Case Study - Saiss Olive Oil
Jawad Abrache
October 29, 2021
This case illustrates the use of linear programming modeling and solution techniques to tackle a basic investment problem. The students need
to: (1) carefully read the case, (2) understand the problem, (3) suggest a
Linear Programming (LP) model of the problem, and (4) solve the latter
using Excel’s solver.
After graduating from business school, Mohammed Rachidi went to
work for an accounting firm in Casablanca. Because his hobby has always been olive oil making, when he had the opportunity a few years
later he purchased five acres plus an option to buy 35 additional acres
of land in the region of Boufekrane (Meknès). He plans eventually
to grow olive trees on that land and make olive oil with them. Mohammed knows that this is a big undertaking and that it will require
more capital than he has at the present. However, he figures that if he
persists, he will be able to leave accounting and live full time from his
olive oil earnings by the time he is 40.
Mohammed is planning to start small. This is necessitated by both
his lack of capital and his inexperience in olive oil making on a large
scale. His plan is first to plant the olive trees on his land. Then he will
need to set up a small trailer where he can live on weekends while
he installs the irrigation system and does the required work to the
trees, such as pruning and fertilizing. To help maintain a positive cash
flow during the first few years, he also plans to buy olives from other
nearby growers so he can make his own label olive oil. He proposes to
market it through a small tasting room that he will build on his land
and keep open on weekends during the spring-summer season.
To begin, Mohammed is going to use $10,000 in savings to finance
the initial purchase of olives from which he will make the first batch
of olive oil. He is also thinking about going to the bank and asking for
a loan. He knows that if he goes to the bank, the loan officer will ask
for a business plan; so he is trying to pull together some numbers for
himself first. This way he will have a rough notion of the profitability
and cash flows associated with his ideas before he develops a formal
plan with a proforma income statement and balance sheet. He has decided to make the preliminary planning horizon two years and would
like to estimate the profit over this period. His most immediate task
is to decide how much of the $10,000 should be allocated to purchasing olives for the first year and how much to should be allocated to
purchasing olives for the second year. Mohammed plans to produce
two brands of olive oil: the Petite Saiss extra virgin olive oil and the
case study - saiss olive oil
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Meknes Best virgin olive oil.
In the first year, each bottle of Petite Saiss requires $2.80 to produce (worth of olives, bottle acquisition, plus production and bottling),
whereas each bottle of Meknes Best costs $2.70. For the second year,
the costs per bottle are $2.75 and $2.85, respectively.
Mohammed anticipates that Petite Saiss will sell for $8.00 a bottle
in the first year and for $8.25 in the second year, while Meknes Best’s
price remains the same in both years at $7.00 a bottle.
In addition to the decisions about the amounts of olives purchased
in the two years, Mohammed must make estimates of the sales for the
two olive oil brands during the two years. A local olive oil making association has told him that marketing is the key to success in any olive
oil business; and generally, demand is proportional to the amount of
effort spent on marketing. Thus, since Mohammed cannot afford to
do any market research about sales levels due to his lack of capital,
he is pondering how much money he should spend to promote each
brand each year. The association has given him a simple rule of thumb
that relates estimated demand to the amount of money spent on advertising. According to that rule, for each dollar spent in the first year
promoting Petite Saiss, a demand for five bottles will be created1 ;
and for each dollar spent in the second year, a demand for six bottles
will result. Similarly, for each dollar spent in the first year for advertising Meknes Best, a demand for eight bottles will be created; and
for each dollar spent in the second year, a demand for ten bottles will
result.
The initial funds for the advertising during the first year will come
from the $10,000 savings. The cash available from olive oil sales in the
first year will be available in the second year for both buying olives
and advertising. Note also that Mohammed may not sell all the bottles
produced in the first year, and any produced bottles that are unsold in
the first year can be placed in inventory and sold in the second year.
A personal concern Mohammed has is to maintain a proper balance
of olive oil products so that he will be well-positioned to expand his
marketing capabilities when he moves to the land and makes olive oil
making his full-time job. Thus, in his mind it is important to ensure
that the number of bottles of Petite Saiss sold each year falls in the
range between 40% and 70% of the overall number of bottles sold.
1. Mohammed needs help to decide how the dollar amount of olives
to buy, how much money to spend on advertising, and how many
bottles to sell of each brand of olive oil in each year, such that the
profit earned is maximized. Propose a linear programming model
for the problem faced by Mohammed. Indicate clearly the model’s
parameters, decision variables, objective, and constraints2 .
The level of demand created from advertising constitutes an upper bound for
the number of bottles sold; i.e., Mohammed cannot possibly sell more than
that level, but may sell less.
1
Although one should normally consider the number of bottles sold (of
each brand, in each year) as an integer
variable, you may ignore this constraint
given the large quantities and just formulate the problem as a regular linear
programming model.
2
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2. Create a spreadsheet model for this problem and solve it using Excel’s Solver.
3. Indicate the optimal investment plan resulting from the solution of
the model3 .
Hint: after solving the model, take the
time to verify a few things: the whole
budget is spent and not exceeded, all
constraints stated by the case are satisfied, etc.
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