TourneSol Canada, Ltd. is a producer of high quality sunflower oil. The company buys raw sunflower seeds directly from large agricultural companies, and refines the seeds into sunflower oil that it sells in the wholesale market.

The company has a maximum input capacity of 150 short tons of raw sunflower seeds every day (or 54,750 short tons per year). Of course the company cannot run at full capacity every day as it is required to shut down or reduce capacity for maintenance periods every year, and it experiences the occasional mechanical problem. The facility is expected to run at 90% capacity over the year (or on average 150 x 90% = 135 short tons per day).

TourneSol is planning to purchase its supply of raw sunflower seeds from three primary growers, Supplier A, Supplier B, and Supplier C. Purchase prices will not set until the orders are actually placed so TourneSol will have to forecast purchase prices for the raw material and sales prices for the refined sunflower oil. The contract is written such that TourneSol is only required to commit to 70% of total capacity up front. Any amounts over that can be purchased only as required for the same price. Historical prices for the last 15 years are in the table below (note that year 15 is the most current year).

Historical Price Data
Marketing Year	Seed Average Price Index $/short ton	Oil Average Price Index $/short ton
1	325.7	507.8
2	292.4	465
3	342	852.2
4	440	664.2
5	284	991.3
6	442	732
7	280	921
8	547.2	1323
9	436	1297.3
10	642.8	1512
11	461	1406
12	782	1864
13	508	1317.4
14	438	1372.4
15	434	1334.4

Sunflower oil contains a number of fatty acids, some which are desirable in food products and others that are not. One desirable fatty acid is oleic acid. TourneSolproduces high oleic oil for the wholesale market, and requires that the oleic acid content be a minimum of 77%. Sunflower oil also contains trace amounts of iodine. The market requires that that iodine content be a minimum of 0.78% and maximum of 0.88%

The oleic acid and iodine content for the sunflower seeds from the three suppliers is given in the table below.

Supplier	Oleic Acid	Iodine
A x	68%	0.86%
B y	72%	0.78%
C z	83%	0.94%

For all three suppliers, it is expected that the average yield of oil from the seeds is 100%.

Because the oleic acid and iodine content varies across the three suppliers, so does the price. It is expected that the cost of supply from the suppliers will be a percentage of the market average price of seeds.

Supplier	Cost as % of Average Market Price of Seed
A	88%
B	100%
C	92%

The company faces an additional variable production cost of $11/short ton and an estimated fixed cost of $1,790,000 over the upcoming production period.

The company is asking you to provide a recommendation on the amount of raw material it should purchase from each supplier to minimize its cost of feedstock.

Management is also looking for an analysis on the profitability of the company in the next production cycle.

Suggested Approach

This is a fairly complex problem. The following approach is suggested:

Use the historical price data set as input to a time series forecast model in order to generate forecasted prices for the average price of sunflower seeds, and oil in the next production period. Use standard measures of error to decide between a three-period moving average model or an exponential smoothing model (with = 0.2). Use the type of model for all three time series forecasts. That is, if you decide to use the moving average model, use a three-period moving average model to fit the relevant data for all three series. Dont use the moving average for one time series and the exponential smoothing model for another time series.

Formulate a linear program to minimize the cost of raw sunflower seeds. Use the average price of seeds forecasted from the previous step in order to determine supplier prices.

Perform a cost-volume-price analysis (review the handout entitled Cost-Volume-Profit Analysis for details) using the average cost per short ton average selling price per short ton.

o You can generate an effective cost per short ton by dividing the total cost of supply (from the linear program) by the total volume (that you assumed in the linear program).

o You can generate an effective selling price per short ton from the expected percentage yields and the forecasted average price of sunflower oil.

o Because of the way that the contract is written, you can assume that the purchase of raw sunflower seeds is a variable cost (you only purchase what you require).

Recall that the cost-volume-price analysis requires you to provide

an algebraic statement of the revenue function and the cost function,

a detailed break-even chart that includes lines for the revenue and for the total cost, fixed cost, and variable cost (a total of four lines), and

a calculation break-even point expressed in number of short tons and percent of capacity.