Operations Research (1): Models and Applications

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.

• Course Overview
• This lecture gives students an overview of what they may expect from this course, including the fundamental concept and brief history of Operations Research. We will also talk about how mathematical programming can be used to solve real-world business problem.
• Linear Programming
• Linear programming (LP) is one of the most important method to achieve the outcome of optimization problems. We can use LP models for various decisions, including production, inventory, personnel scheduling, etc.
• Integer Programming
• In many practical areas, some of the optimization problems occur with integrality constraints imposed on some of the variables. Facility location, machine scheduling, and vehicle routing are some examples. Integer Programming (IP) provides a mathematical way to solve these problems.
• Nonlinear programming
• In the real life, many problems involve nonlinearities. Examples include pricing, inventory, and portfolio optimization. For such problems, we may use Nonlinear Programming (NLP) to formulate them into models and solve them.
• Case Study: Personnel Scheduling
• In this lecture, we introduce a real business case that has been solved with Operations Research by the instructor. The problem is for a company to schedule its customer service representatives to minimize the total amount of staff shortage. We will demonstrate the problem, process of conducting an OR study, integer programming formulation, and result.
• Course Summary and Future Directions
• In the final lecture of this course, we will summarize what we have learned. We will also preview what we may learn in future courses.