BUIS024
Portfolio CW Part 2
Given 20/11/16
Due 9/01/17, 10 am
Note: This is the second part of the coursework given in this module and counts for 30% of your final
grade. All questions must be answered correctly and the coursework must be returned by the due date
above for full credit. All datasets, together with their descriptions, can be found in the “Coursework
Part 2” folder in the module BlackBoard area. Up to five marks may be given for presentation.
Remember that this is meant to be an individual coursework and that any indication that it is
otherwise may result in severe penalties.
Important: Electronic submission is required via BB by 09/01/2017, 10.00 am. The main
report including appendices should be only in ONE file (MS word or pdf); in addition models
must be submitted separately in a single ZIP file.
Problem 1 (25 marks): Forecasting Weekly Sales at Amanta (Albright and Winston)
Amanta Appliances sells two styles of refrigerators at more than 50 locations in the Midwest USA. The
first style is a relatively expensive model, whereas the second is a standard, less expensive model.
Although weekly demand for these two products is fairly stable from week to week, there is enough
variation to concern management at Amanta. There have been relatively unsophisticated attempts to
forecast weekly demand, but they haven’t been very successful. Sometimes demand (and the
corresponding sales) are lower than forecast, so that inventory costs are high. Other times the
forecasts are too low. When this happens and on-hand inventory is not sufficient to meet customer
demand, Amanta requires expedited shipments to keep customers happy—and this nearly wipes out
Amanta’s profit margin on the expedited units. Profits at Amanta would almost certainly increase if
demand could be forecast more accurately.
Data on weekly sales of both products appear in the file Amanta_Data.xlsx. A time series chart of the
two sales variables indicates what Amanta management expected—namely, there is no evidence of
any upward or downward trends or of any seasonality. In fact, it might appear that each series is an
unpredictable sequence of random ups and downs. But is this really true? Is it possible to forecast
either series, with some degree of accuracy, with an extrapolation method (where only past values of
that series are used to forecast current and future values)? Which method appears to be best? How
accurate is it? Also, is it possible, when trying to forecast sales of one product, to somehow
incorporate current or past sales of the other product in the forecast model? After all, these products
might be “substitute” products, where high sales of one go with low sales of the other, or they might
be complementary products, where sales of the two products tend to move in the same direction.
Because Amanta uses expediting when necessary, its sales each week are equal to its customer
demands. Therefore, the terms “demand” and “sales” are used interchangeably.
Problem 2 (20 marks)
The demand for two products in each of the last four weeks is shown below.
Demand
Week 1
Week 2
Week 3
Week 4
Product 1
23
27
34
40
Product 2
11
13
15
14
BUIS024
Portfolio CW Part 2
Given 20/11/16
Due 9/01/17, 10 am
These products are produced using two machines, X and Y. Each unit of product 1 that is produced
requires 15 minutes processing on machine X and 25 minutes processing on machine Y. Each unit of
product 2 that is produced requires 7 minutes processing on machine X and 45 minutes processing on
machine Y. The available time on machine X in week 5 is forecast to be 20 hours and on machine Y in
week 5 is forecast to be 15 hours. Each unit of product 1 sold in week 5 gives a contribution to profit
of £10 and each unit of product 2 sold in week 5 gives a contribution to profit of £4.
It may not be possible to produce enough to meet your forecast demand for these products in week 5
and each unit of unsatisfied demand for product 1 costs £3, each unit of unsatisfied demand for
product 2 costs £1.
(a) Apply a suitable technique to forecast the demand for these products in week 5.
(b) Formulate the problem of deciding how much of each product to make in week 5 as a linear
program.
(c) Solve this linear program graphically.
(d) Solve this problem using Excel Solver and describe your solution.
Problem 3 (25 marks)
Investment Strategy J. D. Williams, Inc. is an investment advisory firm that manages more than $120
million in funds for its numerous clients. The company uses an asset allocation model that
recommends the portion of each client’s portfolio to be invested in a growth stock fund, an income
fund, and a money market fund. To maintain diversity in each client’s portfolio, the firm places limits
on the percentage of each portfolio that may be invested in each of the three funds. General
guidelines indicate that the amount invested in the growth fund must be between 20 and 40 percent
of the total portfolio value. Similar percentages for the other two funds stipulate that between 20 and
50 percent of the total portfolio value must be in the income fund and that at least 30 percent of the
total portfolio value must be in the money market fund.
