When we think about medicine, we usually focus on its effect: How does the drug work against this particular disease?
Manufacturing effective medicines is, of course, a top priority for Danish pharmaceutical giant Novo Nordisk. But that is just one of many elements of pharmaceutical production. Production planning is extremely complex and there are many criteria for success. In addition to creating an effective drug, Novo Nordisk also needs to ensure that production is completed on time, that sufficient quantities of the product are made, but also that stocks are not too full, and finally that production capacity is fully utilized by manufacturing several different products at the same plants.
To ensure optimal planning, Novo Nordisk is now trying something new, says Deenesh K. Babi, Senior Project Manager at Novo Nordisk.
"There are many parameters in the planning-what is the best combination? Mathematical modelling helps us answer that question," says Deenesh K. Babi.
Novo Nordisk is the number one insulin producer for diabetes treatment in the world. In fact, Novo Nordisk produces 50 per cent of the world's insulin supply at its facilities in Kalundborg, Denmark. This means that more than 34 million people worldwide use the Danish pharmaceutical giant's diabetes products every year. In addition, Novo Nordisk also produces drugs to treat obesity, haemophilia, and growth disorders.
Testing a new idea
Like many other pharmaceutical manufacturers, Novo Nordisk has been using large spreadsheets to plan production-until now.
"Excel is an excellent tool, but the spreadsheet can only solve basic problems. When we come across a complex issue, we need complex tools," says Deenesh K. Babi.
Planning the medicine production is an increasingly complex task for Novo Nordisk. That is why the company reached out to DTU Chemical Engineering, which works with mathematical modelling of biochemical processes and production. To begin with, Novo Nordisk tested the idea of whether mathematical modelling could help them optimize production by hiring a student assistant from DTU. This turned out to be a success, and subsequently two master's projects were carried out in collaboration with DTU Chemical Engineering, and in 2021 Simon Brædder Lindahl started a PhD project that will lead to the development of a mathematical modelling tool with broad application in the pharmaceutical production at Novo Nordisk.
Mathematical modelling
When Simon B. Lindahl started the project, his method of choice was integer programming or MILP (Mixed-Integer Linear Programming). Integer programming is commonly used in logistical planning, including in aviation when planning the aircrew roster and determining the routes of each aircraft in order to fully utilize capacity.
"The great thing about integer programming is that you can show whether the plan can actually be implemented, and you can also find the best solution. There are other methods, but they can only indicate a possible solution, and not necessarily the best one," says Simon B. Lindahl.
Moreover, a linear mathematical solution takes less computing time than a nonlinear solution, which is another benefit.
The result of Simon's work is a digital copy of Novo Nordisk's production system combined with a method for evaluating the current capacity, the effect of system changes, and the possibility of producing several products on the same production lines.
The list of input parameters that Simon B. Lindahl is juggling is a testament to how complex the planning is: It includes available production capacity, yield per production step, stock requirements, changeover time between different processes and planned shutdown periods-just to name the most important ones.
One of the benefits of using this type of modelling in production planning is that it is possible to test different scenarios, says Gürkan Sin, Professor at DTU Chemical Engineering and Simon B. Lindahl's supervisor. For example, you can use the modelling tool to model different ways of adding an extra product, so that you avoid building up an unnecessarily large production capacity if it is possible to solve the challenge in a different way.
Morning ritual
To illustrate how changes to the individual parts of a production can lead to an optimization of the entire process, Deenesh K. Babi uses an example from everday life: the morning ritual. We get up, take a shower, maybe we make coffee, eat breakfast, prepare a packed lunch, go to the train station, and go to work.
What if we could take five minutes off the morning ritual? Maybe we could start the coffee machine and let it brew while taking a shower, or we could take the bike to the station instead of walking? Then we could catch a train that leaves five minutes earlier, and if that train is a direct train with fewer stops than the one we usually take, then we could also cut ten minutes off our commute. The result would be arriving at work 15 minutes earlier just by cutting off five minutes of the morning ritual. It's simple mental arithmetic.
Pharmaceutical production planning applies the same principles, but it is a much more complex reality and it is not possible to calculate an optimized production schedule in your head. However, with the help of a mathematical model, you can find the parameters that you need to adjust to get the best result.
For Simon B. Lindahl, it is important to point out what the goal of developing a mathematical model is-and what it is not.
"The goal of developing the mathematical model is to produce a tool that can support decision-makers, not to make the decision for you," Simon says.
He is part of a team where others take his models and adapt them to the exact production that is being planned.
Scaling out
Deenesh K. Babi sees many perspectives in the modelling project. The model can certainly be used when scaling up production. But scaling out is just as important:
"Can the model be used in exactly the same way in other parts of the production? This is an important aspect," says the Senior Project Manager, thus putting into words the concept of scaling out.
The tool will not only create value locally. It will be expanded across a larger part of the company and in that way become even more valuable.
Deenesh points to the DTU collaboration as an integral part of the way Novo Nordisk can continue to grow. By collaborating with students and young researchers, Novo Nordisk can stay at the forefront of research and development and ensure that it is using state-of-the-art solutions.
