Dash, Afaf Aly.El (1984) Chanceconstrained and nonlinear goal programming. PhD thesis, Prifysgol Bangor University.

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Abstract
In this thesis the chanceconstrained linear goal programming approach is developed to cover the following cases when the parameters have nonnegative distributions: the exponential and the 'chisquare distributions. Case 1, when the right hand side coefficients are exponential or chisquare 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 chanceconstrained goal programs. iii 6. We have proved that Sengupta! stransformation for obtaining deterministic programs equivalent to chanceconstrained programs doesnot lead to solvable programs. 7. We haveformulated 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 chisquare random variables; others, deterministic, that is without random variable parameters.
Item Type:  Thesis (PhD) 

Uncontrolled Keywords:  Mathematical statistics Operations research 
Subjects:  Degree Thesis 
Departments:  College of Physical and Applied Sciences > School of Computer Science Degree Thesis 
Date Deposited:  14 May 2015 04:09 
Last Modified:  31 Aug 2016 10:46 
URI:  http://e.bangor.ac.uk/id/eprint/4076 
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