# 5 clues you should invest in mathematical optimization

September 21, 2021 Blog by Cassotis Consulting

We cannot approach this subject without being sure you know what mathematical optimization is and the main benefits of an optimization model. In short, mathematical optimization is a form to represent and solve complex problems on a large scale. Many applications are found in industrial contexts such as production planning, scheduling, raw material procurement, and supply chain capacity. Since those problems are composed of too many variables and constraints, it is hard for human brains to find an optimal solution. That is why investing in mathematical optimization can have a great economical and productivity impact on a business. However, what are the main clues that your company is suited for optimization?

1. ## The company makes complex decisions

Usually, complex decisions are associated with an extended process chain, but that is a limited vision. A hard problem can happen in short chains, too. Therefore, complexity arises from the challenges people have to consider during the decision-making process. Such challenges can be related to a combinatorial context, non-linear impacts between variables, or the size of the problem. To deploy a mathematical model, it is crucial to map all the decision levers, their relations, and the resources/parameters. Only then it is possible to analyze scenarios with different hypotheses and find their optimal solutions.

1. ## High-impact decisions are taken in an uncoordinated way

When a company has an interconnected set of decisions it is essential to coordinate its departments’ actions because aiming at local objectives may not be the best result for the company. It is easier to verify the gain of opportunities when departments have a global vision. This is the main key for the success of the modeling: use the right tool to make decisions knowing it is oriented for the best global result.

1. ## Constantly changing operating environment

At this point, we are not talking about the big changes in a process, but the little ones that have a big impact. We like to exemplify within the context of raw materials procurement, which directly impacts the production chain. Imagine that you have a list of suppliers with different prices and characteristics. Do you believe that the cheapest could not be the best option? That is true! Maybe its lower procurement cost does not compensate for the product it generates. Its quality can interfere with operational factors in downstream processes, causing extra costs or out-of-specs production.

1. ## Difficulty to match production planning to market demand

All companies need to assign their resources to supply their clients. However, for certain periods those resources are not available for production. Think of maintenance time for machinery and equipment, or vacation of employees, or any other scarce resource in your reality. In addition, in many situations, the clients' demands do not match the company's production capacity. Imagine that you have a large demand during a period of low production capacity. How and when will you reprogram the machines' maintenance and employees’ vacations? The answer is not easy, but with the help of a tool, you can predict peaks in demand and adapt the production planning to find better results.

1. ## Difficulty to estimate process capacities

Companies are constantly unaware of the actual production capacities that their resources allow. Resources are all the means needed to complete a product, for example, raw materials, workers, machines and inventory. Regardless of the resource, if it is inside of the model, it can be optimized. Ask these questions now: "Do I have to stock products? For how long?"; " How much product can be stored?" ; "Should the company buy a new machine for a determined part of the process?"; "What are the production bottlenecks?"; "What is the best delivery route?".

If you frequently ask questions like those, have complex decisions to make and/or need to use resources better, you must optimize your business! There is huge potential for improving the utilization of your resources. Cassotis has developed customized optimization solutions to support its clients' decisions in many business contexts, usually using mathematical modelling. The great advantage of working with these technologies is that they are based on equations. After building the base, you can evolve the model considering new relations fast. The responsiveness of the company can save/gain a lot of money based on new conditions.

Author: Guilherme Martino - Senior Consultant at Cassotis Consulting

Co-author:  Fabio Silva - Senior Manager at Cassotis Consulting

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