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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Question
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Chapter 10, Problem 12OQ

a)

Summary Introduction

To determine: The average number that Person X would expect to see in the facilities of Dr. M.

a)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the inter-arrival time of the patients is three minutes and the service time is 2 minutes.

Determine the average number that Person X would expect to see in the facilities of Dr. M (use model 1):

λ=603 minutes=20 per hour

μ=602 minutes=30 per hour

Average number ofpatients in the facilities(Ls)}=λμλ=203020=2 people in a system

Hence, the average number of patients that Person X would expect is 2 in the facilities of Dr. M.

b)

Summary Introduction

To determine: The amount of time spend by a patient in the system including arrival, getting an injection, and leave.

b)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the inter-arrival time of the patients is three minutes and the service time is 2 minutes.

Determine the amount of time spent by a patient in the system (use model 1):

λ=603 minutes=20 per hour

μ=602 minutes=30 per hour

Ws=Lsλ=220=0.10 hours or 6 minutes

Hence, the amount of time spent by a patient in the system is 6 minutes.

c)

Summary Introduction

To determine: The probability that there will be three or more patients on the premises.

c)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the inter-arrival time of the patients is three minutes and the service time is 2 minutes.

Determine the probability that there will be three or more patients on the premises (use model 1):

λ=603 minutes=20 per hour

μ=602 minutes=30 per hour

Probability=1(P0+P1+P2)=1{(1λμ)(λμ)0+(1λμ)(λμ)1+(1λμ)(λμ)2}=1{(12030)(2030)0+(12030)(2030)1+(12030)(2030)2}

  =1(0.3333+0.2222+0.1481)=10.7036=0.2964

Hence, the probability that there will be three or more patients on the premises is 0.2964.

d)

Summary Introduction

To determine: The utilization of the nurse.

d)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the inter-arrival time of the patients is three minutes and the service time is 2 minutes.

Determine the utilization of the nurse (use model 1):

λ=603 minutes=20 per hour

μ=602 minutes=30 per hour

ρ=λμ=2030=0.67 or 67%

Hence, the utilization is 67%.

e)

Summary Introduction

To determine: The average total time of the patient in the system.

e)

Expert Solution
Check Mark

Explanation of Solution

Given information:

It is given that the inter-arrival time of the patients is three minutes and the service time is 2 minutes.

Determine the average total time of the patient in the system (use model 3):

λ=603 minutes=20 per hour

μ=602 minutes=30 per hour

ρ=λμ=2030=0.67 or 67%

The value of Lq is determined using the expected length table.

Ls=Lq+λμ=0.0093+2030=0.676

Ws=Lsλ=0.67620=0.0338 hours or 2.03 minutes

Hence, the average total time is 2.03 minutes.

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