An airline has 20 planes, is short on money, and doesn\'t want to spend any more

Question

An airline has 20 planes, is short on money, and doesn't want to spend any more than necessary to keep the planes safely flying.The cost to perform preventive maintenance (PM) on all 20 planes is $16,000.If a plane has a malfunction between PM inspections, it costs an average of $4000 to fix it.The malfunction history on the planes is as follows:

Months between PM                       Probability of malfunction

            One                                                                .2

            Two                                                                 .3

            Three                                                              .5

                 How often should PM occur to minimize the total expected costs?

Explanation / Answer

PM should occur after every two months. This is because through decision analysis we can find the minimum cost is incurred when PM is occurring in two months. In 1 month if PM is done total cost in a year is .2x$16000x12=$384000. If PM occurs after every two months then total cost is $16000x6x.3=$28800 . If PM occurs after every 3 months total cost incurred is $16000x4x.5=$32000. This is because when PM is occurring after every 2 months, total 6 PMs are required in a year. If PMs are occurring every 3 months, total 4 PMs are required in a year. But if PM occurs after every month, total 12 PMs are required. So we can see expected value for PM after 1 month is $384000, expected value for PM after 2 months is $28800, expected value for PM after 3 months is $32000. SInce expected value is least for 2 months, so PM should occur every 2 months to minimize total costs

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