Wilson Models and its Applications in Decision Sciences


  • Bui Anh Tuan Department of Mathematics Education, School of Education, Can Tho University, Vietnam Author
  • Thu-Quang Luu Faculty of Finance, Banking University of Ho Chi Minh City, Vietnam Author
  • Shin-Hung Pan Department of M-Commerce and Multimedia Applications, Asia University, Taiwan Author
  • Wing-Keung Wong Department of Finance, Fintech Center, and Big Data Research Center, Asia University, Taiwan Corresponding Author




Wilson model, Management system, Economics


Purpose:  The problems of getting the optimal order quantity and reducing reserve management costs play an abundantly important role in economics and several other disciplines such as construction, business, and finance. Thus, it is tremendously meaningful to study the issues.

Design/methodology/approach:  Wilson is a ubiquitous model utilized to get optimize order quantity and reduce reserve management costs. This model was first developed by Harris (1913) and followed up by Wilson (1934) who expanded it to become a Wilson model. Although the Wilson model has been used for a very long time, the theory and applications of this model need to be stated clearly and systematically. To bridge the gap in the literature in this area and provide academics and practitioners with an overview of the Wilson model, in this paper, we explore the issue.

Findings:  We first introduce the general concepts and principles of reserve management. We then present the origin and workaround of the Wilson model and exhibit two examples to illustrate the approach. In addition, we also provide some applications of the Wilson model in Economics.

Originality/Value:  All of the issues presented and discussed in this paper are unique and new in the field.

Practical implications:  This work will help people interested in finance and economics have the best plan to carry out the work in the most cost-effective and efficient way.


Alfaro, L., & Kanczuk, F. (2009). Optimal reserve management and sovereign debt. Journal of International Economics, 77(1), 23-36.

Bakar, M. A. A., Nasir, N. M., Razak, F. D. A., Kamsi, N. S., & Ahmad, A. C. (2018). Provision for Bad & Doubtful Financing and Contingency Reserve Management: Assessing Resilient and Stable Islamic Banks. The Journal of Social Sciences Research, 621-627.

Borio, C., Galati, G., & Heath, A. (2008). FX reserve management: trends and challenges. BIS papers.

Cagnano, A., Bugliari, A. C., & De Tuglie, E. (2018). A cooperative control for the reserve management of isolated microgrids. Applied energy, 218, 256-265.

Castillo-Eguskitza, N., Hoyos, D., Onaindia, M., & Czajkowski, M. (2019). Unraveling local preferences and willingness to pay for diferent management scenarios: A choice experiment to Biosphere Reserve management (No. 2019-05).

Dong, F., Chowdhury, B. H., Crow, M. L., & Acar, L. (2005). Improving voltage stability by reactive power reserve management. IEEE transactions on Power Systems, 20(1), 338-345.

Dooley, M. P., Folkerts-Landau, D., & Garber, P. (2004). The revived Bretton Woods system: the e ects of periphery intervention and reserve management on interest rates & exchange rates in center countries (No. w10332). National Bureau of Economic Research.

Edeki, S. O., Okoli, D. C., Ahmad, H., & Wong, W. K. (2021). Approximate series solutions of a one-factor term structure model for bond pricing. Annals of Financial Economics, 16(04), 1-22.

Feillet, D., Dejax, P., Gendreau, M., & Gueguen, C. (2004). An exact algorithm for the elementary shortest path problem with resource constraints: Application to some vehicle routing problems. Networks: An International Journal, 44(3), 216-229.

Ferreira, A., Zimmermann, H., Santos, R., & von Wehrden, H. (2018). A SocialEcological Systems Framework as a Tool for Understanding the E ectiveness of Biosphere Reserve Management. Sustainability, 10(10), 3608.

Gallo, G., & Pallottino, S. (1988). Shortest path algorithms. Annals of operations research, 13(1), 1-79.

Guimarães, P. R., Candido, O., & Ronzani, A. (2021). Regularization methods for estimating a multi-factor corporate bond pricing model: An application for Brazil. Annals of Financial Economics, 16(01), 2150005.

Han, S. (2017). Managerial Behavior on Risk Taking and Reserve Management for Insurance Companies.

Han, S., Lai, G. C., & Ho, C. L. (2018). Corporate transparency and reserve management: Evidence from US property-liability insurance companies. Journal of Banking & Finance, 96, 379-392.

Harris, F. W. (1913). How many parts to make at once. Factory, the Magazine of Manage-ment. 10: 135136, 152.

Hon, T. Y., Moslehpour, M., & Woo, K. Y. (2021). Review on behavioral finance with empirical evidence. Advances in Decision Sciences, 25(4), 1-30.

Howe, H. F. (1984). Implications of seed dispersal by animals for tropical reserve manage-ment. Biological Conservation, 30(3), 261-281.

Islam, F., Tiwari, A. K., & Wong, W. K. (2021). Editorial and Ideas for Research Using Mathematical and Statistical Models for Energy with Applications. Energies, 14(22), 7611.

Jaiswal, R., Gupta, S., & Tiwari, A. K. (2022). Delineation of Blockchain Technology in Finance: A Scientometric View. Annals of Financial Economics, 2250025.

