Timed event-graphs, a special class of timed Petri nets, are used
for modelling and analyzing job-shop systems. The modelling allows the
steady-state performance of the system to be evaluated under a
deterministic and cyclic production process. Given any fixed processing
times, the productivity (i.e., production rate) of the system can be
determined from the initial state. It is shown in
... [Show full abstract] particular that, given
any desired product mix, it is possible to start the system with enough
jobs in process so that some machines will be fully utilized in
steady-state. These machines are called bottleneck machines, since they
limit the throughput of the system. In that case, the system works at
the maximal rate and the productivity is optimal. The minimal number of
jobs in process allowing optimal functioning of the system is further
specified as an integer linear programming problem. An efficient
heuristic algorithm is developed to obtain a near-optimal solution