Elements of systems management, including decision styles, human information processing, organizational decision processes, and information system design for planning and decision support. Emphasis is on relating theory to practice via written analyses and oral presentations of individual and group case studies. 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 large-scale problems are presented. Nonlinear programming methods are introduced.
Combinatorial analysis is introduced with particular focus on solving integer programming problems.
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 queuing models, inventory models, storage models, and time series models. Emphasis is given to the properties of mathematical representations of systems, to the methods used to analyze mathematical models, and to the translation of concrete situations into appropriate mathematical forms. Primary coverage includes ordinary linear differential and difference equation models, transform methods and concepts from classical control theory, and state-variable methods and concepts from modern control theory. Applications are drawn from social, economic, managerial, and physical systems.