Chance constrained linear programming with exponential family coefficients / Maha Ismail Mahfouz Ismail ; Supervised Abdelnser Saad

Thesis (M.Sc.) - Cairo University - Faculty of Economics and Political Sciences - Department of Statistics

Linear Programming model is an important tool used to solve constrained optimization problems. In fact, the real life problems are usually occurring in the presence of uncertainty. Therefore, the use of the Probabilistic Linear Programming model with random coefficients has drawn much attention in recent years. One of the most frequently used approaches to solve the Probabilistic Linear Programming model is the Chance Constrained Linear Programming approach. In this thesis, a Chance Constrained Linear Programming model with Exponential Family coefficients is proposed, in case of individual Chance Constraints and joint Chance Constraints. Considering the Exponential Family is motivated by its inclusion of most of the commonly used probability distributions. Therefore, the achieved model is general and applicable to many different situations. The proposed model is introduced in different forms depending on the source of randomness; 1) the Univariate model with the R.H.S coefficient or one of the L.H.S technologic coefficients is a random variable, 2) the Bivariate model with both of the R.H.S coefficient and one of the L.H.S technologic coefficients are random variables, and 3) the Multivariate model with some or all of the L.H.S technologic coefficients are random variables. Moreover, the performance of the proposed model is shown by applying it to some numerical examples

Issued also as CD