1. Consider the total production (and sales) of ice cream in Canada (in millions of liters)
for the period 1995 until 2007 (from left to right):
341, 331, 317, 315, 321, 278, 298, 311, 302, 302, 335, 320, 285
Fit a model to ice cream production data using each of the following techniques and
forecast the 2008 production in each case. Also, plot the two moving average
forecasts and the actual, the two exponential smoothing forecasts and the actual, and
the linear trend and the actual (three graphs altogether).
a. Two-year moving average.
b. Four-year moving average.
c. Exponential smoothing with smoothing constant = 0.2.
d. Exponential smoothing with smoothing constant = 0.4.
e. Linear trend (regression).
f. Just by observing the plots, which of the above techniques would you use to
forecast the ice cream production and why? (Hint: The plot overall closest to
actual demand will be most accurate).
g. Alternatively, compute the MAD for each forecasting technique and determine
the most accurate technique.
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2. The number of Toyota Corollas produced in the Cambridge, Ontario, plant during each
month of January 2008 to December 2009 period was as follows:
Assume that the cars are sold in the same month they are produced. Identify an
appropriate forecasting technique, briefly state the reason(s) you chose it, and
forecast Corolla demand in January 2010.
3. Fleet managers have a large pool of cars and trucks to maintain.13 One approach to
the vehicle maintenance is to use periodic oil analysis: the oil from the engine and
transmission are subjected periodically to a test. These tests can sometimes signal
an impending failure (for example, iron particles in the oil), and preventive
maintenance is then performed (at a relatively low cost), eliminating the risk of failure
(failure would result in a relatively high cost). However, oil analysis costs money and
it is not perfect—it can indicate that a unit is defective when in fact it is not, and it can
indicate that a unit is nondefective when in fact it is. As a possible substitute for oil
analysis, the company could simply change the oil periodically, thereby reducing the
probability of failure. The fleet manager for the Southern Company, an electrical utility
based in Atlanta (parent of Georgia Power and Light), has four alternatives: (1) do
nothing, (2) use oil analysis only, (3) replace oil only, or (4) replace oil and do oil
analysis. For option (1) the probability of failure is 0.1, and the cost of failure is $1,200.
For option (2), the probability of failure remains at 0.1. If the unit is about to fail, the oil
analysis will indicate this with probability 0.7; if the unit is not about to fail, the oil
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analysis will indicate this with probability 0.8. The oil analysis itself costs $20, and if it
indicates that failure is about to occur, the oil will be changed at the cost of $14.80
and preventive maintenance will be performed. The cost of preventive maintenance
to restore a unit that is about to fail is $500, whereas the cost of maintenance for a
unit that is not about to fail is $250. For options (3) and (4), probability of failure
decreases from 0.1 to 0.04. Analyze this decision problem.
4. One of the products of Edwards Lifesciences (EL) is artificial heart valves made from
the heart valves of pigs.8 Different sizes of valves are required. However, the size of
a pig’s heart valve cannot be ascertained before the heart is purchased and opened.
Therefore, EL has a mismatch problem: shortages of some sizes and excess of
others. A program was established to document the size distribution of valves supplied
by each supplier, and purchases were made from those suppliers with the needed
sizes. Linear programming was used to determine the set of the suppliers that
collectively satisfied EL’s demand. Suppose EL purchases pig valves from three
suppliers. The cost and size mix of the valves purchased from each supplier are given
in the table below. Each month EL places one order with each supplier. Suppose next
month, 250 large, 300 medium, and 100 small valves are needed. Formulate an LP
that can be used to minimize the cost of acquiring the needed valves and use Excel’s
Solver to solve it.