-Sheng Li & Ren-Xia Chen, 2022. "Minimizing total weighted late work on a single-machine with non-availability intervals," Journal of Combinatorial Optimization, Springer, vol. 44(2), pages 1330-1355, September.

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