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Optimizing Bidders Selection of Multi-Round Procurement Problem in Software Project Management Using Parallel Max-Min Ant System Algorithm

Dac-Nhuong Le1,2,3,*, Gia Nhu Nguyen2,4, Harish Garg5, Quyet-Thang Huynh6, Trinh Ngoc Bao7, Nguyen Ngoc Tuan8

1 Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam
2 Faculty of Information Technology, Duy Tan University, Da Nang, 550000, Vietnam
3 Faculty of Information Technology, Haiphong University, Haiphong, 180000, Vietnam
4 Graduate School, Duy Tan University, Da Nang, 550000, Vietnam
5 School of Mathematics, Thapar Institute of Engineering and Technology, Patiala, 147004, India
6 Hanoi University of Science and Technology, Hanoi, 100000, Vietnam
7 Hanoi University, Hanoi, 100000, Vietnam
8 Department of ICT, Ministry of Education and Training, Hanoi, 100000, Vietnam

* Corresponding Author: Dac-Nhuong Le. Email:

(This article belongs to this Special Issue: Emerging Computational Intelligence Technologies for Software Engineering: Paradigms, Principles and Applications)

Computers, Materials & Continua 2021, 66(1), 993-1010.


This paper presents a Game-theoretic optimization via Parallel MinMax Ant System (PMMAS) algorithm is used in practice to determine the Nash equilibrium value to resolve the confusion in choosing appropriate bidders of multi-round procurement problem in software project management. To this end, we introduce an approach that proposes: (i) A Game-theoretic model of multiround procurement problem (ii) A Nash equilibrium strategy corresponds to multi-round strategy bid (iii) An application of PSO for the determination of global Nash equilibrium. The balance point in Nash Equilibrium can help to maintain a sustainable structure not only in terms of project management but also in terms of future cooperation. As an alternative of procuring entities subjectively, a methodology to support decision making has been studied using Nash equilibrium to create a balance point on benefit in procurement where buyers and suppliers need multiple rounds of bidding. Our goal focus on the balance point in Nash Equilibrium to optimizing bidder selection in multi-round procurement which is the most beneficial for both investors and selected tenderers. Our PMMAS algorithm is implemented based on MPI (message passing interface) to find the approximate optimal solution for the question of how to choose bidders and ensure a path for a win-win relationship of all participants in the procurement process. We also evaluate the speedup ratio and parallel efficiency between our algorithm and other proposed algorithms. As the experiment results, the high feasibility and effectiveness of the PMMAS algorithm are verified.


Cite This Article

D. Le, G. Nhu Nguyen, H. Garg, Q. Huynh, T. Ngoc Bao et al., "Optimizing bidders selection of multi-round procurement problem in software project management using parallel max-min ant system algorithm," Computers, Materials & Continua, vol. 66, no.1, pp. 993–1010, 2021.


This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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