Chapter A, Problem 2CS

Question

☆ Warehouse Tenting at the Port of Miami

The Collector’s Choice Inc. (CCI), a luxury car import company, has an old warehouse at the Port of Miami, Florida, where it temporarily stores expensive sports cars and automotive parts that arrive from Europe. This summer, CCI has noticed that the termite infestation in the warehouse has escalated to a point where tenting cannot be postponed anymore. (Tenting is the process of wrapping a building inside a huge tent that is subsequently filled with a poisonous gas capable of killing most forms of life inside, including insects, plants, pets, and human beings.) CCI’s pest control company’s contract specifies a to-do list of pre-tenting tasks, which include:

►Turning off all air-conditioning units and opening all windows of the warehouse

►Turning off all internal and external lights, including those operating on a timer

►Pruning all outdoor vegetation at least away from the warehouse

►Soaking the soil around the warehouse on the first day of tenting

The requirement of opening all windows is particularly worrisome to CCI because it means turning off the alarm system, leaving the warehouse vulnerable to burglary for 48 hours— the required amount of time for the poisonous gas to do its job. Therefore, Alex Ferrari, the warehouse manager, is thinking about hiring a security company to monitor the facility during that period. CCI's property insurance deductible is $25,000, and Alex is assuming that if thieves are willing to enter a building full of poisonous gas to steal something, they would certainly take more than $25,000 worth of parts— or even an entire car!

After making a few phone calls, Alex gets in touch with ProGuard, a trustworthy local security company that charges $150 per hour to have a security guard stationed outside their warehouse. The city of Miami police records indicate that about 30% of businesses that left their facilities unattended during tenting reported stolen property in the past 3 years. Although Alex thinks ProGuard’s prices are reasonable, and having a guard outside the warehouse would certainly help, he is still not sure whether it is worth spending the extra money. After all, ProGuard’s contract does not guarantee the protection it provides is infallible. In fact, an analysis of the company’s records indicates that 3% of their clients were burglarized over the past 3 years. (Despite this figure, ProGuard is still the best security company in the area.)

2. Come up with a simple rule of thumb that can be applied to decisions of this nature, given any deductible amount d. extra surveillance cost c, and burglary probabilities p₁ (without surveillance) and p₂ (with surveillance).