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 consid...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.展开更多
Traditional linear program (LP) models are deterministic. The way that constraint limit uncertainty is handled is to compute the range of feasibility. After the optimal solution is obtained, typically by the simplex m...Traditional linear program (LP) models are deterministic. The way that constraint limit uncertainty is handled is to compute the range of feasibility. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each constraint limit, one at a time. This yields the range of feasibility within which the solution remains feasible. This sensitivity analysis is useful for helping the analyst get a feel for the problem. However, it is unrealistic because some constraint limits can vary randomly. These are typically constraint limits based on expected inventory. Inventory may fall short if there are overdue deliveries, unplanned machine failure, spoilage, etc. A realistic LP is created for simultaneously randomizing the constraint limits from any probability distribution. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendencies, spread, skewness and extreme values for the purpose of risk analysis. The spreadsheet design presented is ideal for teaching Monte Carlo simulation and risk analysis to graduate students in business analytics with no specialized programming language requirement.展开更多
文摘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.
文摘Traditional linear program (LP) models are deterministic. The way that constraint limit uncertainty is handled is to compute the range of feasibility. After the optimal solution is obtained, typically by the simplex method, one considers the effect of varying each constraint limit, one at a time. This yields the range of feasibility within which the solution remains feasible. This sensitivity analysis is useful for helping the analyst get a feel for the problem. However, it is unrealistic because some constraint limits can vary randomly. These are typically constraint limits based on expected inventory. Inventory may fall short if there are overdue deliveries, unplanned machine failure, spoilage, etc. A realistic LP is created for simultaneously randomizing the constraint limits from any probability distribution. The corresponding distribution of objective function values is created. This distribution is examined directly for central tendencies, spread, skewness and extreme values for the purpose of risk analysis. The spreadsheet design presented is ideal for teaching Monte Carlo simulation and risk analysis to graduate students in business analytics with no specialized programming language requirement.
