Name:
Program:
PROD 2100
Production and Operations Management
Exam: June 2003
Grading :
Question
Grade
Over
Time:
1
2
3
4
5
6
Total
4
4
2
2
4
4
20
9.00 - 11.00
N.B. Each answer needs explanations. In case of ambiguity or of lack of information, first state your
interpretation/assumption and then answer the question.
Have a good exam !
1. The company
The company is called “Petit Pains”. It basically assembles and sells sandwiches. It
also sells drinks. It is located in Louvain-la-Neuve in the “Grand Rue”, the street all
the students take.
2. The products
The basic product is made of half a baguette (standard french loaf) :
 with butter (always),
 with some filling: ham, cheese, pâté, … (on demand),
 with some lettuce and tomato (optional, 50% of the customers).
Standard drinks are also available (coke, sprite, water, …). About half the customers
do order some drinks.
3. The order process
An incoming customer joins a unique waiting queue. When a serving team becomes
available, he places his order (kind of baguette filling, lettuce or not, drinks if any),
waits for the preparation of his order, pays and leaves the shop.
4. The manufacturing process
A serving team can be composed of a single person or of two persons.
In the case of a single person, this only server performs all the operations
successively. In the case of a 2-person team, the first one takes the order and prepares
the sandwich while the second one packs it, prepare the drinks if any, cashes the
money and thanks the customer.
The following table details the successive operations of the manufacturing process
and specifies the time they take on the average. Note that this time varies with the
kind of organization. Indeed, with a 2-person organization, some specialization takes
place and about 20 % of the processing time can be saved.
A-product:
Sequence
of operations
Operation
Number
Duration
in seconds for a
single server
Duration
in seconds for a
2-server team
Person in
charge in a
2-server team
Welcome
and take
order
Op1
Prepare
the
sandwich
Op2
Lettuce
(optional)
Pack the
sandwich
Op4
Prepare the
drinks
(optional)
Op5
Cash
and
Goodbye
Op6
Op3
20
40
20
10
20
30
16
32
16
8
16
24
Server 1
Server 1
Server 1
Server 2
Server 2
Server 2
5. The supply process
The supply is not a problem for most goods that can be cheaply stored except for
bread that has to be ordered every day. The order process is twofold. In the morning,
the manager has to order a given quantity of baguettes. Later on, around 1.30 pm, the
baker passes by and some more baguettes can be bought on the spot.
6. The operations
The shop is open 5 days a week, during the 43 weeks (closed in July and August).
Among these 43 weeks, 28 are considered as “lecture” weeks (see below). The
sandwich sales are almost evenly spread between 11.30 am and 2.30 pm. During the
rest of the day, only drinks are sold.
7. The staff
You are the boss and the only regular employee of this company. You are responsible
for all the major functions : supply, production management, HR, finance, etc. You
hire students on a 4 hours basis. They work from 11 am to 3 pm. They are in charge
of the manufacturing process. They serve the customers during the time the shop is
open, that is, from 11.30 pm to 2.30 pm. The period 11.00 - 11.30 is devoted to the
preparation of the working environment. The period 2.30 – 3.00 pm is devoted to the
cleaning. You take care of the sales of drinks outside this time window.
8. The demand
The demand is mainly generated by the students and by the university staff. Except
for the July and August months, during which the shop is anyway closed, the demand
generated by the university staff is rather stable all over the year. The demand
generated by the students varies according to the type of week. It is much higher for
the “lecture” weeks than for the others. The reason must be that most students stay at
home (away from Louvain-la-Neuve) when there are no lectures. The following two
tables gives examples of sales in number of sandwiches, drawn from last year, for two
samples of 10 weeks without lecture and with lecture.
So, for example, the weekly sales for a non-lecture week amount to about 501
sandwiches on the average, for this sample. The tables also gives you several
differences and sums.
During the last year, the sales were evenly spread from 11.30 am to 2.30 pm every
day of the week.
