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Question:

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. As a by-product, the company also produces sunflower mash (a paste made from the remains of crushed sunflower seeds) that it sells into the market as base product for animal feed.

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 and mash. 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

Mash

Average Price Index

$/short ton

1 127.7 317.8 63

2 192.4 465 87

3 242 662.2 105

4 242 668.2 111

5 274 791.3 124

6 242 732 108

7 290 951 134

8 347.2 1123 153

9 436 1297.3 193

10 422.8 1312 187

11 466 1416 193

12 582 1664 247

13 508 1317.4 242

14 428 1182.4 197

15 434 1334.4 210

​

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. TourneSol produces 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 72% 0.95%

B 82% 0.85%

C 65% 0.72%

​

For all three suppliers, it is expected that the average yield of oil from the seeds is 30%. There is no net loss of material, so the yield of mash from the same supply is expected to be 70%.

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 85%

B 100%

C 90%

The company faces an additional variable production cost of $10/short ton and an estimated fixed cost of $1,750,000 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, oil, and mash 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 α = 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. Don’t 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.

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).

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

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.

Management Report

Prepare a written management report that includes, at a minimum, the following sections:

Purpose of the Report

Description of the Problem

Methodology (which would include the model formulation)

Findings or Results

Recommendations or Conclusions

Be sure to address all relevant points, discuss any assumptions you are making, justify any modeling choices you have made (for example, the choice of time series forecast model), and highlight the following items in your report:

a forecast of the next production period’s average price index for raw sunflower seeds, sunflower oil, and sunflower mash,

a recommendation for the optimal purchasing strategy from the various suppliers,

a cost-volume-profit analysis using for the recommended purchase strategy and the forecasted sunflower oil and mash sales price,

a discussion of the risks and uncertainties that are faced by the company, and

an analysis and opinion on the profitability of the company in the next production period (accounting for the expected profit or loss and the inherent risks/uncertainties.

Remember that you are writing the report from the point of view of a consultant with senior management of TourneSol Canada, Ltd. as the intended audience.

---

Answer:

Sol:

	Moving Avergae(3)		Exponential Smoothing, alpha =	0.2
t	At	Forecast	Abs Error	Sqr(Abs Error)	Abs Error/At		Forecast	Abs Error	Sqr(Abs Error)	Abs Error/At
1	127.7						348.94	221.24	48947.14	1.73
2	192.4						304.69	112.29	12609.49	0.58
3	242						282.23	40.23	1618.74	0.17
4	242	187.37	54.63	2984.80	0.23		274.19	32.19	1036.00	0.13
5	274	225.47	48.53	2355.48	0.18		267.75	6.25	39.07	0.02
6	242	252.67	10.67	113.78	0.04		269.00	27.00	728.98	0.11
7	290	252.67	37.33	1393.78	0.13		263.60	26.40	696.98	0.09
8	347.2	268.67	78.53	6167.48	0.23		268.88	78.32	6134.06	0.23
9	436	293.07	142.93	20429.94	0.33		284.54	151.46	22938.98	0.35
10	422.8	357.73	65.07	4233.67	0.15		314.84	107.96	11656.43	0.26
11	466	402.00	64.00	4096.00	0.14		336.43	129.57	16788.90	0.28
12	582	441.60	140.40	19712.16	0.24		362.34	219.66	48249.45	0.38
13	508	490.27	17.73	314.47	0.03		406.27	101.73	10348.19	0.20
14	428	518.67	90.67	8220.44	0.21		426.62	1.38	1.91	0.00
15	434	506.00	72.00	5184.00	0.17		426.90	7.10	50.48	0.02
16		456.67	456.67				428.32	428.32
		MAD =	98.40				MAD =	101.33
		MSE =		6267.17			MSE =		12122.99
		sigma =		79.17			sigma =		110.10
		MAPE =			0.172902843		MAPE =			0.302962383

