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.

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.

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.

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.

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.