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
Cephalosporin C fed-batch cultivation undergoes great fluctuations. Some key state variables, such as product concentration and carbon source consumption, are very difficult to measure on-line, while these variables a...Cephalosporin C fed-batch cultivation undergoes great fluctuations. Some key state variables, such as product concentration and carbon source consumption, are very difficult to measure on-line, while these variables are essential to process monitoring and control.A neural network based software prediction of the key state variables for cephalosporin C fed-batch fermentation was investigated. A rolling learning-prediction procedure was used to deal with the time variant property of the process, and was also demonstrated to be beneficial to improving prediction accuracy.The successful prediction of the product formation enabled on-line evaluation of the economic performance of a charge and made optimal scheduling possible.The prediction approach was validated with the data of 49 industrial charges.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Cephalosporin C fed-batch cultivation undergoes great fluctuations. Some key state variables, such as product concentration and carbon source consumption, are very difficult to measure on-line, while these variables are essential to process monitoring and control.A neural network based software prediction of the key state variables for cephalosporin C fed-batch fermentation was investigated. A rolling learning-prediction procedure was used to deal with the time variant property of the process, and was also demonstrated to be beneficial to improving prediction accuracy.The successful prediction of the product formation enabled on-line evaluation of the economic performance of a charge and made optimal scheduling possible.The prediction approach was validated with the data of 49 industrial charges.
