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Model Building in Mathematical Programming, 5th Edition by H. Paul Williams

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Chapter 12

The problems

There is no significance in the order in which the following 29 problems are presented. Some are easy to formulate and present no computational difficulties in solution, while others are more difficult in either or both of these respects. Some can be solved with linear programming; others require integer programming or separable programming.

It is suggested that readers attempt to formulate those problems that interest them before consulting the formulations and solutions proposed in Parts III and IV. A computer package may be used on the model, or an intuitive (heuristic) approach to some of the problems may be attempted, using original methods of the reader's own choosing; answers can then be compared with the optimal solutions given in Part IV.

Readers wishing to follow the recommended course of solving the models using a computer package are strongly advised to use a matrix generator/language, as discussed in Sections 3.5 and 4.3. This will enable them to concentrate on the structure of the model as well as facilitating error detection and greatly reducing data preparation.

12.1 Food manufacture 1

A food is manufactured by refining raw oils and blending them together. The raw oils are of 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 at present and in the futures market are given ...

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