For next year, we should foresee some increase in sales. Indeed, no change in the
offer is to be expected and the student population will increase by about 5 %.
However, the university staff population will remain stable.
Although the demand varies in volume over the weeks, it does not vary in structure.
About one half of the customers take the “lettuce” option and the others don’t.
Independently, another half of the customers order some drinks and the others don’t.
week
1
2
3
4
5
6
7
8
9
10
sums….
lecture
0
0
0
0
0
0
0
0
0
0
sales
451
498
511
536
453
546
510
527
452
526
5010
average sales-avg
501
50
501
3
501
-10
501
-35
501
48
501
-45
501
-9
501
-26
501
49
501
-25
0
50
3
10
35
48
45
9
26
49
25
300
week
11
12
13
14
15
16
17
18
19
20
sums….
lecture
1
1
1
1
1
1
1
1
1
1
sales
1543
1480
1411
1445
1544
1503
1368
1602
1426
1568
14890
average sales-avg
1489
-54
1489
9
1489
78
1489
44
1489
-55
1489
-14
1489
121
1489
-113
1489
63
1489
-79
3
54
9
78
44
55
14
121
113
63
79
630
Questions.
1. In this type of “sandwich” business in general,
a. give three examples (one for each) that describe what are the “make to
stock”, “make on order” and “assemble to order” production policies
b. give one major advantage of each policy.
ANSWER:
MTS. The sandwiches are prepared and packed in advance.
(+) speed.
MTO. Everything is done on the basis of the order.
(+) customization, freshness
ATO. All the sandwiches are buttered. Half of them are already prepared with
lettuce.
(+). High speed and relatively high customization.
2. Consider the two types of proposed organizations for the serving team:
a. Compute their productivity (do not forget to state your assumptions, if
any)
b. Not considering the productivity, give a major argument in favour of
each organization and argue.
c. Explain how would you practically choose between the two
organizations.
ANSWER:
a.
1-person: on the average: 120 seconds per customer and per worker
(precisely: every four customer requires 100 seconds, every two customer
requires 120 seconds and every four customer requires 140 seconds)
2-persons: based on the average operation times, the first server is always the
bottleneck; therefore, the average productivity is: 56 seconds per customer and
per 2 workers
assumption: the calculations are based on average operation times. It could be
worse if there are too many variations in the 2-person org (or buffers are
needed to compensate)
b.
1-person: customer contact, flexibility
2-persons: reduced equipment, avoid transition between food and money
c.
I would refer to the order winner. For example, if my company fights on “cost”,
I would orient myself towards 2-P. However, since the location is already an
order winner, I could loose some slight productivity to offer a better service I
can charge.
3. How many teams would you require during a “lecture week” if you organize
your shop with two-persons teams ?
ANSWER:
2-persons: on the average: 56 seconds per customer and per 2 workers.
One team working full time serves 3 * 3600 / 56 = 192.
Amount of work: 300 customers. Therefore two teams are necessary. This will
also give the extra capacity to avoid aking the customer to wait too much.
4. Knowing you have several serving teams, do comment on the waiting line
policy in place.
ANSWER:
FCFS is the policy. This is a socially acceptable rule avoiding anybody to wait
too long (minimization of the maximum waiting time)
One line is preferable to 2 lines. If there are two lines, a specially slow
customer would impede the whole group of customers behind him. On the other
hand, if there are several lines, they could be organized according the type of
service required.
5. For the coming year, consider a “lecture week”. Estimate what the average
demand will be and comment about its accuracy.
ANSWER:
Average. The demand during a “lecture week” is about 1489. The 5% increase
applies to the student population only. Therefore, a first set of bounds for the
average demand will be [1489 ; 1489 * 1.05]. If we point out that there are at
least 1000 students in the customer base, than the bounds can be tighten to
[1489 + 1000 * 0.5 ; 1489 * 1.05].
Standard deviation. It should be derived from the MAD.
Observed MAD is 63. Sigma = 1.25 63 = 79.
