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Course Description:

Use of deterministic and stochastic mathematical models to study and optimize systems. This course includes an introduction to mathematical modeling and the study of linear programming, network models, Markov processes and queuing theory. Students will use computer software for model construction and problem solving.

Prerequisites:

Credit in calculus, probability, statistics, or permission of instructor.

Course Objectives:

• Analyze problem situations and identify the relevant decision variables, parameters, constraints and performance measures associated with those situations.
• Identify and apply appropriate modeling techniques for general classes of problems. Techniques include stochastic and deterministic algorithms such as linear programming, queuing analysis and Markov processes.

Required Topics (approximate weeks allocated):

• Introduction to mathematical modeling (1)
  • Terminology
  • Classification of models
• Linear Programming (3)
  • Formulation
  • Simplex Method
  • Sensitivity Analysis
• Network models (3)
  • Network representations
  • Algorithms for shortest path, minimum spanning tree, maximum flow
• Markov processes (3)
  • Classification of states
  • Steady-state probabilities
  • Absorbing states
• Queuing theory (4)
  • Birth death models
  • Non-birth death models
  • Queuing networks
• Exams (1)