public class MaintenanceScheduling
extends Object
Consider the problem of operating a machine that may be in any of the following
possible states: good as new (0), minor fault (1), major fault (2), out of order (3).
The transition probability from state i to state j during a given period is
1/4 1/4 1/4 1/4
0 1/3 1/3 1/3
0 0 1/2 1/2
0 0 0 1
If a machine is in state 0 at the beginning of a period, no action should be taken;
costs associated with the production of faulty items over the coming period
when a machine is in state 0 are negligible. However, if the machine is in state
1 < i < 2, it is possible to take no action or to repair the machine for $500; once
the machine has been repaired, it returns to state 0 at the beginning of the next
period. If no action is taken in state 1, there will be a cost of $1000 associated
with the production of faulty items over the coming period. If the machine is
repaired in state 1, production will halt during the next period and there will
be a cost of $1500 associated with lost profits. Similarly, if the machine is in
state 2 and no action is taken, there will be a cost of $1500 associated with the
production of faulty items over the coming period. If the machine is repaired,
production will halt and there will be a cost of $2500 associated with lost profits
over the coming period. Finally, if the machine is in state 3, it must necessarily
be repaired to resume production at the beginning of the next period; in this
case repair costs amount to $1000 and lost profits amount to $3000
- Author:
- Roberto Rossi