Chapter 11   Optimization Series, Purchase Order and Stock Size

In this Chapter 11 of ‘Business Economics VI Groundbreaking’, you will become familiar with the existence of functions; by drawing them and calculating them, certain problems can be solved. No two cars, to give just one example, are exactly the same nowadays. The production of series has, where possible, been reduced to single-piece manufacture from before the industrial revolution, but that applies especially to end products. These end products are usually composed of standard components, which are produced in series. Usually with the help of machines, which have to be changed after such a series in order to make something else (possibly a different size, a different color, a different type). Conversion takes time and changeover time implies changeover costs. The less change, the less changeover costs, but the longer the series, in other words larger stocks and stocks bring with them stock costs.
Long series: high inventory costs and few changeover costs.
Shorter series: less inventory costs but more changeover costs.
There must be an optimum somewhere. The same problem occurs in more situations. Consider, for example, a retail trade that purchases goods from the wholesale, on order. The ordering operations, checking deliveries, handling invoices and the like, it all costs the same whether much or little is ordered. Ordering costs, regardless of the batch size and inventory costs depending on the batch size. To solve the problem, there is already something in the aforementioned toolbox of the Operations Research, or something tailor-made can be made for it. In the handbooks, an example is known as Camp’s formula.
At what point are we now on the cost function and what can be gained by moving towards the minimum? Is it possible to win a lot or only a little by shifting something, in other words how steep is the curve on the spot? Nothing changes to the curve itself and therefore the place of the minimum. That curve and that minimum do not depend on our (current) limitations in inventory space or available money or otherwise. There will probably be a non-ideal x with which we will have to work for now. What should we aim for? That’s the question. Insight into the course of such a curve, that’s what it’s about. The total costs y are a function of the series size x:  y = f(x). The minimum of y is easy to find by differentiating and setting the derivative y’ equal to zero (this derivative ‘is the tangent’ to the function f(x)) and where this tangent line runs horizontally, the directional coefficient is zero, the function generally reaches a peak or a trough, and in this case it is clear, the minimum. See APPENDIX: Mathematical Differentiation. This has been added to Chapter 11 of ‘Business Economics VI Groundbreaking’ because some knowledge of mathematics, of analysis, of differentiation, is desperately needed.

This book harshly criticizes out-of-date Business Economics textbooks.

You are very poorly trained in business economics even at Business Schools that ignore ‘Business Economics VI Groundbreaking’.

A self-study book, hardly needing a teacher. Necessary also for many managers in companies to improve their own performance.