This paper shows that it is possible to formalize and to put in a proper form an optimization problem consisting in the optimization of the work-in-progress (WIP) in a manufacturing system, while ensuring a minimum value for the throughput of each product. The decision variables involved in this problem are the lot sizes for the various products and components and the system initial state, as regards the number of tokens in each place of the net. In spite of the limited modelling capability of timed event graphs, the considered structure of manufacturing systems is by no means trivial. Actually, the fact that the set of decision variables includes the lot sizes makes the production flows in the system optimized in practice. The main novelty of this paper with respect to previous works concerns the possibility of dealing with situations in which no machine acts as a bottleneck one. The optimization problem arising is thus more difficult than the two-level optimization problem.
[1]
Didier Dubois,et al.
A linear-system-theoretic view of discrete-event processes
,
1983
.
[2]
A. Di Febbraro,et al.
Performance optimization in manufacturing systems by use of max-plus algebraic techniques
,
1994,
Proceedings of IEEE International Conference on Systems, Man and Cybernetics.
[3]
Jean-Marie Proth,et al.
Performance evaluation of job-shop systems using timed event-graphs
,
1989
.
[4]
A. Di Febbraro,et al.
Optimal lot-sizing in cyclic manufacturing processes
,
1994,
Proceedings of IECON'94 - 20th Annual Conference of IEEE Industrial Electronics.
[5]
J. Quadrat,et al.
Algebraic tools for the performance evaluation of discrete event systems
,
1989,
Proc. IEEE.