Question

In: Operations Management

The Robotics Manufacturing Company operates an equipment repair business where emergency jobs arrive randomly at the...

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-server 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 a $35 per hour cost for customers waiting during the repair process.

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

Round your answers to three decimal places.

Arrival rate = jobs per hour

Service rate = jobs per hour
Show the operating characteristics, including the total cost per hour.

Round your answers to four decimal places.

L_q =

L =

Round your answer to the nearest cent.

TC = $
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. What effect will the new system have on the waiting line characteristics of the repair service? The round total cost to the nearest cent and other answers to four decimal places.

Current System (σ = 1.5) New System (σ = 0)

Lq

L

Wq

W

TC $ $

The firm's director of operations rejected the request for the new system because the hourly cost is $4 higher and the mean repair time is the same. Do you agree?

No
Does paying for the computer-based system to reduce the variation in service time make economic sense?

Yes

How much will the new system save the company during a 40-hour workweek? Round your answer to the nearest cent.

Savings = $

	Current System (σ = 1.5)	New System (σ = 0)
Lq
L
Wq
W
TC	$	$

Expert Solution

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

Round your answers to three decimal places.

Arrival rate = jobs per hour

=8hours/3 jobs= 2.666 hours per job

Jobs per hour=1/2.666

Ans= λ =.375 jobs per hour

Service rate = jobs per hour

= 1 repair job /2 hours

μ =.5 jobs per hour

b.

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

Round your answers to four decimal places.

Lq = λ 2 62 + (λ / μ)2 / (2(1- λ / μ)

=(.375x.375)(1.5x1.5)+(.375/.5)2/(2(1-.375/.5)=.1406x2.25+.5625/ .5

=.8789/.5=1.7578/hour

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

Wq=Lq/ λ =4.688 hour or 281.28 minutes

W=L/ λ = 6.688 hour or 401.28 minutes

Pw= λ /μ=.75
Round your answer to the nearest cent.

TC=CwL+Csk=35x2.508+28x1=$ 115.78

TC = $ 115.78

C.

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

keosha answered 5 months ago

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