Utilizes real-world case studies, for which students must develop systems management and integration strategies. Conceptual and theoretical foundations of mathematical programming techniques. A brief review of linear programming and the simplex method is followed by developments in duality theory and post- optimality analysis. Special methods to solve transportation, networks, and multiobjective programming problems are presented. Nonlinear programming methods include both constrained and unconstrained optimization techniques and algorithms.
Combinatorial analysis is introduced with particular focus on solving integer programming problems.
An in-depth introduction to stochastic systems theory and applications in systems engineering. Markov chains, Poisson processes, birth and death processes, renewal processes, martingales, Brownian motion, stationary processes and ergodic theory. Survey of stochastic models and applications, including queueing models, inventory models, storage models, and time series models. Introduction to stochastic dynamic programming. Emphasis is on the foundations of artifical intelligence, problem solving, search, and decision making with a view toward real world applications.