Institut Fayol – Mines St Etienne

Offre stage Master recherche en Génie Mathématique et Industriel

Anomaly detection and optimization of manufacturing processes: integration of optimal transport and operations research

Détection d’anomalies et optimisation des procédés de fabrication : intégration de la recherche optimale en matière de transport et d’opérations

1 Project description
Anomaly detection [3] involves identifying unusual, atypical, or potentially problematic observations or events within a dataset. When anomalies are not detected and addressed appropriately, they can lead to a range of issues in the manufacturing industry. The use of optimal transport[8] proves to be particularly  relevant in this context. This method allows quantifying the distance between observed data and a reference model [5]. In other words, it assesses to what extent an observation deviates from what would be expected based on the normal distribution of data. This distance measure can be employed to determine whether an observation is an anomaly[1]. Moreover, Operations Research (OR) [2] utilizes mathematical models [6] and analytical methods to improve decision-making and optimize processes. In the manufacturing, various OR strategies can be employed to model and to solve a problem, and then to enhance the decision-making process. For instance, we highlight techniques based on Linear Programming (LP) and Integer Programming (IP) that play a crucial role by efficiently modeling and solving optimization problems. In general, optimization problems are related to finding an allocation of resources that respects all constraints of the problem and that optimizes (minimizes or maximizes) a given objective function. In the literature, many resource allocation problems arising in the manufacturing context are modeled and solved by using OR techniques [9].
The objective of this project is to establish a framework that integrates unsupervised anomaly detection techniques based on optimal transport with operations research strategies to enhance decision-making and resource allocation in the manufacturing process.

The main objectives of this project are:
• Simulating data to represent diverse manufacturing scenarios is a key task aimed at testing and validating our anomaly detection model.
• Developing an optimal transport model involves creating a relevant metric (Wasserstein distance [8], [4]) to measure dissimilarity between the reference distribution and observed sensor data.
• Defining detection thresholds is crucial as it determines what qualifies as an anomaly, playing a key role in establishing clear criteria for anomaly detection [7]
• Optimizing the response to anomalies through operations research includes creating strategies for decisionmaking. This might involve using scheduling algorithms to adjust resources, tasks, or machine settings and reduce disruptions in manufacturing.
• Testing and validating our anomaly detection model in a real industrial environment will be achieved through the exploration of real data from operating industrial sensors. By using the IT’mFactory platform at Ecole des Mines de Saint-Étienne, we will be able to gather real data, similar to industrial data, to test our methods. Keywords: Data, anomaly detection, manufacturing industry, optimal transport, operations research.

2 Basic information
• Internship duration: 5 months
• Starting date: as soon as possible and no later than March 31, 2024
• Location: École des Mines de Saint-Étienne (EMSE), Institut Henri Fayol, Saint-Étienne, France
• Indemnities: Legal amount (
• Supervisors: Marina Krémé, EMSE/LIMOS,,  Arthur Kramer, EMSE/LIMOS,, Mireille Batton-Hubert, EMSE/LIMOS,

3 Candidate profile
• 2nd-year of MSc and/or 3rd-year of an engineering school,
• Strong background in applied mathematics,
• Proficiency in machine learning techniques,
• Knowledge on operations research and discrete optimization,
• Strong programming skills in Python,
• Proficiency in the English language

4 Application
To apply, candidates must send, their CV and a cover letter to Marina Krémé (, Arthur Kramer ( and Mireille Batton-Hubert(


[1] Amina Alaoui Belghiti. Prédiction de situations anormales par apprentissage automatique pour la maintenance prédictive : approches en transport optimal pour la détection d’anomalies. Université Paris-Saclay, 2021.
[2] M. L. Chambers, Frederick S. Hillier, and Gerald J. Lieberman. Introduction to operations research. Journal of the Royal Statistical Society. Series A (General), 139(2):273, 1976.
[3] Varun Chandola, Arindam Banerjee, and Vipin Kumar. Anomaly detection: A survey. ACM Computing Surveys, 41(3):1–58, July 2009.
[4] Xiaoyu Cheng, Maoxing Wen, Cong Gao, and Yueming Wang. Hyperspectral anomaly detection based on Wasserstein distance and spatial filtering. Remote Sensing, 14(12):2730, June 2022.
[5] Mélanie Ducoffe, Ilyass Haloui, and Jayant Sen Gupta. Anomaly detection on time series with Wasserstein GAN applied to PHM. International Journal of Prognostics and Health Management, 10(4), June 2023.
[6] Arthur Kramer, Manuel Iori, and Philippe Lacomme. Mathematical formulations for scheduling jobs on identical parallel machines with family setup times and total weighted completion time minimization. European Journal of Operational Research, 289(3):825–840, 2021.
[7] Anis Hoayek Michel Kamel and Mireille Batton-Hubert. Anomaly detection based on system log data. International Conference on Linked Data Quality and Anomaly Detection, 2023.
[8] Gabriel Peyré and Marco Cuturi. Computational optimal transport. 2018.
[9] Michael L. Pinedo. Planning and Scheduling in Manufacturing and Services. Springer-Verlag, New York, 2nd edition, 2009.


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