How Do I Optimize Workforce Scheduling When Resources Are Short?

The optimizer in the background

Welcome to Circonomit Labs. Today is about combinatorics. At some point I'll also get our applied mathematician in front of the camera, who has done a lot of teaching and explains this very well. For a pragmatic example, though, it's enough if I do it today. I prepared this example for a talk at a logistics trade fair.

We are often asked what is technically behind our product. One core piece, not the only one but a powerful one, is an optimizer. Solvers have existed for many years, and the maths behind language models wasn't exactly invented yesterday either. The exciting part is: how do I even define an optimization problem without mathematicians spending a very long time on it?

What is a combinatorics problem? In a simple optimization I want, for example, to make a profit: if I sell more products or raise the price, more money comes out mathematically, as long as demand doesn't drop. Then you set up a maximization or minimization function. Allocation in logistics is different, especially for the most important bottleneck: qualified employees.

Example: parcels, trucks and drivers

I want to deliver a parcel. For that I need a truck and, as long as there are no autonomous trucks, fortunately also a person. Plus diesel and a route on which an accident might happen or a road might be closed, and 7,000 other influencing factors. Anyone who has to deliver many products always has an allocation problem: is the vehicle available, is the person available? You make money on the delivered goods, and punctuality and on-time delivery play a role too.

Whether you make money depends heavily on whether you calculated correctly. Planned costs are nothing new, but they are surprisingly often not calculated well. In the ideal process, the truck would be filled exactly and all parcels would go to a similar region. Reality is not optimal; the parcels go to two cities instead of one, for example. This is where Circonomit comes in: mapping reality digitally in an easy-to-use way, without the model escalating and leaving you no closer to a decision.

Prioritizing customers as a strategic question

Then there is a huge list of parcels and customers that differ in importance. One is our favourite customer. Another one too, because we earn the most with him, he pays quickly and well. And then there is a customer who isn't our favourite but on whom we depend, because so much order volume hangs on him that we'd lose a lot of volume without him, even if the margin isn't good.

A person can no longer simply calculate this. You can follow it cognitively, but weighing everything against everything with all the numbers and chains in your head becomes difficult. Our method is the same as always: start with the most important decision. Here it is: how do I allocate my most important qualified employees so that I have as few disruptions and outages as possible and workforce scheduling matches revenue planning according to customer importance and contribution margin?

This is where combinatorics comes in, because you have to combine conditions. A simple example: 100 orders need to be delivered, there are 10 trucks, seven cities, and three drivers are sick. How do we allocate the remaining drivers to trucks and cities so that the parcels are delivered in the best possible order?

Workforce scheduling that matches revenue planning

Are we a route planning system? No, we solve optimization problems. Can you optimize routes with it? Sure, but that isn't our scope in the first step. We care about the value of the decision. Workforce scheduling is a decision about where employees are deployed. How I prioritize customers is a strategic question. Combinatorics makes sure the square peg goes into the square hole and the round one into the round hole, and that utilization is as good as possible.

That way I know, as an entrepreneur, scheduler or head of controlling, that my financial bottom line is as good as possible, and whoever assigns the shifts has satisfied employees and very good utilization. All our models have this in common: the translation between strategy and operations. Strategically you have to define how important each customer is. Is volume more important because otherwise we'd shrink significantly? Is a certain market strategically important? Strategy can only be implemented through operational KPIs, such as the utilization rate of drivers and trucks, linked to the money that counts in the end.

That's why there are almost always at least two people at the table with us: one optimizes in percent, the other in euros, and in the end it has to work for the company. Otherwise local optimizations lead to the financial plan saying you can cut ten positions while operations say they need ten more. That's a delta of 20 positions, which quickly adds up to a million a year. Whoever untangles this once and knows the ideal headcount and scheduling quickly saves a high six to seven figure amount with a simple decision model.

We say: we build decision models so that companies make good decisions. Our mathematician says: we build maths models so that at some point nobody has to do maths anymore and everyone can still use mathematical methods for very good decisions.