{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:38:14Z","timestamp":1760060294986,"version":"build-2065373602"},"reference-count":16,"publisher":"MDPI AG","issue":"16","license":[{"start":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T00:00:00Z","timestamp":1755216000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Mathematics"],"abstract":"<jats:p>This work presents the design and implementation of an automated, digital, and modular system to address a real-world industrial challenge: the automation and optimization of production schedules for Computer Numerical Control (CNC) machines in a factory in Portugal. The goal is to replicate and enhance the existing manual scheduling process by integrating multiple data sources and formulating a general Mixed-Integer Linear Programming (MILP) model with constraints. This model can be solved using MILP optimization methods to produce efficient scheduling solutions that minimize machine downtime, reduce tool change frequency, and lower operator workload. The proposed system is implemented using open-source Python abstraction interfaces (Python-MIP), employing state-of-the-art of MILP optimization solvers such as CBC and HiGHS for solution validation. The system is designed to accommodate a wide range of constraints and operational factors, which can be switched on or off as needed, thereby enhancing its flexibility and decision-support capabilities. Additionally, a user-friendly graphical application is developed to facilitate the input of specific scheduling data and constraints, enabling flexible and efficient formulation of diverse scheduling scenarios. The proposed system is validated through multiple case studies, demonstrating its effectiveness in optimizing industrial CNC scheduling tasks and providing a scalable, practical tool for real-world factory operations.<\/jats:p>","DOI":"10.3390\/math13162621","type":"journal-article","created":{"date-parts":[[2025,8,15]],"date-time":"2025-08-15T14:24:28Z","timestamp":1755267868000},"page":"2621","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Automated and Optimized Scheduling for CNC Machines"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9040-5164","authenticated-orcid":false,"given":"Guilherme Sousa Silva","family":"Martins","sequence":"first","affiliation":[{"name":"Centre of Mathematics, University of Minho, 4710-057 Braga, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6235-286X","authenticated-orcid":false,"given":"M. Fernanda P.","family":"Costa","sequence":"additional","affiliation":[{"name":"Centre of Mathematics, University of Minho, 4710-057 Braga, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8387-391X","authenticated-orcid":false,"given":"Filipe","family":"Alves","sequence":"additional","affiliation":[{"name":"DTx\u2014Digital Transformation CoLAB, University of Minho, 4800-058 Guimar\u00e3es, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2025,8,15]]},"reference":[{"key":"ref_1","unstructured":"Google-Developers (2024, September 20). Scheduling. Available online: https:\/\/developers.google.com\/optimization\/scheduling."},{"key":"ref_2","unstructured":"Google-Developers (2024, September 20). Job Shop Scheduling. Available online: https:\/\/developers.google.com\/optimization\/scheduling\/job_shop."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"105731","DOI":"10.1016\/j.cor.2022.105731","article-title":"A survey of job shop scheduling problem: The types and models","volume":"142","author":"Xiong","year":"2022","journal-title":"Comput. Oper. Res."},{"key":"ref_4","unstructured":"CNC-Machines (2024, September 23). What is a CNC Machine?. 2024., Available online: https:\/\/cncmachines.com\/what-is-a-cnc-machine."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Pinedo, M.L. (2022). Scheduling: Theory, Algorithms, and Systems, Springer. [6th ed.].","DOI":"10.1007\/978-3-031-05921-6"},{"key":"ref_6","unstructured":"Baker, K.R., and Trietsch, D. (2013). Principles of Sequencing and Scheduling, Wiley. [2nd ed.]. Wiley Series in Operations Research and Management Science."},{"key":"ref_7","unstructured":"Brucker, P. (2007). Scheduling Algorithms, Springer."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"205","DOI":"10.1016\/j.neucom.2022.11.024","article-title":"A survey for solving mixed integer programming via machine learning","volume":"519","author":"Zhang","year":"2023","journal-title":"Neurocomputing"},{"key":"ref_9","unstructured":"(2024, November 22). CBC (Coin-or Branch and Cut)\u2014Introduction. Available online: https:\/\/coin-or.github.io\/Cbc\/intro.html."},{"key":"ref_10","unstructured":"Team, H.D. (2024, November 21). HiGHS Solvers Documentation. Available online: https:\/\/ergo-code.github.io\/HiGHS\/dev\/solvers\/#solvers."},{"key":"ref_11","unstructured":"Developers, P.M. (2024, September 26). Modeling Examples. Available online: https:\/\/python-mip.readthedocs.io\/en\/latest\/examples.html."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"119","DOI":"10.1007\/s12532-017-0130-5","article-title":"Parallelizing the dual revised simplex method","volume":"10","author":"Huangfu","year":"2018","journal-title":"Math. Program. Comput."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"603","DOI":"10.1007\/s12532-020-00181-8","article-title":"Implementation of an interior point method with basis preconditioning","volume":"12","author":"Mahajan","year":"2020","journal-title":"Math. Program. Comput."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Wang, H., Pan, Y., and Cui, W. (2022). Quantum-Inspired Solvers on Mixed-Integer Linear Programming Problem. arXiv.","DOI":"10.23919\/CCC55666.2022.9902772"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"219","DOI":"10.1287\/opre.8.2.219","article-title":"On the Job-Shop Scheduling Problem","volume":"8","author":"Manne","year":"1960","journal-title":"Oper. Res."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Nemhauser, G.L., and Wolsey, L.A. (1988). Integer and Combinatorial Optimization, John Wiley & Sons, Inc.","DOI":"10.1002\/9781118627372"}],"container-title":["Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2227-7390\/13\/16\/2621\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T18:28:28Z","timestamp":1760034508000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2227-7390\/13\/16\/2621"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,8,15]]},"references-count":16,"journal-issue":{"issue":"16","published-online":{"date-parts":[[2025,8]]}},"alternative-id":["math13162621"],"URL":"https:\/\/doi.org\/10.3390\/math13162621","relation":{},"ISSN":["2227-7390"],"issn-type":[{"type":"electronic","value":"2227-7390"}],"subject":[],"published":{"date-parts":[[2025,8,15]]}}}