In addition, the company attempts to assess the risk tolerance of each client and adjust the portfolio
to meet the needs of the individual investor. For example, Williams just contracted with a new client
who has $800,000 to invest. Based on an evaluation of the client’s risk tolerance, Williams assigned a
maximum risk index of 0.05 for the client. The firm’s risk indicators show the risk of the growth fund at
0.10, the income fund at 0.07, and the money market fund at 0.01. An overall portfolio risk index is
computed as a weighted aver- age of the risk rating for the three funds, where the weights are the
fraction of the client’s portfolio invested in each of the funds.
Additionally, Williams is currently forecasting annual yields of 18 percent for the growth fund, 12.5
percent for the income fund, and 7.5 percent for the money market fund. Based on the information
provided, how should the new client be advised to allocate the $800,000 among the growth, income,
and money market funds? Develop a linear programming model that will provide the maximum yield
for the portfolio. Use your model to develop a managerial report. Include technical details in an
appendix.
Managerial Report
1. Recommend how much of the $800,000 should be invested in each of the three funds. What is the
annual yield you anticipate for the investment recommendation?
2. Assume that the client’s risk index could be increased to 0.055. How much would the yield
increase, and how would the investment recommendation change?
3. Refer again to the original situation where the client’s risk index was assessed to be 0.05. How
would your investment recommendation change if the annual yield for the growth fund were
revised downward to 16 percent or even to 14 percent?
BUIS024
Portfolio CW Part 2
Given 20/11/16
Due 9/01/17, 10 am
4. Assume that the client expressed some concern about having too much money in the growth
fund. How would the original recommendation change if the amount invested in the growth fund
is not allowed to exceed the amount invested in the income fund?
5. The asset allocation model you developed may be useful in modifying the portfolios for all of the
firm’s clients whenever the anticipated yields for the three funds are periodically revised. What is
your recommendation as to whether use of this model is possible?
Problem 4 (25 marks):
SouthFace, Ltd., is a small company that designs, and sells ski jackets and other coats. The creative
design team has laboured for weeks over its new design for the coming winter season. It is now time
to decide how many ski jackets to produce in this production run. Because of the lead times involved,
no other production runs will be possible during the season. Predicting ski jacket sales months in
advance of the selling season can be quite tricky. SouthFace has been in operation for only three
years, and its ski jacket designs were quite successful in two of those years. Based on realized sales
from the last three years, current economic conditions, and professional judgment, 12 SouthFace
employees have independently estimated demand for their new design for the upcoming season.
Their estimates are listed in the Table 4.1 below.
Table 4.1 - Estimated Demands (thousands)
14
13
14
14
15.5 10.5 16
8
5
11
8
15
To assist in the decision on the number of units for the production run, management has gathered the
data in Table 4.2 below.
Table 4.2 - Monetary Values
Variable production cost per unit (C)
Selling price per unit (S)
Salvage value per unit (V)
Fixed production cost (F)
$80
$100
$30
$100,000
Note that S is the price SouthFace charges retailers. Any ski jackets that do not sell during the season
can be sold by SouthFace to discounters for V per jacket. The fixed cost of plant and equipment is F.
This cost is incurred regardless of the size of the production run.
1. SouthFace management believes that a normal distribution is a reasonable model for the
unknown demand in the coming year.
a) What mean and standard deviation should SouthFace use for the demand distribution?
b) Is the normal distribution assumption
2. Use a spreadsheet model to simulate 1000 possible outcomes for demand in the coming year.
Based on these scenarios, what is the expected profit if SouthFace produces Q = 7800 ski jackets?
What is the expected profit if SouthFace produces Q = 12,000 ski jackets? What is the standard
deviation of profit in these two cases?
3. Based on the same 1000 scenarios, how many ski jackets should SouthFace produce to maximize
expected profit? Call this quantity Q.
4. Should Q equal mean demand or not? Explain.
5. Create a histogram of profit at the production level Q. Create a histogram of profit when the
production level Q equals mean demand. What is the probability of a loss greater than $100,000
in each case?