What’s Best for Multivariable Computations

Assume for a minute that you are in the granola business. You buy bran, wheat flakes, raisins, coconut, slivered almonds and dates and combine them in your own secret ratios to produce a tasty cereal.

Let’s further assume that your product label specifies the food values and percentage of minimum daily nutrition requirements that your cereal meets, as well as the net weight of the package. But it doesn’t specify the ratio of bran to wheat to raisins and so on that you use, and, in fact, it is possible for you to vary those ratios quite extensively and still remain within the specifications stated on the label.

Finally, let’s assume that the price you must pay for each of your raw ingredients fluctuates. Therefore, you need to constantly vary the ratios of ingredients if you are going to keep your profits high without changing your price.

Computational nightmares like that are faced by businesses every day. It may be a problem of employee scheduling, shipping costs versus shipping routes or optimizing the mix of products to be manufactured from limited resources.

Electronic spreadsheets such as Lotus 1-2-3 are a vast improvement over pencil and paper in figuring out the best solutions to these kinds of problems, but an even better method is now available, aptly named What’s Best. This $695 software package, which is used in conjunction with Lotus on IBM and compatible personal computers, allows you to quickly find the optimum solution to problems such as those described above.

Published by General Optimization Inc., 2251 N. Geneva Terrace, Chicago 60614, (800) 441-BEST, What’s Best allows you to apply a technique called “linear programming” to Lotus spreadsheets to derive answers to complex multivariable problems.

Imagine that the granola problem is three-dimensional, shaped something like a pyramid made up of separate compartments, each containing one ingredient of the granola. The compartments are flexible so that as the mix of ingredients changes, the shape of the pyramid changes. But it always has a peak somewhere and that is always the point of maximum profit.

Linear programming is a way to describe that pyramid mathematically, squeezing it in and out, pushing it up and flattening it down until the optimum shape is found to match the limits that you have set--in this case, the highest profit that provides the required nutrition and product weight.

As What’s Best works, it flashes a series of graphs onto your screen, allowing you to almost see the three-dimensional machinations that it is going through.

You must begin running What’s Best before you start up Lotus. It will run from a hard disk, but it requires that you have the original program disk in the computer when you start. Then you can remove that disk and start Lotus. What’s Best remains hidden away in your computer’s memory until you are ready to call it into use from a Lotus spreadsheet.

Once you have set up your spreadsheet model properly, operation is quite simple. You press the “PrtSc” key on the IBM and compatibles’ keyboard and a small What’s Best menu flashes onto the middle of your screen.

Basically, you then follow the simple list of commands to use the function keys to tell the program which cells of the spreadsheet contain variables that can be changed in computing the answer, which ones describe the numeric constraints that must be abided by, which are fixed value cells and which are to be either maximized or minimized. That done, another two keystrokes are all that it takes to set What’s Best to the task.

The program disk comes with several sample spreadsheet models, each of which is fully described in tutorial fashion in the manual. They are simple problems, but the manual explains how to use them as building blocks for creating more complex models to solve real-world problems.

What is not so simple is understanding how What’s Best works so that you can set up your own work sheets. If you don’t set it up right, the program can’t solve the problem. It does give useful error messages when that happens that pinpoint which cells are at fault. Still, fixing them isn’t always easy. Getting a firm conceptual grasp on the program is essential, but it might not be everyone’s bowl of cereal.

For one thing, you must be careful to describe the problem mathematically in linear equations. Multiplying one variable by another won’t work because that’s not linear. (The amount you pay for gasoline is linear--gallons times price per gallon. The balance in a savings account earning compound interest is not linear--balance times interest rate plus balance.)

The $695 price seems high for a program that requires another $495 program before it will run, especially considering that it’s a single disk with only 150 kilobytes of program code on it. On the other hand, its cost can probably be justified by many potential users. But if General Optimization would adopt the low-price policy followed so successfully by Sidekick and Turbo Pascal publisher Borland International and drop the price to $99, What’s Best could become a must purchase for practically every Lotus owner.

For the record: In a column published the week of Feb. 2, I described computer-controlled, radio-operated model blimps being used by Apple Fellow and MIT Prof. Alan Kay in a research project involving elementary school children and erroneously attributed development of the blimps to MIT. Instead, the patented models were obtained from LTA Systems Inc. of Santaquin, Utah. Inventor Kent Broadbent says he has sold hundreds of them over the past four years at $600 apiece.

The Computer File welcomes readers’ comments but regrets that the authors cannot respond individually to letters. Write to Richard O’Reilly, Computer File, Los Angeles Times, Times Mirror Square, Los Angeles 90053.