2.8 Conclusions

In our example we have examined a very simple oil blending model. This has consisted of

  • an objective function, to express our aims in producing the blend;
  • several quality constraints;
  • a material balance row, to ensure that we are consistent in the units we use for materials: "what goes in must come out".

In addition, in one variant (CAPCTYFO) we had

  • limits on the availability of components;
  • a requirement for a specified quantity of product.

It is remarkable that these are, in fact, typical examples of nearly all the rows we ever get in LP models. There is only one other type of row:

  • capacity constraints, e.g. on the throughput at a process unit.

We have seen that the objective function is crucial in determining which solution we select as the optimum. Different objective functions (such as one maximising quality and another minimising cost) can give rise to the same optimum solution and apparently minor changes to the objective can cause the solution to change dramatically. We need to be very careful when using LP and very precise in our definitions.

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