OPERATIONS+SUPPLY CHAIN...:CORE >INTL<
OPERATIONS+SUPPLY CHAIN...:CORE >INTL<
5th Edition
ISBN: 9781260547627
Author: Jacobs
Publisher: MCG
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Question
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Chapter 10, Problem 22OQ

a)

Summary Introduction

To determine: The time required for the given operations.

a)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Person X plans for six tellers and the tellers would take 15 minutes per customers. Standard deviation is given as 7 minutes. arrival time of customers is three minutes according to the exponential distribution.

Determine the arrival and service rate using waiting line approximation:

X¯a=3Sa=3X¯s=15Ss=7S=6

Determine interarrival time:

Ca=SaX¯a=33=1

Determine service time:

Cs=SsX¯s=715=0.4667

Determine arrival and service time:

λ=1X¯a=13=0.3333

μ=1X¯s=115=0.06667

ρ=λSμ=0.33336(0.06667)=0.8332

Determine the number of customers waiting in the line:

Lq=ρ2(S+1)1ρ×Ca2+Cs22=0.83322(6+1)10.8332×12+0.466722=0.505770.1668×1.21782=1.8443

Hence, the number of customers waiting in the line is 1.8443.

b)

Summary Introduction

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

b)

Expert Solution
Check Mark

Explanation of Solution

Given information:

Person X plans for six tellers and the tellers would take 15 minutes per customers. Standard deviation is given as 7 minutes. arrival time of customers is three minutes according to the exponential distribution.

Determine the arrival and service rate using waiting line approximation:

X¯a=3Sa=3X¯s=15Ss=7S=6

Determine interarrival time:

Ca=SaX¯a=33=1

Determine service time:

Cs=SsX¯s=715=0.4667

Determine arrival and service time:

λ=1X¯a=13=0.3333

μ=1X¯s=115=0.06667

ρ=λSμ=0.33336(0.06667)=0.8332

Determine the time spent by the customers in the line:

Lq=ρ2(S+1)1ρ×Ca2+Cs22=0.83322(6+1)10.8332×12+0.466722=0.505770.1668×1.21782=1.8443

Ls=Lq+Sρ=1.8443+(6)(0.8332)=1.8443+4.9992=6.8435

Ws=Lsλ=6.84350.3333=20.5325

Hence, the time spent by the customers in the bank is 20.5325.

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:

When the customer arrived at the place, saw the queue and decided to leave before getting into line is said to be balked.

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:

Here, the customer arrives at the place, saw the queue and stand in line. However, he decides to leave before getting service is said to be reneged.

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