Global Supply Chain Management Intermediate Exam

1

International Business and Management

University of Groningen, Faculty of Economics and Business

Global Supply Chain Management

Intermediate Exam Supply Chain Management & Logistics

Process Analysis & Capacity Management

Service Processes and Queuing

October 6th, 2014

9:00~11:00 hrs

Read this before you start:

• During this intermediate exam you are required to hand over your university registration

card (or an official identity card, e.g. passport etc.) so that we can check your student

number against the list of registered students.

• Each student needs to separately hand in both his/her signed exercises and his/her

signed answers form and is required to sign the list of registered candidates.

• You may not leave the examination room until 45 minutes after the start of the

examination and 15 minutes before the end of the examination.

• Multiple versions of this intermediate exam exist.

• Use of a calculator is allowed (according to the rules of the faculty).

• A dictionary is NOT allowed to be used during the exam.

• All electronical equipment (e.g. mobile phones, laptops and MP3 players), except for

your calculator, must remain switched off and stowed away during the full length of the

topic exam.

• Do not round intermediate answers. For example, if you make calculations for waiting

line models, do not round the values of λ and µ before you fill out the formula.

• At the end of this exam, you can find an appendix containing some formulas for queuing

systems. You can use this appendix if appropriate.

• There is ONLY one correct answer for each question.

• The total number of credits equals 10; Your grade = number of credits you have obtained.

• Questions about the intermediate exam can be asked during one of the consultation hours (see

Nestor).

Student name : _____________________________

Student number : � � � � � � �

Version : Intermediate Exam Version 1

Signature : _____________________________

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*-questions (‘relatively simple’ – 2 credits)

Question 1 (0.25 credits) Which of the following activities is not a logistics activity at a distribution centre?

A. Determine the delivery schedule to retailers

B. Replenish stock from suppliers

C. Design the layout of the centre

D. None of the above

Question 2 (0.25 credits) Calvin Large currently has a productivity of 25% in transporting jeans. Management wants to

examine what the productivity will be if the transportation function of jeans is outsourced to a

third party logistics provider. In this analysis the following data can be used:

third party logistics provider

Output: 10,000 jeans per month

Costs: 50,000 euro per month

What is the new productivity (in %) if Calvin Large decides to outsource its

transportation to a third party logistics provider?

A. 20%

B. 25%

C. 30%

D. 40%

Question 3 (0.25 credits) Consider a machine which is busy 60% of its time, idle for 20% of its time and in repair for

20% of its time.

What is the efficiency of this machine?

A. 0.4

B. 0.6

C. 0.75

D. 0.8

Question 4 (0.25 credits) At the mortgage department at RABING, it takes 40 minutes to handling a mortgage requests

from a customer. The arrival rate of jobs is 2 per hour.

What is the utilisation of the mortgage department at RABING?

A. Less than 0.4

B. 0.4 or more, but less than 0.7

C. 0.7 or more, but less than 1

D. None of the above

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Question 5 (0.25 credits)

A customer who arrives, enters the queue, and leaves without service after waiting for

some time is

A. Balking

B. Reneging

C. Being patient

D. All of the above is incorrect


In the M/M/1 model, the negative exponential probability distribution is commonly used

to describe

A. Inter-arrival time

B. Service time

C. Both A and B are correct

D. Both A and B are incorrect


The idea behind simulation is:

A. To imitate a real-world situation

B. To study the properties and operating characteristics of a real-world situation

C. To draw conclusions and make action decisions based upon simulation results

D. All of the above


Consider an M/M/1 system.

What can be said about the difference between LS and LQ?

A. It is equal to the arrival rate.

B. It is equal to the service rate.

C. It is equal to the service time.

D. It is equal to the utilisation.

4

**-questions (‘moderately difficult’ – 5 credits)


OutInterarrival

time:

7 minutes

Process 2

Time required:

exactly 6.25 minutes per product

Process 1

Time required (exactly):

5 minutes per product

Consider the production system depicted above.

What is the estimate for the Work-In-Progress?

A. 1.61 products

B. 7.5 products

C. 8.75 products

D. 9 products


What is the productive utilisation rate of Process 1 in Question 9?

A. 0.13

B. 0.33

C. 0.71

D. 0.98

Batch size: 8

Set-up time: 15 minutes

5


OutInterarrival

time:

5 minutes

Process 1

1 operator

Time required

per product:

Normal(6, ½)

minutes

Process 3

1 operator

Time required

per product:

4 minutes

Process 2

(3 parallel machines)

Time required

per product:

11 minutes

Consider the process depicted above.

What is the bottleneck? A. Arrival process

B. Process 1

C. Process 2

D. Process 3

Question 12 (0.5 credits) Consider the process depicted below.

