Study on Linear Programming in Risk Management

Abstract

The traditional linear programming model is deterministic. Calculating the range of optimality is one technique to deal with uncertainty. After obtaining the best solution (usually using the simplex approach), the effect of altering each objective function coefficient one at a time is considered. This gives the optimality range, which is the range in which the choice variables remain constant. This sensitivity analysis is helpful in getting a sense of the situation for the analyst. It is, however, impractical because objective function coefficients do not tend to remain constant. They are often profit contributions from things sold, and their selling prices change at random. For simultaneously randomising the coefficients from any probability distribution, a realistic linear programme is generated. We also provide a novel method for constructing a copula of random objective function coefficients based on a given rank correlation. The relevant objective function value distribution is produced. For the purposes of risk analysis, this distribution is investigated directly for central tendency, spread, skewness, and extreme values. Risk analysis and business analytics are major subjects in education and knowledge economy preparation.