At Inawisdom, we work with clients across multiple sectors to solve their analytical problems. To ensure we always deliver value for our clients and address their challenges in the most appropriate way, we maintain a diverse data science and machine learning toolkit.

In this blog, we will talk about an often-overlooked tool in that toolkit: mathematical optimisation. We’ll look at how to identify an optimisation problem within your organisation and how optimisation can add tangible business value.

When it comes to long-term business growth, efficiency is key. Improving internal processes, making better use of resources and reducing complexity can lead to lower costs, faster delivery of products or services, and better experiences for customers and employees.

Optimisation helps you achieve this – allowing you to make the best decision when faced with complex scenarios that involve multiple variables and outcomes. When the options and trade-offs are too numerous or the constraints and their interactions are too complicated, optimisation not only lets you make the best decision in a given scenario; it also enables you to consider the impact of changing your business processes in a highly efficient way.

What is mathematical optimisation?

Mathematical optimisation is a set of powerful prescriptive analytical tools that enable you to solve complex business problems and make better use of available resources and data.

An optimisation model comprises:

  • decision variables: the things a business can control, such as the order in which jobs are scheduled on a production line; which packages are loaded onto which delivery truck and the route driven; whether an applicant is offered a credit card and at what interest rate; or the date on which maintenance is scheduled;
  • constraints: the business rules that limit the decisions that can be made, such as the capacity of a delivery truck; the distance a truck can drive on a single tank of fuel; the frequency of rest breaks for drivers; the availability of skilled resources; or the capacity of a production line to perform jobs in parallel; and
  • the objective: a measure that captures the goals of the business, such as maximising revenue or customer satisfaction, minimising risk or reducing carbon footprint.

As well as being able to recommend the best decision, by automating the decision-making process, optimisation gives you the freedom to identify inefficiencies and bottlenecks in your current processes and to explore trade-offs, varied scenarios and your assumptions.

How is optimisation applied?

The applications of optimisation are many and varied:

  • In the energy sector, optimising the distribution of power to better meet demand.
  • In financial services, choosing a mix of assets to maximise returns whilst minimising risk or managing a debt book.
  • In logistics, optimising the routing of packages through a shipping network, which can reduce both the miles driven and miles driven empty. This reduces costs and carbon emissions, and increases capacity to satisfy greater demand, which increases revenue.
  • In manufacturing, optimising the scheduling of production to reduce costs, meet customer demand and increase capacity.
  • In sports, scheduling the best possible league of games to maximise attendance and revenue.

But how can you spot an optimisation problem?

The key characteristics of an optimisation problem are:

  • business goals that require some measure to be improved (either maximised or minimised) – profitability, production volume, process efficiency, risk (the objective);
  • business rules and processes that limit the choices available to the decision maker (the constraints);
  • specific levers that the decision maker has in their control – what to do and what not to do; when to do things and in what order (the decision variables);
  • a large number of alternatives to consider – so many that assessing them manually is time consuming or impractical; and
  • a business imperative to improve things with a clear return on investment.

How do data science and machine learning combine with optimisation?

Data science and machine learning provide predictions of how a system will respond to changes, which allows an optimisation model to assess the impact of alternative configurations of the decision variables and determine the best action.

These predictions capture uncertainties due to factors outside the control of the decision maker and can be incorporated into both:

  • the objective, to assess the impact of uncertainty on a measure; and
  • the constraints, to assess whether different decisions will mean a given configuration of decision variables is not viable.

For example, a revenue objective when making decisions about allocating credit depends on both the interest rate and uncertainty about how much an applicant will borrow and how likely they are to default on payments. Similarly, satisfying a customer delivery window (the constraints) depends on the route driven by a delivery van and uncertainties in travel time due to congestion.

Optimisation and machine learning solve different problems; but real impact comes from combining the two approaches.

Optimisation in action: How can you optimise predictive maintenance?

Maintaining your portfolio of physical assets – whether that’s production machines, a fleet of vehicles, or any other equipment – requires a balance between keeping the assets functioning properly and minimising the disruption to business operations. A fixed schedule can mean that some assets are serviced too soon, before it’s really needed, so that you end up paying for maintenance unnecessarily. Others are maintained too late, resulting in reduced productivity or even asset failures and damage – leading to additional repair costs that could have been avoided by timely maintenance.

Predictive models, based on historical data and streamed data input from IoT sensors on your assets, give an indication of the condition of an individual asset and when maintenance is due. But how do you identify the best time to maintain individual assets to avoid peaks and troughs of maintenance, and to ensure engineers with the right skills are available at the right time?

Optimisation can solve this predictive maintenance problem. The decision variables include:

  • when to maintain each asset,
  • where to maintain each asset (where there is a choice),
  • which engineers to allocate to the maintenance of each asset, and
  • the scheduling of individual tasks.

The constraints include:

  • the availability of engineers, including planned and unplanned absences;
  • the engineer’s skillset (do they match the minimum requirement for a given task?); and
  • the capacity of a given maintenance location to accommodate multiple assets in parallel.

The objective function will minimise several factors simultaneously, whilst accounting for the impact of delaying maintenance:

  • the cost of maintenance,
  • the cost of taking an asset out of service, and
  • the impact on asset efficiency and CO2 emissions of maintenance.

Within the optimisation model, predictive models can be used to forecast how asset condition will degrade over time based on factors such as age and the expected workload, as well as how different levels of maintenance will impact condition.

Knowing how an asset’s condition will decline over time due to wear-and- tear, combined with a model of how different maintenance levels improve the asset’s condition, allows the optimisation model to determine the best maintenance schedule.


Optimisation models give you the tools to make the most efficient and effective use of your business’ resources whilst maximising revenue and customer satisfaction. By accounting for the business objective, decision variables and constraints, optimisation models can help you make better decisions and develop more efficient processes across a wide range of use cases.

If you’re looking to get started with optimisation technology, Inawisdom can help. Our “discover first, invest later” approach can help tackle your most pressing business problems and achieve significant return on investment.