Open Access
Research Article
A study of subject allocation to faculties in colleges as a quadratic assignment problem
J. Vijayarangamjvijayarangam75@gmail.comDepartment of Mathematics Sri Venkateswara College of Engineering SriperumbudurChennai, Tamil Nadu, 602117, IndiaView full profile → , Sreelakshmi Subbarayansreelakshmi_maths@sirmvit.eduDepartment of Mathematics Sir M. Visvesvaraya Institute of Technology Krishnadevaraya Nagar Hunasamaranahalli International Airport RoadBangalore, Karnataka, 562157, IndiaView full profile → , *J. ViswanathCorresponding authormathsviswa@gmail.comDepartment of Mathematics Vel Tech Rangarajan Dr. Sagunthala R & D Institute of Science and Technology AvadiChennai, Tamil Nadu, 600062, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 01 Nov 2025
- Published Online:
- 01 Jun 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-2169
- Pages:
- 2381–2390
Abstract
The Quadratic Assignment Problem (QAP) is an optimization problem that deals with the assignment of a set of facilities to an equal number of locations while minimizing the overall cost, based on pairwise distance and flow data. Traditionally applied in fields such as facility layout and scheduling, QAP provides a structured approach to solving complex allocation problems. This paper presents an innovative study that models the subject allocation process in educational institutions as a QAP which would ensure an efficient and balanced assignment of subjects to faculty members and optimize the results. First, we establish the required flow and distance matrices by incorporating faculty experience and the prerequisite dependencies among some chosen subjects. Then, we apply heuristic methods to solve the formulated problem and derive an optimal assignment of subjects to faculty members. The proposed approach aims to provide a systematic and optimized framework for subject allocation, offering valuable insights into resource management in educational institutions.
Keywords
Subject Classifications
90B80
References
[1] J. Kou, “Estimating the number of clusters via the GUD statistic,” J. Comput. Graph. Statist., vol. 23, no. 2, pp. 403–417 (Jun. 2014), doi: 10.1080/10618600.2013.778778. [2] T. C. Koopmans and M. Beckmann, “Assignment problems and the location of economic activities,” Econometrica, vol. 25, no. 1, pp. 53–76 (Jan. 1957).
[3] G. B. Dantzig, “Application of the simplex method to the transportation problem,” in Activity Analysis of Production and Allocation, T. C. Koopmans, Ed. New York: Wiley, pp. 358–373 (1951).[4] G. B. Dantzig, R. Fulkerson, and S. M. Johnson, “Solution of a large-scale traveling-salesman problem,” Journal of the Operations Research Society of America, vol. 2, no. 4, pp. 393–410 (Nov. 1954).[5] T. C. Koopmans and S. Reiter, “A model of transportation,” in Activity Analysis of Production and Allocation, T. C. Koopmans, Ed., Cowles Commission Monograph No. 13, New York, NY, USA: Wiley, pp. 222–259 (1951).[6] Y. Zhou, J. K. Hao, and B. Duval, “Frequent pattern-based search: A case study on the quadratic assignment problem,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 52, no. 3, pp. 1503–1515 (Mar. 2022), doi: 10.1109/TSMC.2020.3027860.[7] E. Arza, A. Perez, E. Irurozki, and J. Ceberio, “Kernels of Mallows models under the Hamming distance for solving the quadratic assignment problem,” Swarm and Evolutionary Computation, vol. 59, Art. no. 100740 (Dec. 2020).[8] A. Acan and A. Ünveren, “A great deluge and tabu search hybrid with two-stage memory support for quadratic assignment problem,” Appl. Soft Comput., vol. 36, pp. 185-203 (Jul. 2015).[9] Y. Aksan, T. Dokeroglu, and A. Cosar, “A stagnation-aware cooperative parallel breakout local search algorithm for the quadratic assignment problem,” Comput. Ind. Eng., vol. 103, pp. 105-115 (Jul. 2017).[10] K. Anstreicher, N. Brixius, J. P. Goux, and J. Linderoth, “Solving large quadratic assignment problems on computational grids,” Math. Program., vol. 91, no. 3, pp. 563-588 (2002).[11] Assignment problem, Wikipedia. [Online]. Available: https://en.wikipedia.org/wiki/Assignment_problem. [Accessed: May 1, 2026] (2026).[12] Quadratic assignment problem, Wikipedia. [Online]. Available: https://en.wikipedia.org/wiki/Quadratic_assignment_problem. [Accessed: May 1, 2026] (2026).[13] A. Khandelwal and A. Kumar, “Exploring fuzzy assignment dynamics: A computational journey with ‘R’,” Journal of Information and Optimization Sciences, vol. 46, no. 3, pp. 815–829 (2025), doi: 10.47974/JIOS-1835.[14] J. Dutta and S. C. Pal, “A note on Hungarian method for solving assignment problem,” Journal of Information and Optimization Sciences, vol. 36, no. 5, pp. 451–459 (2015), doi: 10.1080/02522667.2014.926711.[15] K. J. Hu, “Fuzzy goal programming technique for solving flexible assignment problem in PCB assembly line,” Journal of Information and Optimization Sciences, vol. 38, no. 3–4, pp. 423–442 (2017), doi: 10.1080/02522667.2016.1187922.[16] T. Nakai, “Sequential stochastic assignment problem with rejection,” Journal of Information and Optimization Sciences, vol. 2, no. 2, pp. 169–180 (1981), doi: 10.1080/02522667.1981.10698699.
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