Three-Machine Example

Consider the automated manufacturing system shown in Figure 2. A robot takes a raw part from the input storage and loads either machine 1 or machine 2. Machine 1 spray-paints its part in a shade of red, while machine 2 spray-paints its part in a shade of blue. Each machine is capable of unloading its painted part into a buffer of finite capacity. A third machine, machine 3, loads itself with (any) two painted parts form the buffers, puts the parts together into a new part, and then releases this new part via conveyor to an output storage. We will assume here that Machine 3 is capable of loading one part at a time.

  
Figure 2: An Automated Manufacturing System

Now consider the following set of specifications, not all of which need be taken at a time:

• Safety 1:
  The robot only loads a machine i if machine i is idle (i=1,2).
• Safety 2:
  The robot does not load machine i unless the capacity of its respective buffer allows for another piece ( i=1,2).
• Mutual Exclusion:
  If the robot is loading one machine, then it is not available to load the other machine.
• Priority: Whenever both machines 1 and 2 are available, machine 1 is to be given priority when being loaded by the robot.
• Fair Use of Resource:
  The robot is to load machines 1 and 2 alternatively, starting, say, with machine 1.
• Different Types for M3:
  Machine 3 is to load itself only with two parts of different color (so the parts must come from different buffers).
• Same Types for M3:
  Machine 3 is to load itself with any two parts of the same color (so both parts must come from the same buffer at any one time).