Optimal Resource Allocation: With Practical Statistical Applications and Theory

CHAPTER 9

Comments on Calculation Methods

9.1 Comparison of Methods

Optimal redundancy is a very important practical problem. The solution of the problem allows one to improve reliability at a minimal expense. But here, as in many other practical problems, questions arise: What is the accuracy of the obtained results? What is the real effect of the use of sophisticated mathematics?

These are not unreasonable questions.

We have already discussed what it means to design an “accurate” mathematical model. It is always better to speak about a mathematical model which more or less correctly reflects a real object. But let us suppose that we are “almost sure” that the model is perfect. What price are we willing to pay for obtaining numerical results? What method is best, and best in what sense?

The use of excessively accurate methods is, for practical purposes, usually not necessary because of the uncertainty of the statistical data. On the other hand, it is inexcusable to use approximate methods without reason.

We compare the different methods in the sense of their accuracy and computation complication.

The Lagrange multiplier method (LMM) demands the availability of continuous, differentiable functions. This requirement is met very rarely: one usually deals with the essentially discrete nature of the resources. But LMM sometimes can be used for a rough estimation of the desired solution.

The steepest descent method (SDM) is very convenient from a computational viewpoint. It is reasonable ...