Industry meets mathematics: modelling, simulating and optimizing the stock of an automotive spare parts wholesaler

Executive summary

This collaboration between the Laboratory for Mathematical Engineering (LEMA) and the NORS group, allowed this big player in the Portuguese automotive spare parts market to have an efficient management of their stocks and orders. The project included automatic warning systems, suggested order quantities, and a new system for replacing the traditional ABC leading to considerable gains considering both the quantity in stock as well as the level of service.


Challenge overview

The NORS Group, through their aftermarket spare parts business, identified some needs on developing a mathematical model to support the activities of their operations department. With this purpose, they presented this challenge to LEMA, wondering if industrial mathematics could help them to solve the following problem. Daily, the operations department – group main responsible for the stock management in this business – processes a big amount of data in order to give an efficient response to the company needs in terms of stock.  With that purpose, an efficient tool for forecast analysis was needed, as well as a model that allowed some parameterizations in order to accomplish the manager’s decisions regarding the quality of service ratio desired. A particular characteristic of this problem is that the references set have very different behaviours regarding the amount of sales per month. Indeed, the same product family may have high rotation references and also very low rotation products leading to the need of applying very different methodologies and forecast techniques.

In the end, industrial and mathematical partners agreed on developing a completely new tailor-made model, based on updated techniques of forecasting that allows the managers to parameterize the amount of risk they want to take in terms of quality of service parameters. This model returns, an optimal quantity to be ordered regarding each of the references on their portfolio and with respect to a determined objective function developed.

Implementation of the initiative

This project was initiated with the NORS team responsible for this department, a statistician and a numerical mathematician from LEMA, who later were joined by an Engineering Mathematics MSc student. In order to find a good balance between accuracy and speed of execution, several meetings were held to discuss intermediate results, allowing NORS to assess the model’s adherence to reality and to use their feedback to adapt the model even more closely to NORS reality. This was made with success, and the first prototype was concluded in 6 months.


The problem

There were some main concerns with this challenge: first the heterogeneity of data made very challenge to find a model that fits all the references used by NORS. Second, the scalability and complexity of the model were a concern as there were more than 200.000 references to be analysed and the outputs must be calculated in some acceptable time. Also, the model should adapt easily if the company changes their policy in terms of quality of service, budget or other parameters.

Results and achievements

A new mathematical model for stock management of spare parts was developed. Six months after the model implementation with several families of products being tested, the level of service raised 1%, the mean stock value decreased about 12%, in a period where the sails increased more than 2%. It was also developed a software tool that implement automatically all the features that NORS asked in the beginning of the project, as well as some upgrades made during the development phase. An easy to use graphical user interface was developed to operate the software, reducing the order processing times in more than 70%, when compared with NORS native system.


Lessons learned and replicability

The LEMA team who worked on this project found it very challenging as it relies on several mathematical fields, needed a real team work to address the different questions posed by the industrial partner. Also, developing the model, seeing the upgrade in the quality of the results and, at the same time, being sure that mathematics was helping a company and their workers daily was fantastic. Finally, being able to complete all the project phases (from modelling to the software development) recurring only to mathematicians and to know that, with this work, they helped to improve the viewing of mathematics in the industrial community was the ultimate reward, specially when this project opened the first position for a mathematician inside the NORS group.

In the NORS point of view, this was a big challenge because it configured a different approach to one of their most critical issue. The effectiveness of their stock management process is crucial for the parts business success, as they were changing the key drivers of the purchase process and stock management model. This mathematical approach allows them to predict the sales level of each part with accuracy and, at the same time, parameterize the level of risk they want to take, while managing the spare parts business in a optimized way considering the NORS main management guidelines.


Manuel Cruz (LEMA/ISEP)
Sandra Ramos (LEMA/ISEP)
Margarida Pina (NORS Group)
Ricardo Costa (NORS Group)


Manuel Cruz (LEMA/ISEP)
Sandra Ramos (LEMA/ISEP)
LEMA – Laboratory for Mathematical Engineering
School of Engineering – Polytechnic of Porto
Rua Dr. Bernardino de Almeida 431
4200-072 Porto

Margarida Pina (NORS Group)
Aftermarket Development Managing Director
Rua Conde da Covilhã, 1637
4100-189 Porto

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