Assume that:

• The inter-arrival time of products is 5 minutes;

• There are three parallel machines at the first activity, each takes a processing time of 15

minutes per product;

• There is a single operator at Activity 2 who has a capacity of processing 15 products per

hour;

• There are 2 parallel operators at Activity 3; both take 10 minutes per product.

Activity 2

Activity

3a

Activity

3b

Activity

1a

Activity

1c

Activity

1b

19 minutes

Time required

per product:

6 minutes

Time required

per product:

20 minutes Normal(7, 1)

minutes

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What is the throughput time of this process?

A. 19 minutes

B. 24 minutes

C. 29 minutes

D. 35 minutes

Question 13 (0.5 credits) Consider the process depicted below.

Assume that:

• Jobs have an inter-arrival time of 30 seconds. 50% goes to 1a and the rest goes to 1b;

• There are two parallel machines at Activity 1, one takes 40 seconds per job, the other one

takes 1.5 minutes per job;

• Activity 2 is performed by a machine that has a set-up time of 2 minutes and a processing

time of 25 seconds per job. The batch size used is 12.

What is the departure rate of this process?

A. 100 jobs per hour

B. 102.86 jobs per hour

C. 120 jobs per hour

D. 130 jobs per hour

Question 14 (0.5 credits) Consider an ATM where on average 14 customers arrive per 30 minutes (Poisson arrivals).

The average service time equals 2 minute (negative exponentially distributed).

How many customers are on average waiting before using the ATM?

A. 13.07

B. 14.00

C. 28.00

D. 30.00

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Question 15 (0.5 credits) Trucks, using a single-channel loading dock at a warehouse, arrive 24 hours a day according

to the Poisson probability distribution. The time required to load/unload a truck is exactly 1.2

hours. The mean arrival rate is 15 trucks per day.

What is the average time a trucks spends in the system?

A. Less than 0.100 days

B. 0.100 days or more, but less than 0.15 days

C 0.15 days or more, but less than 0.2 days

D. 0.2 days or more

Question 16 (0.5 credits) The reference desk of the library at the RUG receives requests for assistance. Assume that a

Poisson probability distribution with a mean rate of 8 requests per hour can be used to

describe the arrival pattern and that service times follow a negative exponential probability

distribution with a mean service rate of 10 requests per hour.

What is the probability that there are totally 3 requests observed at the reference desk?

A. Less than 0.1


C. 0.125 or more, but less than 0.15

D. 0.15 or more

Question 17 (0.5 credits) The Utrecht museum “Van speelklok tot pierement” shows mechanical instruments. One of

the instruments, a beautiful “orchestron”, plays exactly 4 minutes for € 4. Visitors of the

museum wanting to let the “orchestron” play and paying the € 4 arrive according to a Poisson

distribution with a mean rate of 9 per hour.

What is the average time visitors wait to use the “orchestron”?

A. Less than 3 minutes

B. 3 minutes or more, but less than 6 minutes

C. 6 minutes or more, but less than 7.5 minutes

D. 7.5 minutes or more

Question 18 (0.5 credits) Patients arrive at a medical centre with one doctor at an average rate of 2 per hour. The

average time it takes the doctor to treat the patient is 20 minutes. The arrivals follow a

Poisson probability and the service times follow a negative exponential probability function.

After treatment, patients immediately leave the centre.

What is the average number of patients in the centre?

A. Less than 1.5


C. 2.5 or more, but less than 3.5

D. 3.5 or more

8

***-questions (‘exam questions’ – 3 credits)


Consider the process depicted above. Suppose that Process 1 has the same batch size as that of

Process 2.

What is the minimum batch size to ensure that the departure rate of the system is no less

than 15 per hour?

A. No more than 5

B. Larger than 5, no more than 10

C. Larger than 10, no more than 15

D. Larger than 15


An after-sale service centre is evaluating its queuing system. The centre is operated for 8

hours per day. As a first step, the manager would like to know the cost of the current system.

It is assumed that on average 2 customers arrive every half an hour (Poisson distributed).

There is one clerk, who can handle one customer every 12 minutes (negative exponentially

distributed service times). Customer waiting time (which does not include service time) can

be valued at € 45 per hour for one customer. The clerk costs €20 per hour. The clerk works for

8 hours per day, including one hour of lunch and breaks. The clerk gets paid for all the 8

hours.

What is the cost per day of this system?

A. Less than € 3000

B. € 3000 or more, but less than € 3400

C. € 3400 or more, but less than € 3800

D. € 3800 or more, but less than € 4200

Question 21 (0.75 credits) Consider a production system consisting of three stages. A product arrives at the production

system every 6 minutes to be processed. Each product must visit all three stages. Products

first go to process 1 which consists of 3 employees working in parallel. An employee can

process a product in 10 minutes. Next, the product goes to process 2, where 2 parallel

operating machines are available. A machine at process 2 needs 8 minutes per product.

