(392l) Supply Chain Optimization in the Collection of Used Cooking Oil

The fast growth of the urban population has increased their waste production rate. If these materials are not adequately managed, they can lead to water contamination, solid degradation, and air pollution. One residue of major concern are Used Cooking Oils (UCOs). The UCOs are the residual vegetable oils derived from frying and cooking in restaurants, households, and food industries. Their mishandling can lead to various problems such as floods, pollution of ecosystems, pest proliferation, damage to infrastructure, and even public health problems due to their illegal collection and redistribution as new. That's the case of Bogotá, the capital city of Colombia. Bogotá, a Latin American city with 11.8 million inhabitants in its metropolitan area, generates about 350,000 metric tons of used cooking oils (UCOs) that are neither recycled nor treated through chemical or physical processes. Due to its large scale, the management of UCOs is a major issue in the city. Previously, a supply chain optimization approach has been proposed to tackle this situation [2]. In this study, data on UCO-producing sites was sourced from a major vegetable oil producer in Colombia and analyzed to relate the locations and their rate of produced waste information. In that work, the UCOs recollection scheme was formulated as three problems: a zone clustering problem where the problem complexity was reduced by splitting the city into balanced distribution zones, a routing problem to optimize the logistics of visiting each UCO source within each zone subject to capacity constraints, and a warehouse location problem, identifying the location for the UCO deposit by minimizing costs while avoiding specific residential areas designated by city policies. In this previous work, these problems were addressed as optimization problems and tackled through metaheuristic algorithms. Despite metaheuristics' versatility, the lack of guarantees in finding the global optimum encouraged solving the supply chain problem using other approaches. In this work, mathematical programming and machine learning techniques are used, and to implement these, novel formulations are required for each problem.

The clustering problem was formulated as a k-means problem and addressed using machine learning (ML) heuristics and as a mixed-integer non-linear programming (MINLP) problem. In the k-means problem, optimality conditions were tested based on [3]. After obtaining the clusters, the routing problem was posed as a capacitated vehicle routing problem (CVRP). In [2], the problem was solved by arranging the locations in a priority rank, and from that list, a subset of them was chosen to set a route. Although initially found via heuristics [2], this route was formulated as a traveling salesperson problem (TSP) and solved using Google's OR Tool [4] and Concorde [5]. The original problem contained extra constraints that were verified post-solution. In contrast, we posed the original problem as a monolithic CVRP and solved it using metaheuristics implemented in the library pyVRP [3]. Finally, having set the clusters and defined the routes, a central recollection point is located considering local policies for industrial facility location. The restricted areas and their complementary regions were decomposed using simplexes using the Shapely [6] library in Python, which led to a disjunctive programming formulation of the location of the distribution center.

Performance metrics such as time of execution and quality of the solution related to the objective of the problem were computed to compare the different solution algorithms. As an example of the improved performance using the right analytic tools compared to metaheuristics, in the clustering problem, using the k-means formulation led to a 13.3% better solution based on the total distance to the centroids compared to the solutions reported in the literature [2] and found it 200 times faster. This shows how the correct formulation and matching of analytics, optimization, and machine learning techniques can lead to significant improvements in addressing real-world applications aimed at improving the sustainability of our society.

References

[1] Tatiana Bahamon, Every year Bogotá generates more than 35,000 tons of used oil and does not use it (in Spanish), UNAL Journal, Mar. 2025. [Online]. Available: https://periodico.unal.edu.co/articulos/cada-ano-bogota-genera-mas-de-3…

[2] J. S. Rodríguez, A. Orjuela, and J. G. Cadavid, Characterization and optimization of a used cooking oils collection chain – Study case Bogotá, Colombia, Chem. Eng. Res. Des., vol. 184, pp. 59–71, Aug. 2022, doi: 10.1016/j.cherd.2022.05.049.

[3] N. A. Wouda, L. Lan, and W. Kool, PyVRP: a high-performance VRP solver package, Inf. J. Comput., vol. 36, no. 4, pp. 943–955, 2024, doi: 10.1287/ijoc.2023.0055.

[4] L. Perron and V. Furnon, OR-Tools. (May 07, 2024). Google. [Online]. Available: https://developers.google.com/optimization/

[5] D. Applegate and W. Cook, Concorde TSP solver. 2006.

[6] S. Gillies et al., Shapely. (Apr. 03, 2025). Zenodo. doi: 10.5281/ZENODO.5597138.