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 23OQ

a)

Summary Introduction

To determine: The time for each line at each of the cashier windows.

a)

Expert Solution
Check Mark

Explanation of Solution

Determine the arrival and service rate using waiting line approximation:

X¯a=4Sa=4X¯s=7Ss=3S=2

Determine interarrival time:

Ca=SaX¯a=44=1

Determine service time:

Cs=SsX¯s=37=0.4286

Determine arrival and service time:

λ=1X¯a=14=0.25

μ=1X¯s=17=0.1429

ρ=λSμ=0.252(0.1429)=0.875

Determine the time for each line at each of the cashier windows:

Lq=ρ2(S+1)1ρ×Ca2+Cs22=0.87502(2+1)10.8750×12+0.428622=0.72100.125×1.1842=3.4147

Hence, the time for each line at each of the cashier windows is 3.4147.

b)

Summary Introduction

To determine: The time spent by the customer in the bank.

b)

Expert Solution
Check Mark

Explanation of Solution

Determine the arrival and service rate using waiting line approximation:

X¯a=4Sa=4X¯s=7Ss=3S=2

Determine interarrival time:

Ca=SaX¯a=44=1

Determine service time:

Cs=SsX¯s=37=0.4286

Determine arrival and service time:

λ=1X¯a=14=0.25

μ=1X¯s=17=0.1429

ρ=λSμ=0.252(0.1429)=0.875

Determine the time spent by the customer in the bank:

Lq=ρ2(S+1)1ρ×Ca2+Cs22=0.87502(2+1)10.8750×12+0.428622=0.72100.125×1.1842=3.4147

Ls=Lq+Sρ=3.4147+(2)(0.8750)=3.4147+1.75=5.1647

Ws=Lsλ=5.16470.25=20.6588

Hence, the time spent by the customer in the bank is 20.6588.

c)

Summary Introduction

To determine: The term for the given information.

c)

Expert Solution
Check Mark

Explanation of Solution

Determine the term for the given information:

Whenever the cashier spends idle, the amount of time stays the same and it would not increase or decrease.

d)

Summary Introduction

To determine: The term for the given information.

d)

Expert Solution
Check Mark

Explanation of Solution

Determine the term for the given information:

There would be a decrease in the average amount of time a customer spends in the bank.

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