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MSCI 224 Techniques for Management Decision Making

创建日期：2024-05-09 17:41:36

所属分类：管理Management

标签： MSCI 224

Techniques for Management Decision Making

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MSCI 224 Techniques for Management Decision Making

CLOSED BOOK EXAMINATION (3 HOURS)

FORMULA SHEET PROVIDED

Calculators and standard dictionaries are permitted.

In Part A, answer the one question that has been set.

In Part B, answer three out of the four questions.

Answer each question in a separate booklet.

If you write answers to all four questions in Part B, please cross out the answer
that should not be marked. Otherwise, the marker will mark only the first three
answers encountered.

Show all your workings.
DO NOT TURN THIS PAPER OVER UNTIL YOU ARE TOLD TO DO SO

Formula Sheet

Networks
PERT: Mean Duration of an Activity =
6
4 bma ++
Variance of the Duration of an Activity =
2
6





 − ab
where a = optimistic estimate
b = pessimistic estimate
m = most likely estimate

Forecasting (Exponential Smoothing)

Single (Simple) Exponential Smoothing

tmt Sy =+ˆ (m = number of periods ahead to forecast)
1)1( −−+= ttt SyS αα ( 10 << α ) Smoothed level

Holt’s Method

ttmt mbSy +=+ˆ (m = number of periods ahead to forecast)
))(1( 11 −− +−+= tttt bSyS αα ( 10 << α ) Smoothed level
11 )1()( −− −+−= tttt bSSb ββ ( 10 << β ) Smoothed trend

Winters’ Method

Lmtttmt FmbSy −++ += )(ˆ (m as before; L = length of the seasonal cycle)
))(1()/( 11 −−− +−+= ttLttt bSAFyAS ( 10 << A ) Smoothed level
Ltttt FBSyBF −−+= )1()/( ( 10 << B ) Smoothed seasonality
11 )1()( −− −+−= tttt bCSSCb ( 10 << C ) Smoothed trend

Simulation (Random Sampling)

Negative exponential distribution: )1ln( Rmx −−=

Uniform distribution, U[a,b]: Rabax )( −+=

where m = mean, a and b are lower and upper limits, and R is a uniform [0.1] rand. var.
(paper continues over)
3
Area in one tail for the standard normal distribution

Z = (X – m) / s where m is the mean and s is the standard deviation

0 Z
4
Random Number Table

PART A: Answer Question A1 in this section of the paper.

Question A1 (25 marks)

A dental hospital has two dental nurses and one dentist. The dentist has specialist knowledge and
skills for dealing with patients who require specialist treatments (e.g. fillings, root canals). If the dentist
is busy and a patient requires a specialist treatment they must wait until the dentist becomes free.
Patients with general dental problems can see any of the staff, but the dentist will only attend to a
general patient if both dental nurses are busy. Customers wait in the waiting room if they cannot be
seen immediately. The hospital opens at 9am and closes at 5pm each day.
The time between general patients arriving at the dental hospital follows a negative exponential
distribution with mean of 0.2 hours, and the time between special treatment patients arriving at the
dental hospital follows a negative exponential distribution with mean of 0.5 hours. The service time
of a general patient is described by a uniform distribution between 0.5 and 1 hours, and the service
time of a specialist treatment patient can be described by a uniform distribution between 1 and 2
hours.
a) How can random numbers can be used to model the variability in this situation? Specify the
formulae you would use.
(25% of marks)
b) Using discrete event simulation, simulate the system up to the time of departure of the 1st
patient requiring general treatment. How long does each customer wait to be seen by one of
the dental staff? Do all your calculations to 3 decimal places.

