Many aspects of our modern life are affected by mathematical optimisation. Imagine an arbitrary day in your life. You wake up, get ready and commute to work by taking a local train. Here, you encounter your first major application area of mathematical optimisation: public transport. All kinds of aspects are optimised to provide a good service as efficiently as possible: the placement of stations and design of lines, the distribution of trains or buses to the lines during the day matching the demand, as well as the assignment of drivers to vehicles, such that regular working hours and sufficient breaks are ensured.
A day full of optimisation
You arrive at work and find your daily list of tasks. In service jobs like maintenance or renovation, which require each person to finish a bunch of projects each day, the assignment of projects to the available workers is usually optimised as well. The goal is to best match the project’s requirements to the skills of each worker, while minimising travel distance and thereby maximising the overall profit of the company. So, you grab all the tools you need today, jump on your cargo bike, and set off to your first assignment. You don’t need to think about the route, but just follow the optimised tour calculated by your navigation app.
After work, you make a quick stop at your local grocery store. Again, there is a lot of optimisation involved to ensure that the shelves are filled with fresh goods every day. Apart from a good demand forecast, this requires well-optimised logistics in the background and an optimised supply chain of groceries moving from harvesting and production into each of the shops.
In the evening, there is the long-anticipated match of your soccer club against their archenemy, and you head to the stadium. Albeit not the most well-known application, the schedule of major sports leagues is usually the result of an optimisation model as well. Here, the difficulty lies in finding a match plan for the season, which fulfils the vast variety of constraints. Next to the obvious balancing of home and away games for each team, the promotion department wants a good distribution of highlight matches over the season, local holidays block certain dates, and the arena management wants to avoid conflicts with concert planning.
Beyond the everyday examples
So, you see, while most of it happens in the background, mathematical optimisation touches many aspects of our day-to-day life. Of course, there are numerous other applications areas of mathematical optimisation. If you are interested in more concrete examples, have at look at our previous cases in the energy sector and on supply chain. Or just contact us directly if you are interested in more details about any of the mentioned topics, we would love to tell you more!