TITLE:
Randomized Objective Function Linear Programming in Risk Management
AUTHORS:
Dennis Ridley, Felipe Llaugel, Inger Daniels, Abdullah Khan
KEYWORDS:
Linear Programming, Random, Objective Function, Profit Distribution, Risk, Monte Carlo Simulation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.3,
March
9,
2021
ABSTRACT: The traditional linear programming model is deterministic. The way that uncertainty is handled is to compute the range of optimality. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each objective function coefficient, one at a time. This yields the range of optimality within which the decision variables remain constant. This sensitivity analysis is useful for helping the analyst get a sense for the problem. However, it is unrealistic because objective function coefficients tend not to stand still. They are typically profit contributions from products sold and are subject to randomly varying selling prices. In this paper, a realistic linear program is created for simultaneously randomizing the coefficients from any probability distribution. Furthermore, we present a novel approach for designing a copula of random objective function coefficients according to a specified rank correlation. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendency, spread, skewness and extreme values for the purpose of risk analysis. This enables risk analysis and business analytics, emerging topics in education and preparation for the knowledge economy.