Mathematical Optimization

Expect the unexpexcted – with mathematical optimization

“Expect the unexpected” – this is a saying that is frequently heard. As logical and intuitive as this message may sound, it is seldom put into practice in the business world. This is because the exact opposite is the case in many companies’ planning processes: You plan with the expected in mind; in other words, on the basis of historical data. However, it seems as if those days are over.

AI and Machine Learning alone cannot withstand disruption

Even the most sophisticated technology such as AI or Machine Learning are not in the position to ward off disruption. The problem isn’t the technology itself  but the data with which it works as this data often consists of historical values. However, it is in the nature of disruption to radically break with the past so that historical data is unsuitable for predicting an uncertain future.


Mathematical optimization lets you deal with an uncertain future

If historical data is no longer sufficient to predict the future, then this is where mathematical optimization comes in. Why? It enables you to create an image of your business in which all the relevant parameters are represented. Each change, no matter how great, no matter how short-term, can be simulated and integrated into the planning process. The result is always an optimal target achievement which considers all the given circumstances. How does this work? Let’s explain the three core components step by step.

1.) The optimization model: A complex reality becomes mathematics

The first and most important step is to transfer your company, along with all of its relevant data and dependencies, into a mathematical model. This procedure is frequently termed as “the digital twin”. The term is misleading insofar as it implies that the entire venture would be depicted. However, the only part that is actually depicted is the one which is deemed relevant for a specific optimization issue. Otherwise the model would not only be unnecessarily complex but its calculation would take far too long in practice. The optimization targets, on the other hand, are important. These are often maximation or minimization targets (for example, maximizing profitability or minimizing manufacturing costs). The optimization can be geared towards several targets. These are prioritized and weighed up among each other. In this way, it is possible to align competing objectives.

But one thing after the other. A mathematical model thus consists of:

a) Decision variables

This concerns decisions which need to be made during the course of the planning process. Let’s take a fictional example from the area of production planning: here you have to make decisions on manufacturing sequences, decisions regarding machine scheduling, decisions on personnel costs and so on.

b) Parameters

Parameters limit your scope for action. In our example these could be: maximum stock, maximum store capacity, machines working at full capacity, maximum affordable staff capacity, maximum throughput times, etc.

c) Optimization targets

Targets determine how the mathematical model should work. Based on our example, the target could be: maximum machine capacity with the highest profitability.

Based on these requirements the model in our example calculates a production plan which has the machines running at full capacity, prefers products with as large a contribution margin as possible, avoids extraordinary bonuses and shift bonuses and maximizes throughput. Of course, this is a very simplified example yet it shows fairly clearly how the mathematical optimization model works.

2.) The algorithm: The optimization model in use

The presence of the mathematical model certainly does not solve an optimization problem just yet. To do this, it needs highly sophisticated software. This is what brings the mathematical model to life. For the user it also serves as a user interface which makes daily work with data and optimization processes possible in the first place.

3.) The solver: the calculating power for the algorithm

In order to be able to use the mathematical model which has been transferred into the algorithm, we need special solvers. These process the data and make the algorithms applicable. They go through an inconceivably large amount of potential decisions and calculate possible solutions for the optimization problem along all framework parameters. While doing so they continuously compare the results until an optimal solution has been found. Solvers are available from several providers which offer both commercial and free licenses.

Using mathematical optimization to prevent disruption

If you want to take your planning to the next level then mathematical optimization offers an unbeatable advantage for your business.  COVID-19 is most certainly a prime example of disruptive events at present, yet we encounter disruptions in many different areas. Natural catastrophes, extreme weather conditions, geo-political upheavals, extreme demand fluctuations – there are so many examples of parameters which make traditional planning based on historical data become obsolete. Curious? Contact us to learn more.

Mathematical Optimization

Is it worth deploying mathematical optimization in your business?
Find the answers in our factsheet

In our factsheet What are the benefits of mathematical optimization? we ask 5 questions to help you assess whether mathematical optimization brings benefits to your organization.

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