How and why mathematical optimization is used to support decision-making?

Even if mathematical optimization is the most consolidated technology providing a very high return on investment, it is yet the most unknown and undervalued.

I guess that one of the main reasons for this Cinderella-like status is the fact that it is not easy to explain. Especially when the explanations are provided by an expert on the topics.

Let me give try to show what mathematical optimization is using a real-world example. The bad news of these months spot-lighted how tricky is the supply chain in the natural gas logistic. For a description of how natural gas supply actually works, you can read a past post at this link: https://www.linkedin.com/feed/update/urn:li:activity:6934516223577620480/

Simplifying the treatment as much as possible, a mathematical optimization system is described by the following structures:

1. There is a set of variables, called decision variables. The value assigned in output to these variables represents the quantitative result, the solution, that we are looking for. For example, how much natural gas to buy each day from a long-term supply contract is an example of a decision variable.
2. The value to be assigned to decision variables is limited by a set of constraints. Each solution must be compatible with the constraints. For example, the volumes of gas purchased each day are between a minimum and a maximum; at the same time, the volumes purchased in a month must be limited by a monthly minimum and a monthly maximum. At the same time, the volumes purchased in a year must be between an annual minimum and an annual maximum.
3. Among all possible solutions, the mathematical optimization system must provide one that maximizes or minimizes an objective function. For example, the solution must minimize the cost of procurement conditioned to a share of the risk that we can bear.

One very important thing. With the actual technology, most part of optimization problems doesn’t need a specific algorithm to be written in some programming language. Indeed, there are many valuable pieces of software, both commercial and free, that accept in input the description of the problem to be solved, i.e. variables, constraints, and objective function.

With such technologies, we move the programming of a mathematical optimization tools into the realm of descriptive programming, i.e. the analyst has to provide a description of the problem to solve rather than the algorithmic steps to perform.

This paradigm shift is a real game changer because take affordable the development of solvers for real-world and complex problems. And, most valuable, the adaptation to changes in business domains, such as the introduction of new technologies or new regulations.

Would you like to understand how mathematical optimization can be applied to your own business? Feel free to contact me ^_^