American Journal of Modeling and Optimization
ISSN (Print): 2333-1143 ISSN (Online): 2333-1267 Website: https://www.sciepub.com/journal/ajmo Editor-in-chief: Dr Anil Kumar Gupta
Open Access
Journal Browser
Go
American Journal of Modeling and Optimization. 2020, 8(1), 7-14
DOI: 10.12691/ajmo-8-1-2
Open AccessArticle

Sensitivity Analysis in Linear Fractional Programming with Optimality Condition

Ladji Kané1, , Moussa Konaté1, Moumouni Diallo1 and Lassina Diabaté1

1Department of Applied Mathematics, Faculté des Sciences Economiques et de Gestion, Bamako, Mali

Pub. Date: September 25, 2020

Cite this paper:
Ladji Kané, Moussa Konaté, Moumouni Diallo and Lassina Diabaté. Sensitivity Analysis in Linear Fractional Programming with Optimality Condition. American Journal of Modeling and Optimization. 2020; 8(1):7-14. doi: 10.12691/ajmo-8-1-2

Abstract

In this paper, an overview of theoretical and methodological issues in simplex method-based sensitivity analysis is proposed. The paper focuses somewhat on developing shortcut methods to perform Linear Fractional Programming (LFP) sensitivity analysis manually and in particular changes in the parameter of the LFP model. Shortcut methods for conducting sensitivity analysis have been suggested. Simple examples are given to illustrate this proposed method.

Keywords:
LFP model sensitivity analysis simplex

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  E.B. Bajalinove, Linear Fractional Programming: Theory, Methods, Applications and Software, Kluwer Academic Publishers, 2003.
 
[2]  E.B. Bajalinove, A. Tangian, Adjusting objective function to a given optimal solution in linear and linear fractional programming, in: A. Tangian, J. Gruber (Eds.), Constructing and Applying Objective Functions, in: Lecture Notes in Economics and Mathematical Systems, 510, Springer, 2001.
 
[3]  Arsham, H. (1992). Post optimality analysis of the transportation problem. The Journal of the Operational Research Society, 43(2), 121-139.
 
[4]  Anderson, D. R., Sweeney, D. J., Williams, T. A., & Wisniewski, M. (2009). An introduction to management science: quantitative approaches to decision making. South-Western CENGAGE Learning UK.
 
[5]  Bazaraa, M., & Jarvis, J. (1990). Linear Programming and Network Flows. New York: Wiley.
 
[6]  Baird, B. F. (1990). Managerial Decisions Under Uncertainty. An Introduction to the Analysis of Decision Making. New York, USA: Wiley.
 
[7]  Bradley, S., Hax, A., & Magnanti, T. (1977). Applied Mathematical Programming. Reading, MA: Addison-Wesley.
 
[8]  Bianchi, C., & Calzolari, G. (1981). A simulation approaches to some dynamic properties of econometric models. In: Mathematical Programming and its Economic Applications, 607-21.
 
[9]  Clemson, B., Tang, Y., Pyne, J., & Unal, R. (1995). Efficient methods for sensitivity analysis. Syste Dynamics Review, 11(1), 31-49.
 
[10]  Dantzig, G. B. (1963). Linear Programming and Extensions. A report prepared for United States Air Force Projected Rand. Retrieved from http://www.rand.org/content/dam/ rand/pubs/reports/2007/R366part1.pdf.
 
[11]  Dantzig, G. B. (1978). Are dual variables prices? If not, how to make them more so. Technical report. Systems Optimization Laboratory, Department of Operations Research Stanford University.USA
 
[12]  Eschenbach, T. G. & McKeague, L. S. (1989). Exposition on using graphs for sensitivity analysis. The Engineering Economist, 34(4), 315-333.
 
[13]  Gal, T. (1979). Postoptimal Analysis, Parametric Programming, and Related Topics. New York, USA: McGraw-Hill.
 
[14]  Gal, T., & Greenberg, H. J. (1997). Advances in sensitivity analysis and parametric programming. Boston: Kluwer.
 
[15]  Gass, S. (1985). Linear Programming: Methods and Applications, 5th ed. New York: McGraw-Hill
 
[16]  Hamby, D. M. (1994). A review of techniques for parameter sensitivity analysis of environmental models. Environmental Monitoring and Assessment Journal, 32, 135-154.
 
[17]  Khan, U. I., Bajuri, H. N., & Jadoon, A. I. (2008). Optimal production planning for ICI Pakistan using linear programming and sensitivity analysis. International Journal of Business and Social Science, 2(23), 206-212.
 
[18]  Luenberger, D. (1984). Linear and Nonlinear Programming, 2d ed. Reading, Mass: Addison-Wesley.
 
[19]  Murty, K. (1983). Linear Programming. New York: Wiley.
 
[20]  Murty, K. (1995). Operations Research: Deterministic Optimization Models 1st Edition. Prentice Hall.
 
[21]  Taha, H. (2010). Operations Research: An Introduction, 9th Edition. USA.
 
[22]  Yang, B. H. (1990). A study on sensitivity analysis for a non-extreme optimal solution in linear programming (Ph.D. Thesis). Seoul National University, Republic of Korea.