Finally, the product goes to a checking station. The checking station (Process 3) is manned by

3333 minutes

Setup time per batch: 15Setup time per batch: 15Setup time per batch: 15Setup time per batch: 15 minutes Setup time per batch: 10Setup time per batch: 10Setup time per batch: 10Setup time per batch: 10 minutes

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one person (a different person than the employees at process 1 and 2), who needs 5 minutes

per product for a quality check. (Hint: products cannot be stored between any two successive

processes.)

What is the work-in-progress for this system?

A. No more than 2

B. Larger than 2, no more than 4

C. Larger than 4, no more than 8

D. Larger than 8

Question 22 (0.75 credits) At a polling station people come in to vote according to a Poisson process. There is only one

staff who handles the voting process. The time to complete a vote takes on average 45

seconds (negative exponentially distributed). People arrive at a rate of 60 per hour.

What is the probability that there is no people in waiting to vote?

A. No more than 0.3

B. Larger than 0.3, no more than 0.4

C. Larger than 0.4, no more than 0.5

D. Larger than 0.5

Appendix: a few formulas

Calculating WIP: L = λW

WIP =

∑=

n

i

ii X1

ρ

1

International Business and Management

University of Groningen, Faculty of Economics and Business

Global Supply Chain Management

Intermediate Exam Supply Chain Management,

Process Design and Capacity Management

Service Processes and Queuing

ANSWERS VERSION 1

*-questions (‘relatively simple’ – 2 credits)

1D

2A

productivity = output/input = 10,000/50,000 = 0.2

3C

efficiency = 0.6/(0.2+0.6) = 0.75

4D

5B

6C

7D

8D

In an M/M/1 system the following equation holds:

Ls = Lq + λ/ µ

Therefore the difference between Ls and Lq equals the utilisation.

**-questions (‘moderately difficult’ – 5 credits) 9C

We use Little’s equation since the arrive is the bottleneck.

The throughput time is 61.25 minutes.

The arrival rate is 60/7 per hour.

We have (60/7)*(61.25/60)=8.75 products

10.C

We ignore the set-up time for productive utilization.

60/(7*12)=0.71

11 B

Arrival rate = 12 per hour

Production rate at Process 1 is 60/7 per hour.

Production rate at Process 2 is 9 per hour.

Production rate at Process 3 is 10 per hour.

It is clear that the bottleneck is Process 1.

2

12C

15+60/4+ 10= 29 minutes

13.A

Arrival rate is (3600/30) = 120 jobs per hour.

At Activity 1, the design capacity of 1a is 3600/40= 90 jobs per hour and the design capacity

of 1b is 60/1.5= 40 jobs per hour. So, the departure rate of activity 1 is 60+40= 100 per hour.

At Activity 2, 12 jobs can be done in 2 + 5 = 7 minutes. Thus, the design capacity is 60*12/7=

102.86 jobs per hour.

The departure rate is equal to 100 per hour.

14 A

M/M/1

λ = 28 per hour; µ=30 per hour 2

13.07( )

qL

λ

µ µ λ= =

−

15.B

M/D/1

λ = 15 per day; µ=20 per day

)(2

2

λ−µµ

λ−µ=SW = 0.125 day

16. B

M/M/1

λ = 8 per hour; µ=10 per hour

3 2 3n n np P P= > >= − = 0.1024

17. B

M/D/1


2 ( )qW

λ

µ µ λ= =

−0.05 hour = 3 minutes

18. B

M/M/1


sL

λ

µ λ=

−= 2 patients

3

***-questions (‘exam questions’ – 3 credits)

19 B

The arrival rate is 20 products per hour.

Since we need to find the minimum batch size that makes departure rate no less than 15 per

hour, we should require the design capacity of process 1 and 2 no less than 15.

For Process 1, we have 60�

3� + 10≥ 15.

For Process 2, we have 60�

2� + 15≥ 15.

To satisfy both inequality above, the minimum batch size is 10..

20 C

M/M/1

λ = 32 per day

µ = 35 per day

)( λµµ

λ

−=qW = 0.305 day =0.305*8=2.438 hours

Salary: 8*20 = 160

Total cost 160+2.438* €45*32 = € 3670.86

21B

calculate design capacities per process

Arrivals: 60/6 = 10 products/hour

process 1: 3* 60/10 = 18 products/hour

process 2: 2*60/8 = 15 products/hour

process 3: 60/5 = 12 products/hour

The arrival process is the bottleneck.

By using Little’s equation, we have WIP=10x(10+8+5)/60= 3.83

22C

M/M/1

λ = 60 per hour

µ = 3600/45 = 80 per hour

�� + �� = 1 − �� = 0.4375

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Global Supply Chain Management Intermediate Exam