Operations Research (1): Models and Applications

Course Provided by: National Taiwan University
Course Taken on: Coursera
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Description

Operations Research (OR) is a field in which people use mathematical and engineering methods to study optimization problems in Business and Management, Economics, Computer Science, Civil Engineering, Industrial Engineering, etc. This course introduces frameworks and ideas about various types of optimization problems in the business world. In particular, we focus on how to formulate real business problems into mathematical models that can be solved by computers.

Knowledge

  • Formulate different types of mathematical models to tackle optimizationproblems with business applications.
  • Technically, the concepts and applicationsof Linear Programming, Integer Programming, and Nonlinear Programming will be delivered.
  • Solve an optimization problem with oneof the most accessible software: Microsoft Excel.

Outline

  • Course Overview
  • Prelude
  • 1-1: Motivation.
  • 1-2: Business analytics.
  • 1-3: Mathematical programming.
  • 1-4: History.
  • 1-5: Preview for this course.
  • NTU MOOC course information
  • Quiz for Week 1
  • Linear Programming
  • 2-0: Opening.
  • 2-1: Introduction.
  • 2-2: Elements of a mathematical program (1).
  • 2-3: Elements of a mathematical program (2).
  • 2-4: Linear programming.
  • 2-5: Graphical approach.
  • 2-6: Three types of LPs.
  • 2-7: Simple LP formulation - Product mix.
  • 2-8: Simple LP formulation - Production and inventory.
  • 2-9: Simple LP formulation - Personnel scheduling.
  • 2-10: Compact LP formulation - Production and Inventory.
  • 2-11: Compact LP formulation – Product mix.
  • 2-12: Computers – The Solver add-in and Example 1 – producing desks and tables.
  • 2-13: Computers – Example 2: personnel scheduling.
  • 2-14: Closing remarks.
  • Quiz for Week 2
  • Integer Programming
  • 3-0: Opening.
  • 3-1: Introduction.
  • 3-2: IP formulation (1).
  • 3-3: IP formulation (2).
  • 3-4: Facility location – Overview.
  • 3-5: Facility location – Covering.
  • 3-6: Facility location - UFL.
  • 3-7: Machine scheduling - Overview.
  • 3-8: Machine scheduling - Completion time minimization.
  • 3-9: Machine scheduling - Makespan minimization.
  • 3-10: Traveling salesperson problem - Basics.
  • 3-11: Traveling salesperson problem - Subtour elimination.
  • 3-12: Computers – Example 1 – personnel scheduling.
  • 3-13: Computers – Example 2 – facility location.
  • 3-14: Closing remarks.
  • Quiz for Week 3
  • Nonlinear programming
  • 4-0: Opening.
  • 4-1: Introduction.
  • 4-2: The EOQ problem.
  • 4-3: Formulating the EOQ model.
  • 4-4: The portfolio optimization problem.
  • 4-5: Portfolio optimization.
  • 4-6: Linearizing an absolute value function.
  • 4-7: Linearizing max_min functions.
  • 4-8: Linearizing products 1A.
  • 4-9: Linearizing products 1B 1C and 1D.
  • 4-10: Linearizing products 2A.
  • 4-11: Linearizing products 2B, 2C, and 2D.
  • 4-12: Remarks - why linearization.
  • 4-13: Computers – Portfolio optimization problem.
  • 4-14: Closing remarks.
  • Quiz for Week 4
  • Case Study: Personnel Scheduling
  • 5-0: Opening.
  • 5-1: Background and motivation.
  • 5-2: Research objective.
  • 5-3: Problem description - objective.
  • 5-4: Problem description - constraints.
  • 5-5: Model formulation - objective.
  • 5-6: Model formulation - constraints.
  • 5-7: Results.
  • 5-8: Closing remarks.
  • Quiz for Week 5
  • Course Summary and Future Directions
  • 6-1: Review for this course.
  • 6-2: Preview for the next course.
  • A story that never ends.
  • Quiz for Week 6
  • English
  • 孔令傑 (Ling-Chieh Kung)
  • Coursera