Question

Marathon petroleum distribution company manages 600 gas stations in Michigan. Each gas station typically has four underground storage tanks (UGST), three for gasoline and one for diesel. The UGST develop leaks sometimes due to corrosion or changes in soil conditions. Based on historical data, Marathon estimates that the probability that a given UGST develops a leak during a given year is 0.002 for gasoline storage tanks and higher at 0.003 for diesel storage tanks potentially due to higher density of diesel and higher sulfur content. Marathon also estimates that an average leaking tank results in $10,000 in repair costs, $5000 worth lost fuel and $50,000 in clean up costs. Further, disruption to the gas station operations during repairs to the leaking tank, results in lost sales of $100,000 on which the gas station would have earned a pretax profit of $20,000.

An insurance company offers an insurance policy that would pay for repair costs, lost fuel costs and clean up costs (but not for business interruption and lost sales) in the case a UGST develops a leak. The insurance premium is $150 per UGST/year.

Alternatively, Tank Repairs Incorporated has developed a new technology of spray coating the insides of the UGSTs with a special self-sealing polymer, which would reduce the probability of leakage to 0.0005 per year/tank. However, the coating has to be done every year when the tanks are emptied for cleaning and inspection. Tank Repairs Inc. offers to coat the UGSTs managed by Marathon at the rate of $140/tank. Each time a tank is coated, it results in incremental lost sales of $200 on which Marathon would have earned a profit of $40.

What should Marathon do? Show all your intermediate steps and calculations clearly and state your assumptions.

Answer 1

total number of Gas stations = 600

One gas station = 3 Gasoline UGST & 1 Diesel UGST

Therefore the total number of Gasoline UGSTs = 600*3 = 1800

And the total number of Diesel stations = 600*1 = 600

Probability of leakage for Gasoline = 0.002 and Probability for Diesel = 0.003.

Hence, Number of Gasoline UGSTs leaked on average = 1800*0.002 = 3.6; Number of Diesel UGSTs leaked = 1.8

Cost on account of leakage of a tank: Repair Cost = $10000; Lost fuel = $5000;Cleanup cost= $50000 and Lost sale =$100000

By availing the Insurance we will save all the cost except the cost of lost sales.

So, the benefit from insurance = Number of leaked UGSTs * Total cost on leakage

= 5.4 * 65000 = $351000

Premium Paid to Insurance = $150* 2400 = $360000.

The loss of profit from lost sales = 5.4* 20000 = $108000

So we will lose total= 360000+108000 - 351000 =$117000 by availing the insurance.

By Coating the UGSTs the probability of leakage = 0.0005

Hence the number of UGSTs leaked per year = 0.0005* 2400 = 1.2

Total cost = $65000* 1.2 =78000

Total lost Profit from sales = $20000*1.2 = $24000

Incremental loss of sales from coating = $40* 2400 = $96000

Coating Cost = 140* 2400 = $336000

Total cost from Coating = $534000.

Hence Marathon will avail the insurance.