A SALTY HAMBURGER

A hamburger consists of beef, spices, soymeal, and other ingredients. If you were Mr. McDonald and produced them in the millions, you might want a flexible recipe that minimizes costs as the prices of the ingredients fluctuate from day to day. How many per cent beef, how many per cent spices, etc., for the cheapest hamburger at this week's prices?

With no conditions attached, the problem is silly, for the cheapest hamburger is that which uses only the cheapest ingredient: The solution is a "hamburger' made 100% of salt.

But put some restrictions on the problem. There must be (say) at least 80% beef in the hamburger, at most 2% combined spices, the ratio of salt to beef must not be greater than some maximum value, and there are other constraints that will keep the hamburger tasty. Now the problem has become mathematically interesting. It is solved by a technique called "linear programming which used to be quite a chore until computers came into the picture.

Mathematically, the problem is identical to an energy problem: How many per cent of the total energy consumption should be in coal, gas, oil, etc., to achieve the optimum energy mix for the US? "Optimum" may mean maximum resource conservation, or alternatively, maximum energy gain. With no conditions attached, the answer is the analogue of the salty hamburger: Strip-mine everything in sight (see preceding item). This answer is obvious without a computer, and if the environmentalists were consistent, they would be the ones to clamor loudest for strip mining so as to maximize resource conservation; but consistency is not exactly their strong point.

In reality, of course, there must be some constraints. Cars do not run on coal, and the present percentages of the total pie cannot be changed overnight, for example.

We programmed a computer, not for the entire economy, but for the electric power industry, and we tried various constraints. For example, we told the computer, in effect: Use up to double the present percentages of the plentiful fuels (coal, nuclear), not more than half the present percentages of the fuels in short supply (gas, oil), cut imports to zero, and leave the present percentage of hydropower unchanged (due to lack of sites); what is the optimum energy mix that will maximize resource conservation (or alternatively, energy gain)?

In this and similar versions of the problem, you don't really need a computer; it will simply use up the permissible maximum of the "best" fuel (strip-mined coal), then use up the constraint of the next best (deep mined coal), and so on, until it hits a total of 100%.

So we made it work a little harder In the last few months the cost of fossile fuels has increased to a level where the average fossil fuel cost per output kilowatt-hour is almost 6 times higher than that of nuclear fuel (2 mils/kWh). We therefore put in an additional constraint: The average operating cost per kWh must not exceed a given value. This time the computer came up with percentages of the total (optimum) fuel mix that were not at all obvious.

Example: Use up to 30% strip-mined coal, up to 30% deep-mined coal, up to 10% nuclear; not more than 10% onshore oil, not more than 1% offshore oil, not more than 8% imports; use exactly 20% gas and 12% hydropower; keep costs (depreciation plus fuel costs) to less than 17 mils/ kWh; what is the mix that will maximize energy conservation? Solution: 30% s.m.coal, 30% d.m.coal, 6.5% nuclear, 1.5% imports, remainder gas and hydro as directed, no domestic oil [for electric power] at all.

These numbers, of course, are no better than the model assumed, and they are of no direct use to anybody but a bureaucrat who thinks he can decree how many power plants will use what kind of fuel. But the purpose of computer modeling is not so much to provide hard numbers as to gain insight into a complicated mechanism. We have a lot of print-outs, but if our explanations on achieving maximum over all efficiency had to be limited to three words, they would be these: coal, coal, coal!