Being Precise.

Using the same computer and the same program and the same data there was a different result. How can that be? Was I responsible?
It was the IBM Shell computer which I had just updated the IBM operating system as bugs in the data-base processing had been fixed up. Shell had a big computer with 64K while Caltex and BP had only 32k. That meant that Shell had the responsibility for doing the refinery planning using IBM’s Linear Programming Package which required at least 44k. The oil companies shared the one oil refinery. The package would find the optimum output for the refinery operation given a number of technical constraints.
The constraints could be represented by a polygon in many dimensions in which the answer would reside at an extremity to maximize the profitability of the output. The program would climb up the edges of the imaginary multi-dimensional polygon choosing the best route until it could go no further giving the best result while just staying inside the limiting polygon. A lot of number crunching is involved best described as matrix calculations. When doing divisions in a computer the results are usually imprecise as the results get truncated losing a little precision on the way. The program kept storing up a list of numbers called eta-vectors. These would be used in a matrix re-inversion process to catch up the lost precision. Because the new operating system took up more memory this matrix re-inversion happened at a different stage and a different choice was made in the edge of the polygon to follow and thus end up at a different answer. Nobody in NZ was specialised enough to understand all this but the Shell headquarters in The Hague promptly telexed up the explanation. In the original printout there was an A which was disregarded. It was a message to say that there was a valid alternative solution which we uncovered in the second run of the optimization. Panic over! I have kept the telex as a souvenir. I think this something to remember with computer modeling, precision can be lost.

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