Operations and Supply Chain Management (Mcgraw-hill Education)
Operations and Supply Chain Management (Mcgraw-hill Education)
15th Edition
ISBN: 9781259666100
Author: F. Robert Jacobs, Richard B Chase
Publisher: McGraw-Hill Education
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Chapter 10, Problem 17OQ

a)

Summary Introduction

To determine: The percentage utilization of the operator.

a)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 25 per hour and the service time is 2 minutes.

Determine the percentage utilization of the operator (use model 1):

λ=25 per hour

μ=602 minutes=30 per hour

ρ=λμ=2530=0.833 or 83.3%

Hence, the utilization of the clerk is 83.3%.

b)

Summary Introduction

To determine: The average number of documents in the system.

b)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 25 per hour and the service time is 2 minutes.

Determine the average number of documents in the system (use model 1):

λ=25 per hour

μ=602 minutes=30 per hour

Average number of documentsin the system(Ls)}=λμλ=253025=5 document

Hence, the average number of documents in the system is 5 documents.

c)

Summary Introduction

To determine: The average time in the system.

c)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 25 per hour and the service time is 2 minutes.

Determine the average time in the system (use model 1):

λ=25 per hour

μ=602 minutes=30 per hour

Ws=Lsλ=525=0.20 hours or 12 minutes

Hence, the average time in the system is 12 minutes.

d)

Summary Introduction

To determine: The probability that there will be four or more documents in the system.

d)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 25 per hour and the service time is 2 minutes.

Determine the probability that there will be four or more documents in the system (use model 1):

λ=25 per hour

μ=602 minutes=30 per hour

Probability=1(P0+P1+P2+P3)=1{(1λμ)(λμ)0+(1λμ)(λμ)1+(1λμ)(λμ)2+(1λμ)(λμ)3}=1{(12530)(2530)0+(12530)(2530)1+(12530)(2530)2+(12530)(2530)3}

  =1(0.1667+0.1389+0.1157+0.0965)=10.5178=0.4822

Hence, the probability that there will be four or more documents in the system is 0.4822.

e)

Summary Introduction

To determine: The average number of documents in the system if another clerk were added.

e)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 25 per hour and the service time is 2 minutes.

Determine the average number of documents in the system if another clerk were added (use model 1):

λ=25 per hour

μ=602 minutes=30 per hour

Lq=λ2μ(μλ)=30230(3030)=

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