Optimization Theory

In this chapter, we will look at three different classes of problems: Linear Programming (LP), Integer Programming (IP) and Non-linear Programming (NLP) problems. Under IP, we will look at Pure Integer Programming, Mixed Integer Programming (MIP) and Binary Integer Programming (BIP). Specifically, for BIP, we can learn how to use binary variables to convert intractable LP or IP problems to become tractable. Finally, we will also look at NLP to understand the characteristics of NLP solutions and conditions, which allow us to determine if the solution obtained is a global optimal solution. We will end the chapter with two case studies on how optimization concepts and models are applied in a real-world scenario to optimize the container mix for carbon footprint reduction.