Food Manufacture 1: When to Buy and How to Blend


Problem Statement

A food is manufactured by refining raw oils and blending them together.[2] The raw oils come in two categories:

vegetable oils

VEG 1

 

VEG 2

non-vegetable oils

OIL 1

 

OIL 2

 

OIL 3

Each oil may be purchased for immediate delivery (January) or bought on the futures market for delivery in a subsequent month. Prices now and in the futures market are given below (in £/ton):

 

VEG 1

VEG 2

OIL 1

OIL 2

OIL 3

January

110

120

130

110

115

February

130

130

110

90

115

March

110

140

130

100

95

April

120

110

120

120

125

May

100

120

150

110

105

June

90

100

140

80

135

The final product sells at £150 per ton.

Vegetable oils and non-vegetable oils require different production lines for refining. In any month it is not possible to refine more than 200 tons of vegetable oils and more than 250 tons of non-vegetable oils. There is no loss of weight in the refining process and the cost of refining may be ignored.

It is possible to store up to 1000 tons of each raw oil for use later. The cost of storage for vegetable and non-vegetable oil is £5 per ton per month. The final product cannot be stored, nor can refined oils be stored.

There is a technological restriction of hardness on the final product. In the units in which hardness is measured this must lie between 3 and 6. It is assumed that hardness blends linearly and that the hardnesses of the raw oils are

VEG 1

8.8

VEG 2

6.1

OIL 1

2.0

OIL 2

4.2

OIL 3

5.0

What buying and manufacturing policy should the company pursue in order to maximize profit?

At present there are 500 tons of each type of raw oil in storage. It is required that these stocks will also exist at the end of June.



[2] Reproduced with permission of John Wiley & Sons Ltd. (Williams 1999, pp. 231–232).