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nuts (the drill) and screws (the cutter), a machine for assembling bolts (the
assembler), and an automatic guided vehicle system (AGV) for moving
pieces between machines. Each machine has an input buffer for raw pieces
and an output buffer for finished pieces. The buffers have finite capacities.
The machines can execute only one task at a time (machining a nut or a
screw and assembling a nut with a screw). The AGV can transport only one
piece at a time. An automated inventory system supplies raw pieces to and
collects finished pieces from the work cell.
Pieces are taken sequentially, at random instants of time, from the inven-
tory system and placed in the input buffer of the machine where the first
operation is performed (the drill or the cutter). The machines are able to
pick up one piece at a time from their input buffers and to place them in
the operation position. As soon as one operation is finished, the piece is
evacuated from the machine and dropped in the output buffer. When the
input buffer is empty or the output buffer is full, the machine stops.
The AGV transports semi-finished pieces (nuts and screws) from the drill
and cutter to the assembler. It is equipped with a robotic arm that unloads
pieces from the drill and cutter output buffers and loads pieces onto the
assembler input buffer. For the sake of simplicity, we assume that the AGV
transports only one piece at a time. The inventory system picks up bolts
from the assembler output buffer at random instants of time.
The work cell controller, with a real-time dispatcher, assigns pieces to the
machines as soon as they become idle, and issues requests for missions to
the AGV system. The objective of this case study is to develop a prototype
of the work cell controller in order to test the correct behaviour of the
real-time dispatcher before installation in the real work cell controller.
Operations synchronization
The task of the real-time dispatcher is to synchronize the machines' activities.
For this purpose, the following considerations should be taken into account.
The drill and the cutter need raw pieces to produce nuts and screws. As
long as raw pieces are available in their input buffers, the drill and the
cutter continue the production of nuts and screws.
The assembler needs a nut and a screw to produce a bolt. As long as nut
and screw pairs are available in its input buffer, the assembler continues
the production of bolts.
If the three machines never fail, if they have the same processing time
if the automated inventory systems supplies raw pieces and consumes
bolts with the same frequency
then the machines' buffers never get empty or full, the machines never
stop, and the throughput is equal to
and if the following relation holds:
η #
In any other situation, when the machines are unreliable, or the machine
processing times and the inventory supply and consumption frequency
differ, the buffers might get full or empty and the machines might need to
stop and restart.
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