But this applies to the previous demand. Since it is scaled by about 1.05, Sigma
will be scaled by sqrt(1.05).
6. Assume, to fix ideas, that the demand in a “lecture week” is 1500 sandwiches
with a standard deviation of 50. Let us now focus on the control of the
inventory of baguettes for a “lecture week” day. We have two questions here
to solve: “how many baguettes do you order in the morning to the backer?”
and “how many baguettes do you order when he passes by around 1.30?”. Let
us focus on the first one.
a. State which precise objective you aim at when facing this question
b. Choose the quantity you will order in order to meet this objective
ANSWER:
A. Your goals are always to maximize the service and to reduce the costs.
The service is maximized by minimizing the stockout probability before the
second delivery (or by avoiding to pay the penalty costs related to these
stockouts). The costs are reduced by avoiding the holding costs related to
baguettes that could not be sold.
Therefore, you first want to order enough, not to experience a stockout at 1.30
pm. You should order enough to cover the demand during the first two hours.
Second, you do not want to buy so much that you have too many breads at the
end of the day (after three hours of sales).
Mathematically, you should order a quantity Q such that
a). Prob[dem(2 hours) > Q] is low (let us say, 0.01)
b). Prob[dem(3 hours) < Q] is large (let us say, 0.99)
B. Demand in 2 hours =
normal (average = 200, sigma = sqrt(2/15) * 50)=N(200, 18)
Demand in 3 hours =
normal (average = 300, sigma = sqrt(3/15) * 50)= N(300,22)
Q= 245 seems the best.
It is 2.5 sigma above the average demand during 2 hours and
2.5 sigma below the average demand during 3 hours.
Distribution normale N(0,1)
z
= nombre d'écarts types
P(z) = Prob [ x  z ]
E(z)
z
0,0000
0,1000
0,2000
0,3000
0,4000
0,5000
0,6000
0,7000
0,8000
0,9000
1,0000
1,1000
1,2000
1,3000
1,4000
1,5000
1,6000
1,7000
1,8000
1,9000
2,0000
2,1000
2,2000
2,3000
2,4000
2,5000
2,6000
2,7000
2,8000
2,9000
3,0000
3,1000
3,2000
3,3000
3,4000
3,5000
3,6000
3,7000
3,8000
3,9000
4,0000

= nombre moyen de manquants =  ( x  z) pN ( 0,1) ( x) dx
z
P(z)
0,5000
0,4602
0,4207
0,3821
0,3446
0,3085
0,2743
0,2420
0,2119
0,1841
0,1587
0,1357
0,1151
0,0968
0,0808
0,0668
0,0548
0,0446
0,0359
0,0287
0,0228
0,0179
0,0139
0,0107
0,0082
0,0062
0,0047
0,0035
0,0026
0,0019
0,0014
0,0010
0,0007
0,0005
0,0003
0,0002
0,0002
0,0001
0,0001
0,0001
0,0000
E(z)
0,3989
0,3509
0,3069
0,2668
0,2304
0,1978
0,1687
0,1429
0,1202
0,1004
0,0833
0,0686
0,0561
0,0455
0,0367
0,0293
0,0232
0,0183
0,0143
0,0111
0,0085
0,0065
0,0049
0,0037
0,0027
0,0020
0,0015
0,0011
0,0008
0,0005
0,0004
0,0003
0,0002
0,0001
0,0001
0,0001
0,0000
0,0000
0,0000
0,0000
0,0000
E(-z)
0,3989
0,4509
0,5069
0,5668
0,6304
0,6978
0,7687
0,8429
0,9202
1,0004
1,0833
1,1686
1,2561
1,3455
1,4367
1,5293
1,6232
1,7183
1,8143
1,9111
2,0085
2,1065
2,2049
2,3037
2,4027
2,5020
2,6015
2,7011
2,8008
2,9005
3,0004
3,1003
3,2002
3,3001
3,4001
3,5001
3,6000
3,7000
3,8000
3,9000
4,0000