@INPROCEEDINGS{gaubert90, author={S. Gaubert}, title={An algebraic method for optimizing resources in timed event graphs}, booktitle={Proceedings of the 9th International Conference on Analysis and Optimization of Systems, {\rm Antibes, June 1990}}, editor={A.Bensoussan and J.L. Lions}, series={Lecture Notes in Control and Information Sciences}, year={1990}, number={144}, publisher={Springer}, }

A min-linear system theory has been developed for timed event graphs using dioid algebraic structures. This in particular allows modeling and evaluating performance of flexible workshops and distributed processing systems. In this paper, we use this theory to study the problem of resource optimization, {\em i.e.}, minimizing the cost of some resources (machines, pallets, processors) in order to achieve a given rate of production, or optimizing the rate of production itself. This problem reduces to an integer linear programming problem. We use rational symbolic computation in the dioid algebra to simplify and generate the corresponding simplex.

The presentation of this early paper on the subject is dated: the results are superseded by those reported in the last chapter (IX) of the Thesis (in French), in a Lecture given at the Belgian-French-Netherlands Summer School on Discrete Event systems, and in a Technical Note.