Question

Dazzle Productions is about to launch the latest tour of one of the hottest musical acts of the decade. The concert is to play at huge arenas. Lighting, staging and production affects are the best available, yet very costly. Each time a show is cancelled, Dazzle Productions must absorb an average rescheduling cost of $325,000. This cost includes transportation, lodging, setup and teardown, publicity, and administrative costs. In order to minimize the necessity to reschedule concert dates, Dazzle productions has asked you to study the benefit of leasing backup sound boards for the tour. The sound board used for this tour costs an average of $5,000 per show to lease and transport. The soundboard has a failure rate of 20%. If Dazzle Productions wants to minimize the expected cost of rescheduling a show, how many spare sound boards should the tour carry?

Answer 1

Failure probability of N parallel soundbox systems = 0.20^N

The expected cost of rescheduling = 325000*0.20^N

Cost of soundboards = 5000*N

N	Expected rescheduling cost = 325000 x 0.2^N	Cost of soundboxes = 5000*N	Total cost
1	65000	5000	70000
2	13000	10000	23000
3	2600	15000	17600 (min)
4	520	20000	20520

Both from the table and from the chart, it is clear that the expected ttoal cost will be minimized at N=3. Since they have one soundbox with them, it is advisable to carry 2 extra soundboxes.