		Moving Avergae(3)		Exponential Smoothing, alpha =	0.2
t	At	Forecast	Abs Error	Sqr(Abs Error)	Abs Error/At		Forecast	Abs Error	Sqr(Abs Error)	Abs Error/At
1	317.8						1015.60	697.80	486924.84	2.20
2	465						876.04	411.04	168953.88	0.88
3	662.2						793.83	131.63	17326.98	0.20
4	668.2	481.67	186.53	34794.68	0.28		767.51	99.31	9861.60	0.15
5	791.3	598.47	192.83	37184.69	0.24		747.64	43.66	1905.80	0.06
6	732	707.23	24.77	613.39	0.03		756.38	24.38	594.17	0.03
7	951	730.50	220.50	48620.25	0.23		751.50	199.50	39800.06	0.21
8	1123	824.77	298.23	88943.12	0.27		791.40	331.60	109958.31	0.30
9	1297.3	935.33	361.97	131019.87	0.28		857.72	439.58	193230.31	0.34
10	1312	1123.77	188.23	35431.79	0.14		945.64	366.36	134222.41	0.28
11	1416	1244.10	171.90	29549.61	0.12		1018.91	397.09	157681.27	0.28
12	1664	1341.77	322.23	103834.32	0.19		1098.33	565.67	319985.72	0.34
13	1317.4	1464.00	146.60	21491.56	0.11		1211.46	105.94	11222.91	0.08
14	1182.4	1465.80	283.40	80315.56	0.24		1232.65	50.25	2525.00	0.04
15	1334.4	1387.93	53.53	2865.82	0.04		1222.60	111.80	12499.35	0.08
16		1278.07	1278.07				1244.96	1244.96
		MAD =	286.83				MAD =	306.16
		MSE =		51222.06			MSE =		111112.84
		sigma =		226.32			sigma =		333.34
		MAPE =			0.181893948		MAPE =			0.36438398

 

		Moving Avergae(3)		Exponential Smoothing, alpha =	0.2
t	At	Forecast	Abs Error	Sqr(Abs Error)	Abs Error/At		Forecast	Abs Error	Sqr(Abs Error)	Abs Error/At
1	63						156.93	93.93	8823.47	1.49
2	87						138.15	51.15	2615.98	0.59
3	105						127.92	22.92	525.20	0.22
4	111	85.00	26.00	676.00	0.23		123.33	12.33	152.12	0.11
5	124	101.00	23.00	529.00	0.19		120.87	3.13	9.82	0.03
6	108	113.33	5.33	28.44	0.05		121.49	13.49	182.08	0.12
7	134	114.33	19.67	386.78	0.15		118.79	15.21	231.19	0.11
8	153	122.00	31.00	961.00	0.20		121.84	31.16	971.20	0.20
9	193	131.67	61.33	3761.78	0.32		128.07	64.93	4216.07	0.34
10	187	160.00	27.00	729.00	0.14		141.06	45.94	2110.94	0.25
11	193	177.67	15.33	235.11	0.08		150.24	42.76	1828.07	0.22
12	247	191.00	56.00	3136.00	0.23		158.80	88.20	7780.09	0.36
13	242	209.00	33.00	1089.00	0.14		176.44	65.56	4298.62	0.27
14	197	227.33	30.33	920.11	0.15		189.55	7.45	55.52	0.04
15	210	228.67	18.67	348.44	0.09		191.04	18.96	359.51	0.09
16		216.33	216.33				194.83	194.83
		MAD =	43.31				MAD =	46.46
		MSE =		1066.72			MSE =		2277.33
		sigma =		32.66			sigma =		47.72
		MAPE =			0.163837708		MAPE =			0.29569601

All the three time-series data shows that we are getting lower estimates of error in the case of Moving Average. So we finalize the 3-year Moving average figures for all these time series data.

Marketing Year	Seed	Oil	Mash
Average Price Index	Average Price Index	Average Price Index
$/short ton	$/short ton	$/short ton
16	456.67	1278.07	216.33

--------------------------

Let XA, XB, and XC be the short tons of seeds procured from supplier A, B, and C. These are the decision variables.

Formulation in Excel follows

Final Solution

	XA	XB	XC
Seed procured (short ton)	19053	26937	3285
Oil (Short ton)	5715.9	8081.1	985.5
Mash (Short ton)	13337.1	18855.9	2299.5	Total Revenue
Selling price of oil ($/ short ton)	1278.07	1278.07	1278.07	18893069.78
Selling price of mash ($/ short ton)	216.33	216.33	216.33	7461762.525
Market price of seed ($/ short ton)	456.67	456.67	456.67	26354832.3
% on market price	85%	100%	90%
Purchase cost of seed ($/ short ton)	388.17	456.67	411.00
Variable Cost ($/ short ton)	10	10	10	Total Var. Cost
Total var. Cost ($/ short ton)	398.17	466.67	421.00	21540008.13
				Total Fixed Cost	Total Profit
				1750000	3064824.172

 

CVP Analysis

The Breakeven point can be found again by using Solver, this time without any constraints and only equating total profit with zero.

The question perhaps tells us to calculate the breakeven without the considering the variable cost of purchase and to take the market price of seed only. In that case, there is no significance for taking 3 suppliers separately. So, we take, X as the break-even quantity.

Revenue at break-even = 1278.07*0.30*X + 216.33*0.7*X

Variable Cost at breakeven = (456.67+10)*X

Fixed Cost = 1750,000

At breakeven, total profit = 0 i.e. Revenue at break-even - Variable Cost at breakeven - Fixed cost = 0

Solving for X, we will get X = 25,667

 

 

 

 

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