Sensitivity and Joint Investment Analyses of a Multi-objective Investment Optimization Model of two Businesses in Ghana

Stephen B. Twum1 and Jones Akanyare2
1Department of Mathematics, C. K. Tedam University of Technology & Applied Sciences
2Department of Mathematics, University for Development Studies, Tamale, Ghana
DOI – http://doi.org/10.37502/IJSMR.2022.51201

Abstract

This paper is a further development of an earlier work reported in the literature by the authors. In that work, the investment problems of two businesses in Ghana were formulated as bi-objective optimization models in which their expected returns and risks were optimized simultaneously using real data from the two.  The current work investigates the two models under a sensitivity analysis and about the potential benefits that a joint investment could hold for the two businesses. The rates of return parameters were identified as the most likely to vary over the period of the investments. Therefore, they were varied up and down by 5% and up and down by 10%, considered as reasonable levels of variation. A random selection procedure was employed to obtain two random sets of rates of return parameter values for the two businesses, from which expected return and risk values were obtained for each of the models. The results of running the models (in MATLAB) showed that the impact of parameter variations was not significant, as far as the Pareto optimal solutions which are the amounts to invest, were concerned; the objective function values of returns and variances varied however, since their coefficient values varied with the values of the parameters varied. The formulated joint model produced results that showed that a joint investment could be more profitable than separate investments, even though that had a much higher risk.

Keywords: Sensitivity analysis, Variation of parameters, Joint modeling, Pareto optimal solutions.

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