Operations and Supply Chain Management
Operations and Supply Chain Management
14th Edition
ISBN: 9780078024023
Author: F. Robert Jacobs
Publisher: MCG
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Chapter 10, Problem 18OQ

a)

Summary Introduction

To determine: The percentage utilization of the graduate student.

a)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 4 per hour and the service time is 10 minutes.

Determine the percentage utilization of the graduate student (use model 1):

λ=4 per hour

μ=6010 minutes=6 per hour

ρ=λμ=46=0.667 or 66.7%

Hence, the utilization of the graduate student is 66.7%.

b)

Summary Introduction

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

b)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 4 per hour and the service time is 10 minutes.

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

λ=4 per hour

μ=6010 minutes=6 per hour

Average number of studentsin the system(Ls)}=λμλ=464=2 students

Hence, the average number of students in the system is 2 students.

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 4 per hour and the service time is 10 minutes.

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

λ=4 per hour

μ=6010 minutes=6 per hour

Ws=Lsλ=24=0.50 hours or 30 minutes

Hence, the average time in the system is 30 minutes.

d)

Summary Introduction

To determine: The probability that there will be four or more students in the line.

d)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 4 per hour and the service time is 10 minutes.

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

λ=4 per hour

μ=6010 minutes=6 per hour

Probability=1(P0+P1+P2+P3)=1{(1λμ)(λμ)0+(1λμ)(λμ)1+(1λμ)(λμ)2+(1λμ)(λμ)3}=1{(146)(46)0+(146)(46)1+(146)(46)2+(146)(46)3}

  =1(0.3333+0.2222+0.1481+0.0988)=10.8024=0.1976

Hence, the probability that there will be four or more students in the line is 0.1976.

e)

Summary Introduction

To determine: The average number of students in the line if the arrival rate is increased to 6 per hour.

e)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the arrival rate is 4 per hour and the service time is 10 minutes.

Determine the average number of students in the line if the arrival rate is increased to 6 per hour (use model 1):

λ=4 per hour

μ=6010 minutes=6 per hour

Lq=λ2μ(μλ)=626(66)=

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