Lee, S. M., Pho, K. H., & Li, C. S. (2021). Validation likelihood estimation method for a zero-inflated Bernoulli regression model with missing covariates. Journal of Statistical Planning and Inference, 214, 105-127.

Little, R. J.: Regression with missing Xs: a review. Journal of the American Statistical Association, 87(420), 1227-1237 (1992).

McAleer, M. (2021). A critique of recent medical research in JAMA on COVID-19. Advances in Decision Sciences, 25(1), 1-102.

Mohan, V., Singh, J. G., & Ongsakul, W. (2015). An e cient two stage stochastic optimal energy and reserve management in a microgrid. Applied Energy, 160, 28-38.

Moslehpour, M., Pan, S. H., Tiwari, A. K., & Wong, W. K. (2021). Editorial in Honour of Professor Michael McAleer. Advances in Decision Sciences, 25(4), 1-14.

Nhan, D. T. T., Pho, K. H., ANH, D. T. V., & McAleer, M. (2021). Evaluating the efficiency of Vietnam banks using data envelopment analysis. Annals of Financial Economics, 16(02), 2150010.

Pallottino, S., & Scutella, M. G. (1998). Shortest path algorithms in transportation models: classical and innovative aspects. In Equilibrium and advanced transportation modelling (pp. 245-281). Springer, Boston, MA.

Pho, K. H. (2022). Goodness of fit test for a zero-inflated Bernoulli regression model. Communications in Statistics-Simulation and Computation, 1-16.

Pho, K. H. (2022). Improvements of the Newton–Raphson method. Journal of Computational and Applied Mathematics, 408, 114106.

Rahman, A. M., & Chowdhury, A. H. (2016, December). Reactive power reserve manage-ment to prevent voltage collapse in Bangladesh power system. In 2016 9th International Conference on Electrical and Computer Engineering (ICECE) (pp. 423-426). IEEE.

Rezaei, N., & Kalantar, M. (2015). Stochastic frequency-security constrained energy and reserve management of an inverter interfaced islanded microgrid considering demand response programs. International Journal of Electrical Power & Energy Systems, 69, 273-286.

TajMazinani, M., Hassani, H., & Raei, R. (2022). A Comprehensive Review of Stock Price Prediction Using Text Mining. Advances in Decision Sciences, 26(2), 116-152.

Truong, B. C., Pho, K. H., Nguyen, V. B., Tuan, B. A., & Wong, W. K. (2019). Graph Theory and Environmental Algorithmic Solutions to Assign Vehicles: Application to Garbage Collection in Vietnam, Advances in Decision Sciences, 23(3), 1-35 (2019).

Truong, B. C., Pho, K. H., Dinh, C. C., & McAleer, M. (2021). Zero-inflated Poisson regression models: Applications in the sciences and social sciences. Annals of Financial Economics, 16(02), 2150006.

Poole, W. (1968). Commercial bank reserve management in a stochastic model: implications for monetary policy. The Journal of finance, 23(5), 769-791.

Vandoorn, T. L., Vasquez, J. C., De Kooning, J., Guerrero, J. M., & Vandevelde, L. (2013). Microgrids: Hierarchical control and an overview of the control and reserve management strategies. IEEE industrial electronics magazine, 7(4), 42-55.

Wilson, R. H. (1934). A scienti c routine for stock control. Harvard University.

Wong, W. K. (2020). Review on behavioral economics and behavioral finance. Studies in Economics and Finance. 37(4), 625-672. https://doi.org/10.1108/SEF-10-2019-0393.

Wong, W.K. 2021. Editorial Statement and Research Ideas for Behavioral Financial Economics in Emerging Market. International Journal of Emerging Markets 16(5), 946-951. https://doi.org/10.1108/IJOEM-07-2021-991

Wong, W. K. (2022). Editorial Statement and Research Ideas on Using Behavioral Models in Environmental Research and Public Health with Applications. International Journal of Environmental Research and Public Health, 19(12), 7137.

Woo, K. Y., Mai, C., McAleer, M., & Wong, W. K. (2020). Review on efficiency and anomalies in stock markets. Economies, 8(1), 20.

Wright, O. T., Cundill, G., & Biggs, D. (2018). Stakeholder perceptions of legal trade in rhinoceros horn and implications for private reserve management in the Eastern Cape, South Africa. Oryx, 52(1), 175-185.

Zhao, T., Li, Y., Pan, X., Wang, P., & Zhang, J. (2017). Real-time optimal energy and reserve management of electric vehicle fast charging station: Hierarchical game approach. IEEE Transactions on Smart Grid, 9(5), 5357-5370.

Zhou, C., Zhao, Y., Connelly, J. W., Li, J., & Xu, J. (2017). Current nature reserve management in China and effective conservation of threatened pheasant species. Wildlife Biology, 2017(4).



How to Cite

Bui Anh Tuan, Thu-Quang Luu, Shin-Hung Pan, & Wong, W.-K. (2023). Wilson Models and its Applications in Decision Sciences. Advances in Decision Sciences, 26(5), 15-39. https://doi.org/10.47654/v26y2022i5p15-39