Case study: Vehicle assembly
Alpha Alliance, a large automobile manufacturing company, organises the vehicles
it manufactures into three families: a family of trucks, a family of small cars, and a
family of midsized and luxury cars. One plant in Victoria assembles two models
from the family of midsized and luxury cars. The first model, the Eagle, is a fourdoor sedan with vinyl seats, plastic interior, standard features, and excellent gas
mileage. It is marketed as a smart buy for middle-class families with tight budgets,
and each Eagle sold generates a modest profit of $3,500 for the company. The
second model, the Silhouette, is a two-door luxury sedan with leather seats,
wooden interior, custom features, and navigational capabilities. It is marketed as
a privilege of affluence for upper-middle-class families, and each Silhouette sold
generates a healthy profit of $5,500 for the company.
Mark Evans, the manager of the assembly plant, is currently deciding the
production schedule for the next month. Specifically, he must decide how many
Eagles and how many Silhouettes to assemble in the plant to maximise profit for
the company. He knows that the plant possesses a capacity of 50,000 labour-hours
during the month. He also knows that it takes six labour-hours to assemble one
Eagle and eight and a half labour-hours to assemble one Silhouette.
Because the plant is simply an assembly plant, the parts required to assemble the
two models are not produced at the plant. Instead, they are shipped from other
plants in New South Wales to the assembly plant. For example, tires, steering
wheels, windows, seats, and doors all arrive from various supplier plants. For the
next month, Mark knows that he will only be able to obtain 25,000 doors from the
door supplier. A recent labour strike forced the shutdown of that particular
supplier plant for several days, and that plant will not be able to meet its
production schedule for the next month. Both the Eagle and the Silhouette use the
same door part.
In addition, a recent company forecast of the monthly demands for different
automobile models suggests that the demand for the Silhouette is limited to 3,800
cars. There is no limit on the demand for the Eagle within the capacity limits of the
assembly plant.
a. Formulate and solve a linear programming model to determine the number
of Eagles and the number of Silhouettes that should be assembled. How
much profit will this strategy generate? How many doors and labour-hours
are required and unused?
Before he makes his final production decisions, Mark plans to explore the
following questions independently, except where otherwise indicated. Some of
these problems do not require re-optimisation, and sensitivity analysis will be
adequate. If a problem requires re-formulation, you must show and discuss the new
model.
b. The marketing department knows that it can pursue a targeted $400,000
advertising campaign that will raise the demand for the Silhouette next
month by 25 percent. Should the campaign be undertaken? If it should, how
much an additional profit will the campaign generate?
c. Mark knows that he can increase next month's plant capacity by using
overtime labour. He can increase the plant's labour-hour capacity by 30 per
cent. With the new assembly plant capacity, how many Eagles and how
many Silhouettes should be assembled? How much profit will this strategy
generate? How many doors and labour-hours are required and unused?
d. Based on part c, Mark knows that overtime labour does not come without
an extra cost. What is the maximum amount he should be willing to pay for
all overtime labour beyond the cost of this labour at regular-time rates?
Express your answer as a lump sum.
e. Mark explores the option of using both the targeted advertising campaign
and the overtime labour-hours. The advertising campaign raises the
demand for the Silhouette by 25 percent, and the overtime labour increases
the plant's labour-hour capacity by 30 percent. How many Eagles and
Silhouettes should be assembled using the advertising campaign and
overtime labour-hours? How much profit will this strategy generate? How
many doors and labour-hours are required and unused?
f. Knowing that the advertising campaign costs $400,000 and the maximum
usage of overtime labour-hours costs $1,800,000 beyond regular time
rates, is the solution found in part e a wise decision compared to the
solution found in part a?
g. Automobile Alliance has forecasted that the demand for Silhouette will
decrease to 2,500 cars next month. To maintain the current market share,
Mark has decided to offer the promotional price, which will reduce the
marginal profit of Silhouette to $4,950. Mark fears that a new optimised
solution will cause the flood of Eagle cars into the market due to the
reduction of Silhouette’s profit, he has decided that the number of Eagles
assembled should not exceed 4,700 cars and that the production ratio of
Eagle to Silhouette must not exceed 2:1. How many Eagles and Silhouettes
should be assembled? How much profit will this strategy generate? How
many doors and labour-hours are required and unused? What is the
production ratio of Eagle to Silhouette based on the results?
h. The company has identified a new robotic machine that reduce the
assembling time for each Eagle and Silhouette to four and six hours
respectively. Mark has been asked to come up with a new production
strategy based on the new assembling time. How many Eagles and
Silhouettes should be assembled? How much profit will this strategy
generate?
i. Based on part h, if the robotic machine costs $3,000,000, what should Mark
recommend to the company? Why?
j. Mark now makes his final decision by combining all the new considerations
described in parts f and i. Determine the numbers of Eagles and Silhouettes
to be assembled, the new profit, and the amount of required and unused
resources.
k. Based on part j, if an automotive-part supplier approaches Mark to sell
their car doors which are compatible with Eagle and Silhouette with the
price of $800 per door. Should Mark procure the doors from this supplier?
If so, how many doors should be ordered? Why?
Details:
A case study is a scenario in a particular professional context which students
are expected to analyse and respond to, guided by specific questions posed
concerning the situation. In many cases, the scenario or case study involves a
number of issues or problems that must be dealt with in a professional
workplace. Case study assignment requires students to demonstrate their
developing knowledge of theories and quantitative methods to make informed
decisions and provide recommendations to either prevent or solve some of the
issues in that scenario.
•
Students will be provided a case study and associated questions.
•
Students are required to
o
read the case and associated questions carefully. Highlight the main
points of the case and any issues that you can identify. Read the
questions closely and analyse what they are requiring you to do. Read
the case again, linking the information that is relevant to each question
you have been asked.
•
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develop a quantitative model to solve the problem.
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answer to the case questions based on the output of your analysis.
Students are required to submit
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a Word file to explain your mathematical models, to report your
answers, and to write recommendations for decision makers based on
the identified solutions, and
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an Excel file to demonstrate how you use spreadsheet to identify the
solutions. You must ensure that the file is in a workable condition before
the submission.
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If quantitative method is required to be linear programming, students must
use the Solver to solve this problem. No intuitive or hubristic approach is
acceptable.
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