Thesis (Ph.D.)-Cairo University - Faculty of Computers and Artificial Intelligence - Department of Operations Research and Decision Support

Bibliography: p. 163-170.

The Extremal Algebra is a modern branch of algebra which is concerned with the max or min of the function. The Extremal Algebra included the max-min algebra and min-max which solved the problem in the worst case or best case. The Extremal Algebra is suitable for formulating many real life problems such as logistics problem, transportation problem, supply chain problem and water network, etc. to guarantee the quality of service. This thesis studies the max-min separable optimization problem under max-min separable constraints which was presented in the previous works. This problem was solved by two separate algorithms one finds the optimal solution of optimization problem under max-min inequality constraints and the other algorithm finds the solution in case of equality constraints. Our problem has been studied in stochastic environment to satisfy the real situation of some real problems such as transportation problem, logistic problem... etc. The stochastic parameters have been manipulated in different positions of constraints as (right hand side or left hand side)