#### If your business, which may be large-scale and complex, relies upon data and you want to better meet key objectives, then there is a strong chance that mathematical models can help.

Beyond data analysis and predictive modelling techniques used by most data scientists, optimisation falls into the mathematical heading of prescriptive analytics. Optimisation methods not only extract information from data and explore various ‘what-if scenarios’ to help decision makers understand and assess their landscape and options, but go further by assessing those scenarios and informing the decision maker which is best and why, for any given objective.

## Why use optimisation?

In a world where data is everywhere, technology is ever advancing, and competition is high, it is vital to maximise both;

a) efficiencies in your business given the current level of resources and capacity and;

b) new opportunities and the return on investment these may bring.

Whilst the mathematical sciences may sometimes feel intangible and inaccessible, there is more in common between your business know-how and our application of mathematical models than meets the eye. For instance, in the last paragraph, from both a business and mathematical perspective the key word here is maximise. It is this concept of ‘making the most out of something’ that will build the foundations of an optimisation model, and provide the critical solutions you require for your business.

Note, minimising is also important in terms of reducing your business risks and costs to as little as possible. Optimisation models have the ability to provide solutions that maximise or minimise your primary objective, for example they can:

Maximise
• Profit
• Operational efficiency
• Customer satisfaction
Minimise
• Time
• Costs
• Unmet demand

## What is optimisation?

Optimisation is a mathematical approach that uses the data available and a problem formulation to create optimal (i.e. the best) solutions. There are different types of optimisation techniques, and which one is applicable to any given problem will depend on the type of data and the structure of the problem formulation. We won’t focus on the technical details or the diversity of techniques here, suffice to say that optimisation approaches in general have the ability to handle large-scale complex data in a variety of ways.

Some examples of real-world optimisation problems might be along the lines of:

• minimising operational costs, whilst maintaining stock and buffer levels
• maximising return on agricultural products, balancing growth with market rates
• minimising unmet demand in real time, allowing for rapid technology advances
• maximising customer satisfaction, subject to variations in production chain
• minimising travel time in schedules, ensuring collection and delivery periods are adhered to

The first half of each of these optimisation problem statements refers to the objective: the aspect to be maximised or minimized. The second half of each of these problem statements refers to the constraints:  the conditions under which the optimisation is to perform. It is the objective and the constraints combined that make up the problem formulation, referred to earlier.

Max or Min [Objective] subject to Constraints

Combine this formulation with your business data, and we have the requisites to perform an optimisation approach such that you can reach your business goals.

Visually, think of your data plotted in a large space. The constraints define a region within that space where a solution can exist, this is known as the feasible region. The objective then looks at this feasible region, which in 3D will have peaks and troughs, and identifies where the maximum or minimum lies.

As alluded to above, there are three things to identify in your business to know if optimisation is the right solution for you:

• Does your business use data, that can be large-scale and complex?
• Do you want to improve your business, and can specify what you want to maximise/minimise?
• Is your objective subject to real-world conditions or limitations that you know of?

If you answer yes to all three of the above, then it is likely the problem you face can be approached using optimisation, which will create efficiencies in your business and provide you with the best possible solution going forward.