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Using Min-Plus dioid algebra, we employ algebraic techniques to express GMECs as weighted inequalities. The solution involves translating the constraints into Min- Plus linear equations that describe the behavior of NTEGs. We provide sufficient conditions for the existence of causal control laws, considering both the initial marking of the NTEGs and the parameters of the GMECs. To demonstrate the practical application of the approach, we include a case study that illustrates the effectiveness of the proposed control strategy.<\/jats:p>","DOI":"10.1051\/ro\/2025165","type":"journal-article","created":{"date-parts":[[2025,12,15]],"date-time":"2025-12-15T08:47:29Z","timestamp":1765788449000},"page":"597-614","source":"Crossref","is-referenced-by-count":0,"title":["Formal solution for the generalized mutual exclusion constraints problem in a class of timed Petri Nets"],"prefix":"10.1051","volume":"60","author":[{"given":"Jihene","family":"Rajah","sequence":"first","affiliation":[{"name":"LURPA, ENS Paris-Saclay","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Said","family":"Amari","sequence":"additional","affiliation":[{"name":"LURPA, ENS Paris-Saclay","place":["France"]},{"name":"LIPN, University of Sorbonne","place":["France"]}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"250","published-online":{"date-parts":[[2026,3,18]]},"reference":[{"key":"R1","unstructured":"Kim J.H. and Li T.E., Schedule stabilization and robust timing control for timed constrained cluster tools, in 2003 IEEE International Conference on Robotics and Automation. 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