Are they really optimized?
Who guarantees us that the planning we propose for our fleet cannot be improved?
Suppose we have to visit 10 points (customers, warehouses, bars, depots…) starting from our central warehouse (the 11 red points in the first image):
What is the optimal order to visit them in such a way that we travel as few kilometers as possible?
This is a classic problem in Operations Research, the TSP (Travelling Salesman Problem) for one vehicle; or the VRP (Vehicle Routing Problem) for more than one vehicle.
The first question we ask ourselves (or should ask ourselves) is how many possible routes are there… Indeed, many (in the image we show 3 examples). But let’s be more precise, we may be surprised:
- If the problem had only 2 nodes and only one vehicle, there would be 2! routes (factorial of 2 = 2 x 1), i.e. 2 possible routes (from A to B, or from B to A).
- If the problem had 3 nodes, we go up to the factorial of 3, 3! = 3 x 2 x 1 = 6 possible plannings.
- But, if we increase to the 11 nodes in our image, we go to the hair-raising figure of 11! = 39.916.800 possible plannings. In effect, almost 40 million possible solutions.
And the worst thing is not only that, but most of our logistical problems often contain more pickup (or delivery) points for goods and certainly more than one vehicle. Just to give one more example, a problem with 50 nodes and 10 vehicles has 50! × 9! = 1,10 × 1070 solutions.
Who can guarantee that the planning we propose for our fleet cannot be improved?
In the following image we show in a very graphic way the capacity of improvement in the KPIs associated to the daily planning of our fleet when we plan our operations with a solution such as MathIT.Logistics.
If we could order these millions of possible schedules from worst to best, we would have, on the one hand, the worst (the red dot) and the best (blue dot).
In our experience, the planning that a human-expert usually performs (orange dot) is always far from optimal, even if he/she spends many hours on this hard – and of ephemeral value – task.
Well, with MathIT.Logistics we can significantly improve, in seconds or minutes, the human-expert using very powerful and scientifically proven algorithms in all kinds of VRP problems.
And what is improvement?
We mean the profitability of the operation, the total costs, the number of vehicles required, the kilometers used, the service levels of the operation, always depending on the most important requirements or objectives for each customer and each scenario.
And how much can the human-expert be improved?
Logically, it depends on the complexity of the problem and the specific scenario, restrictions or operating environment conditions, but you can improve between 10% and 20% in these indicators, in addition to many other additional benefits that, in order not to make this post too long, we will leave pending for a future publication.
Do the math and tell us about it!
Acerca del autor
Professor at the Pablo de Olavide University (UPO) and PhD in Mathematics from the University of Seville. Senior Optimization Consultant at oga.
Passionate about Mathematics, as a fundamental science, but especially about Applied Mathematics. What motivates him most is solving real problems and that is why, after more than 20 years of experience, he has worked in Pure Mathematics, Operations Research, Multiobjective Optimization, Evolutionary Computation and finally in Machine Learning and Business Analytics.