APPLIED MATHEMATICS


Course Credits: 3 Units

Prerequisites: Math 114

Math 183 - Linear and Integer Programming

Course Description

Origin and nature of operations research; linear programming models and formulation, graphical method, simplex method, duality theory, sensitivity analysis; transportation problem, transshipment problem, assignment problem; integer-linear programming model and formulation, branch and bound method, cutting-plane algorithm, implicit enumeration

Course Learning Outcomes

After completion of the course, the student should be able to:

  1. Discuss the basic concepts and methodology of operations research.
  2. Formulate a mathematical model or representation of real-world problems.
  3. Apply appropriate methods in solving linear and integer programs; and transportation models and its variants.
  4. Perform graphical and analytical sensitivity analysis.
Course Outline

UNIT 1. Linear Programming (LP) Formulation and Graphical Solution

  1. Introduction to Operations Research
  2. Linear Programming Formulation
  3. Graphical LP Solution
  4. Solution Forms
  5. Graphical Sensitivity Analysis

UNIT 2. Simplex Method

  1. Standard Form of an LP Model
  2. Simplex Method in Maximization Problem
  3. Simplex Method in Minimization Problem
  4. Artificial Starting Solution
  5. Special Cases in the Simplex Method

UNIT 3. Duality and Post-Optimal Analysis

  1. Construction of the Dual from the Primal
  2. Optimal Dual Solution
  3. Simplex Tableau Computations
  4. Economic Interpretation of Duality
  5. Dual Simplex Method
  6. Post-Optimal Analysis
  7. Algebraic Sensitivity Analysis

UNIT 4. Integer Programming and Transportation Model

  1. Integer Programming Algorithms
  2. Transportation Model
  3. Finding Starting Basic Feasible Solution of a Transportation Problem
  4. Transportation Algorithm
  5. Transshipment Model
  6. Assignment Model