29. The Robotics Manufacturing Company operates an equipment repair business whe

Question

29.The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the rate of three jobs per 8-hour day. The company’s repair facility is a single-channel system operated by a repair technician. The service time varies, with a mean repair time of 2 hours and a standard deviation of 1.5 hours. The company’s cost of the repair operation is $28 per hour. In the economic analysis of the waiting line system, Robotics uses $35 per hour cost for customers waiting during the repair process.

a.What are the arrival rate and service rate in jobs per hour?

b.Show the operating characteristics including the total cost per hour.

c.The company is considering purchasing a computer-based equipment repair system

that would enable a constant repair time of 2 hours. For practical purposes, the standard

deviation is 0. Because of the computer-based system, the company’s cost of the

new operation would be $32 per hour. The firm’s director of operations said no to the

request for the new system because the hourly cost is $4 higher and the mean repair

time is the same. Do you agree? What effect will the new system have on the waiting

line characteristics of the repair service?

d. Does paying for the computer-based system to reduce the variation in service time

make economic sense? How much will the new system save the company during a

40-hour work week?

Explanation / Answer

Answer:

29. a.

= 3/8 = .375

µ = 1/2 = .5

b.

L= Lq + / µ = 1.7578 + .375 / .5 = 2.5078

TC =cw L+csk = 35 (2.5078) + 28 (1) = $115.71c.Current System ( = 1.5)

New System ( = 0)

Lq=1.7578

Lq =1.125

L=2.5078

L=1.875

W q=4.6875

Wq=3.00

W =6.6875

W =5.00

TC =$115.77

TC =cw L+csk = 35 (1.875) + 32 (1) = $97.63

d. Yes; Savings = 40 ($115.77 - $97.63) = $725.60

Note: Even with the advantages of the new system, W q= 3 shows an average waiting time of 3hours. The company should consider a second channel or other ways of improving the emergencyrepair service

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