Test Exam
Disclaimer:
•
This test exam consists merely of computational questions, during the actual exam interpretations could be asked as well.
•
The total number of points including the free points equal 95 for this test exam; in the actual exam the total number of points will be 100.
Questions can be answered in English or Dutch. Explain every step in your reasoning. The number of points for a correctly answered question is shown in front of the question; 10 points are free.
1. A company that is introducing a new product has to choose between four different manufacturing methods, referred to as methods A, B, C, and D.
Depending on the demand for the product (high, medium, or low), they have forecast different levels of revenue for the year (values are in thousands).
Method A
Method B
Method C
Method D
High
$80
$22
$9
$44
Medium
$61
$46
$14
$55
Low
$38
$100
$52
$24
a) (6p) Which method is best in accordance with a decision criterion of maximin? b) (9p) Which method is best in accordance with a decision criterion of minimax regret?
2. Acme Machine is a job shop that makes specialty parts for the airline industry.
The figure below shows the block plan for key manufacturing departments in its current facility. The closeness matrix is given as well.
Current block plan
C
D
B
A
E
F
Closeness matrix
Trips between departments
A - Burr & Grind
B - NC Equipment
C - Shipping & Receiving
D - Lathes & Drills
E - Tool Crib
F – Inspection
A
-
B
8
-
C
3
0
-
D
0
3
0
-
E
9
0
8
0
-
F
5
0
9
3
3
-
a) (10p) What is the weighted-distance score of the current block plan? Use rectilinear distance (the distance between departments C and D is one unit of distance).
b) (5p) Find a better block plan in terms of weighted-distance score by exchanging the locations of two departments.
3. The B. Sharp Company has a rapidly growing product line that requires two work centers, X and Y for manufacture. Work Center X has a current capacity of 50,000 units per year, and Work Center Y is capable of 55,000 units per year. In year 1, sales of the product line are expected to reach 53,000 units.
Growth is projected at an additional 3,000 units each year through year 3. Pretax profits are expected to be $60 per unit throughout the 3-year planning period. The company considers to expand both Work Centers X and Y at the end of year 0 to a capacity of 60,000 units per year, at a total cost for both
Work Centers of $500,000.
a) (5p) What are the pretax combined cash flows for years 0 through 3 that are attainable to the expansion?
b) (5p) Ignoring tax, depreciation, and the time value of money, determine how long it will take to recover (pay back) the investment.
c) (5p) What is the net present value of the combined cash flows if the discount rate is 20%?
4. John Boots is a shoeshiner at a busy intersection in downtown Luther.
Customers arrive at a rate of 8 per hour and wait in line until they are served. It takes John 5 minutes on average to polish a pair of shoes with a standard deviation of 1.5 minutes. Arrivals tend to follow a Poisson distribution, and service times follow a normal distribution.
a) (5p) What is the average utilization of the system?
b) (5p) What is the average waiting time in line of customers?
5. The daughter of the owner of a local hamburger restaurant is preparing to open a new fast-food restaurant called Hasty Burgers. Based on the arrival rates at her father’s outlets, she expects customers to arrive at the drivethrough window according to a Poisson distribution, with a mean of 20 customers per hour. The service rate is flexible; however, the service times are expected to follow an exponential distribution. The drive-through window is a single-server model.
a) (10p) What service rate is needed to keep the average time in the service system (waiting time and being served) to 6 minutes?
b) (5p) What fraction of the time is the drive-through window employee without work?
6. A local moving company has collected data on the number of moves they have been asked to perform over the past three years. Moving is highly seasonal, so the owner decides to apply the multiplicative seasonal method to forecast the number of customers for each quarter of the coming year. In the table below, the number of moves for each quarter for the past three years is given. Quarter
1
2
3
4
Year 1
25
40
45
30
Year 2
27
45
55
37
Year 3
33
45
58
40
a) (10p) Forecast the number of moves for each quarter of year 4, based on an estimate of total year 4 number of moves of 188.
b) (5p) The actual demand in year 4 turns out to be 35, 47, 61, and 40 for quarters 1, 2, 3, and 4, respectively. Calculate the mean absolute deviation
(MAD).
Formula Sheet
Break-Even Analysis
•
Break-even quantity:
•
Evaluating processes, make-or-buy indifference quantity:
=
=
Planning Capacity
•
•
−
− −
Capacity requirement for one service or product:
=
�]
100
[1 − �
[ + � � ]product 1 + [ + � � ]product 2 + ⋯ + [ + � � ]product n
=
[1 − �
�]
100
Capacity requirement for multiple services or products:
Financial Analysis
•
Present value of future amount:
•
Straight-line depreciation:
M/G/1 Waiting Line Models
•
Utilization:
=
=
(1 + )
=
−
mean service time mean inter-arrival time
•
Average waiting time in line:
•
Coefficient of variation:
M/M/1 Waiting Line Models
= ×
CV =
1 + CV 2
×
1−
2
standard deviation mean •
Customer arrival Poisson distribution:
•
Service time exponential distribution:
•
Average utilization of the system:
•
Probability that customers are in the system:
•
Probability that zero customers are in the system:
•
Average number of customers in the service system:
•
Average number of customers in the waiting line:
•
Average time spent in the system, including service:
() −
!
=
( ≤ ) = 1 − −
=
= (1 − )
0 = 1 −
=
−
=
=
1
−
•
Average waiting time in line:
•
Little’s Law:
= =
Forecasting Demand
•
•
•
•
Simple moving average: +1 =
+ −1 + −2 + ⋯ + −+1
+1 = Weight1 ( ) + Weight 2 ( −1 ) + Weight 3 ( −2 ) + ⋯ + Weight ( −+1 )
Weighted moving average:
Exponential smoothing:
Forecast error:
+1 = + (1 − ) = −
CFE = ∑
�=
CFE
∑ 2
MSE =
∑( − � )2
−1
=�
MAD =
MAPE =
∑| |
(∑| |⁄ )(100%) 