Use 4-digit random numbers from the formulae sheet. For each process, use the following
number stream:
• General patient inter-arrival times (5th row) : 6524 3011 7654 4608 8595 5921 2692
8923 2024 2108 …
• Special Treatment patient inter-arrival times (7th row): 7493 5070 3768 5243 5010
3662 3924 6180 0823 9804
• General patient service times (1st row): 1869 8478 8578 4023 9576 2595 5664 6042
0073 3181
• Special Treatment patient service times (3rd row): 1139 9393 4279 6670 6454 5597
4593 5746 5139 0827
(40% of marks)
c) The staff at the dental hospital are interested in improving patient experience. On the
outcome of a survey, long waiting times appear to be the largest cause of poor customer
experiences. Firstly, explain how simulation can be used to investigate the waiting time of
customers in the current system. Secondly, suggest a simple change that could be made to
the system to improve waiting times, and how simulation could be used to investigate the
impact of this change.
(25% of marks)
d) Would it be appropriate to use a warm up period for this system? Justify your answer.
(10% of marks)
- please turn over for Part B
6
PART B: Answer three of the four questions in this section of the paper.

Question B1 (25 marks)
A sports goods manufacturer makes snowboards. The following table shows the actual sales (in £000s)
each quarter in years 2017 and 2018. Do all your calculations to 3 decimal places.
Year Period Sales
2017 1 493
2 752
3 1194
4 1348
2018 1 521
2 802
3 1501
4 1719

a) Forecast the sales for all quarters of year 2019 by using 3-points moving average method after
de-seasonalising the data with the proper moving average method. Use multiplicative
seasonal method.
(30% of marks)

The following table is calculated using the Winter’s exponential smoothing method using
smoothing constants A, B and C all equal to 0.15. The table shows the actual sales y (in £000s),
smoothed values S, seasonal factors F, and trend factors b for each quarter of 2016, 2017 and
2018.
Year Period Y (sales) S F b
2016 1 421 766.503 0.562 25.083
2 669 798.568 0.826 27.178
3 1022 823.499 1.247 26.504
4 1142 846.359 1.359 25.411
2017 1 493 873.406 0.563 25.902
2 752 902.639 0.828 26.901
3 1194 937.927 1.255 29.417
4 1348 974.713 1.366 31.628
2018 1 521 982.059 0.553 24.343
2 802 995.061 0.821 20.941
3 1501 1070.010 1.299 37.142
4 1719 1152.530 1.404 50.756
b) Calculate the sales for all 4 quarters in year 2019 in £000s using Winter’s method. Use the
appropriate values given in the table above in your calculations.
(20% of marks)

c) The actual sales for 2019 quarter 1 were 647 (in £000s). Calculate the S, F and b values for
2019 period 2.
(20% of marks)

- question continues over
7
Q B1, continued

d) If the actual sales in year 2019 are 647, 955, 1803 and 2011 (in £000s), what is the mean error,
mean absolute error and mean square error of moving average and Winter’s methods in year
2019. What can you say about the accuracy of these two methods?
(20% of marks)

e) One of the difficulties in using Winter’s method is that initial values are required for the
smoothed level, trend and seasonal factors. One way of starting Winter’s method is to use
initial values of the smoothing level, trend and seasonal factors that are based on the first few
values of the series. Explain a suitable procedure to obtain such initial values.
(10% of marks)

Question B2 (25 marks)
A construction project consists of the following activities, with their predecessors, durations (in weeks)
and resource requirements (in workers):
Activity Duration Predecessors Resource Requirement
A 5 2
B 4 2
C 3 1
D 5 A,B 1
E 4 B,C 2
F 2 D 2
G 2 D,E 1
H 6 F 1
I 5 G 1

a) Draw a network diagram for the project. Calculate the earliest and latest start and finish times
for each activity, and the total, free and interfering floats for each activity. State the project
duration and the critical path.
(30% of marks)

b) Draw the Gantt Chart and resource allocation graph for the project. Calculate the weekly
resource requirement throughout the project if each activity starts at their earliest start time.
Report the maximum resource level requirement throughout the project.
(20% of marks)

It is recognised that the previous analysis does not take into account the uncertainties in
activity durations. Estimates have been made of the expected means and variances of each of
the activity times, for the same activities and network as before, as shown in the table below.
Assume that the lengths of the project activities are mutually independent.

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