OCP

Creation of two mathematical models in Python language, with the aim of solving a Business Steering problem concerning the logistical routing of products to customer ports. Optimization of routing times and parking times on port quays enables a reduction in port costs, thanks to mass data processing in a supercomputer.

Creating mathematical models to solve business steering problems in logistics can be a rewarding challenge, but it was a complex one. There were several reasons for this:

Real data:
Obtaining accurate and complete data is a challenge. Models depend heavily on data quality to produce relevant results.

Problem complexity:
Some logistics problems were NP-hard, meaning that no efficient algorithm existed to solve them in polynomial time. This made exact problem solving impractical for large instances.

Dimensionality:
Models became complex with increasing dimensionality, especially when we started dealing with large numbers of customers, ports, or other logistical entities.

Scaling:
Models had to be able to scale to different sizes of data sets. Ensuring scalability while maintaining acceptable performance was a REAL CHALLENGE.
Multi-objective optimization:
Our problem had several objectives to optimize (minimizing costs and lead times simultaneously), so defining a single objective function was tricky. On the other hand, the results of mathematical models could sometimes be difficult to interpret, especially for non-technical stakeholders. Communicating the results in an understandable way was no easy task.

We worked on two models: one aimed at optimizing routes to reduce transit times, the other at minimizing parking times on port quays for both dry and liquid products.

We played on the following elements to succeed in our challenge:

Problem complexity:
We used approximation methods (heuristics) for the NP-hard problem, with parallel solving approaches to speed up the process.

Dimensionality:
We applied dimension reduction techniques such as Principal Component Analysis (PCA) or clustering methods to group similar entities and reduce model complexity.

Integration of realistic constraints:
We involved logistics experts to translate real-world constraints into mathematical terms. We ensured that the models accurately reflected operational conditions.

Scaling:
We used distributed and parallel optimization techniques to manage large data sets. We explored the use of Big Data technologies, but didn’t go any further.

Algorithmic complexity:
We chose algorithms from the academic literature in collaboration with optimization experts, and followed an agile and iterative approach to allow frequent updates of the model to keep it relevant.

Integration with the Supercomputer:
We collaborated with experts in High-Performance Computing (HPC) to ensure efficient integration and that our model is compatible with the architecture of the Supercomputer.