Chance-constrained and nonlinear goal programming
In this thesis the chance-constrained linear goal programming approach is developed to cover the following cases when the parameters have non-negative distributions: the exponential and the 'chi-square distributions. Case 1, when the right hand side coefficients are exponential or chi-square random vdriables. Case 2. when the input coefficients are exponential or chisquare random variables. The following have been achieved: For Case 1 1. We have developed a method for constructing deterministic linear goal programs equivalent to the original probabilistic linear goal programs. 2. We have given a probabilistic interpretation to the deviational random variables and the deviational random variable levels. For Case 2 We have developed a method for constructing deterministic nonlinear goal programs through the definition of the probabilistic deviational variables. 4. We have transformed the equivalent deterministic nonlinear goal programs into equivalent signomial goal programs. S. We have developed a computational algorithm for solving nonlinear goal programs generally and, more particularly, deterministic nonlinear goal programs equivalent to chance-constrained goal programs. iii 6. We have proved that Sengupta! s-transformation for obtaining deterministic programs equivalent to chanceconstrained programs does-not lead to solvable programs. 7. We have-formulated and solved a practical application - namely that of finding the "optimal distribution of exports and, imports to the marine, ports" using the methods and the algorithm presented in the thesis. The methods can be used when a program has mixed goals, some with right hand side coefficients or input coefficients that are exponential or chi-square random variables; -others, deterministic, that is without random variable parameters.