Question

M6_IND3. Steve Jobs is a computer technician in an investment company. He responds to a variety of complaints from investment advisors regarding their computers performance. He receives an average of one computer per hour to repair. It takes him an average of 40 minutes to repair any of these computers. Steve believes that adding a second repair technician would significantly improve his department’s efficiency. He has a friend, Steve Wozniak, who is looking for a job. He estimates that adding an assistant, but still keeping the department running as a single-server system, would double allow computer to be repaired in half the time, an average of 20 minutes to repair these computers. The investment advisors earn $40 for the company, on average, while the computer technicians earn $16 per hour. An investment advisor who does not have access to his computer is unable to generate revenue for the company. a) Consider the performance of the office before the new technician is added. On average, how many computers (to the nearest 0.01 computers) are in the system given the arrival and service rates? b) Consider the performance of the office before the new technician is added. On average, how many hours (to the nearest 0.01 hour) does each computer spend in the system given the arrival and service rates? c) Consider the performance of the office before the new technician is added. Based on the average number of computers in the system, what is the total system cost (technicians cost and waiting cost) per hour (to the nearest $/hour)? d) Consider the performance of the office after the new technician is added. On average, how many computers (to the nearest 0.01 computers) are in the system given the arrival and service rates? e) Consider the performance of the office after the new technician is added. On average, how many hours (to the nearest 0.01 hour) does each computer spend in the system given the arrival and service rates? f) Consider the performance of the office after the new technician is added. Based on the average number of computers in the system, what is the total system cost (technicians cost and waiting cost) per hour (to the nearest 0.01 $/hour)? g) Based on your cost analysis - is it worth it to add another technician?

Answer 1

Arrival rate, ? = 1 per hour

Service rate before the new technician is added, ?1 = 60/40 = 1.5 per hour   

Service rate after the new technician is added, ?2 = 60/20 = 3 per hour   

Cost of waiting, Cw = $ 40 per hour (this is the cost of investment advisor)

Cost of server, Cs = $ 16 per hour (this is the cost of computer technician)

a)

Average number of computers in system, L = ?/(?₁-?) = 1 / (1.5-1) = 2.00 computers

b)

Average number of hours spent in system, W = 1/(?₁-?) = 1/(1.5-1) = 2.00 hours

c)

Total system cost per hour = Cs + Cw*L = 16 + 40*2 = $ 96 per hour

d)

Average number of computers in system, L = ?/(?₂-?) = 1 / (3-1) = 0.50 computers

e)

Average number of hours spent in system, W = 1/(?₁-?) = 1/(3-1) = 0.50 hours

f)

Total system cost per hour = Cs + Cw*L = 16*2 + 40*0.5 = $ 52 per hour

g)

Based on above cost analysis, total cost per hour after the technician is added is lower. Therefore it is worth to add another technician.