At the beginning of each week, a machine is eitherrunning or broken down. If the machine runs throughout theweek, it earns revenues of $100. If the machine breaks downduring a week, it earns no revenue for that week. If themachine is running at the beginning of the week, we mayperform maintenance on it to lessen the chance of abreakdown. If the maintenance is performed, a runningmachine has a .4 chance of breaking down during the week;if maintenance is not performed, a running machine has a .7chance of breaking down during the week. Maintenancecosts $20 per week. If the machine is broken down at thebeginning of the week, it must be replaced or repaired. Bothrepair and replacement occur instantaneously. Repairing amachine costs $40, and there is a .4 chance that the repairedmachine will break down during the week. Replacing abroken machine costs $90, but the new machine is guaranteedto run throughout the next week of operation. Use dynamicprogramming to determine a repair, replacement, andmaintenance policy that maximizes the expected net profitearned over a four-week period. Assume that the machine isrunning at the beginning of the first week.
At the beginning of each week, a machine is either
running or broken down. If the machine runs throughout the
week, it earns revenues of $100. If the machine breaks down
during a week, it earns no revenue for that week. If the
machine is running at the beginning of the week, we may
perform maintenance on it to lessen the chance of a
breakdown. If the maintenance is performed, a running
machine has a .4 chance of breaking down during the week;
if maintenance is not performed, a running machine has a .7
chance of breaking down during the week. Maintenance
costs $20 per week. If the machine is broken down at the
beginning of the week, it must be replaced or repaired. Both
repair and replacement occur instantaneously. Repairing a
machine costs $40, and there is a .4 chance that the repaired
machine will break down during the week. Replacing a
broken machine costs $90, but the new machine is guaranteed
to run throughout the next week of operation. Use dynamic
programming to determine a repair, replacement, and
maintenance policy that maximizes the expected net profit
earned over a four-week period. Assume that the machine is
running at the beginning of the first week.
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