Archive for July, 2012|Monthly archive page

Can a computer do envy-free divison?

In Education, Interdisciplinary Science on July 28, 2012 at 10:15 PM

We have all studied division. In the world of simple mathematics, 8 divided by 2 is always 4.  But what about dividing a cake into 2 equal pieces? A computer program can always divide 8 by 2 and give 4 as answer, but can a computer program divide a cake into 2 equal pieces? Let us make it a bit more complicated. Say the cake has to be divided between persons A and B and in such a way that neither of them feels that the other person got more. This means that neither A or B will envy the share received by the other. So here the notion of equal division has to be understood in the context of the result leading to an envy-free solution. This is the subject of “Fair Division” also known as cake cutting problem. It is studied in politics, mathematics, economics and the like. Methods and algorithms have been proposed to achieve fair division but all require inputs from the parties involved in the division at different stages of the procedure. Note that these inputs need not be disclosed as these could be the feelings/assumptions/conclusions running in the minds of the parties involved. This means that different inputs at different stages can lead to different outcomes. Does it remind of “Observer Effect” in Physics? Yes. The inputs(observation of a current state of division) by a party affects the outcome of division (phenomenon being observed). It is impossible (?) for a computer to solve a problem of this type entirely on its own. Such problems arise routinely in allocation of goods, dispute resolution, negotiation of  treaties etc.

Borrowing terms from economics, a number can be treated as ‘a homogeneous good’ while a cake is essentially ‘a heterogeneous good’ as different parts of it can taste different. Hence, its envy-free division is far more complicated. If you are interested, try to read “Fair Division-From cake-cutting to dispute resolution“, an excellent book by Steven J. Brams (political scientist) and Alan D. Taylor (mathematician).

Learning Electronic Product Pricing

In Design Methodologies, Education on July 19, 2012 at 4:14 PM

Do you ever wonder about how pricing for a product is done? In simple terms, the retail price has to be greater than the raw material cost. To this, one has to add manufacturing, marketing and some other costs (like labor etc.) depending on the industry segment. While there are different pricing models like the software pricing model, capital asset pricing model etc. in different market segments, in order to get a feel of how pricing is done in electronics industry, one could start with a teardown analysis and BOM (bill of materials) analysis of a product. The IHS iSuppli Teardown Analysis Service is a nice place to start. It shows teardown analysis of various electronic products in the market. The BOM cost (plus the expected manufacturing cost) generated from this analysis can be compared with the retail price of the device. This can give some insight into the product strategy being followed by the product company. Of course the actual BOM cost is expected to be slightly lower when volume production is taken into account.  An analyst/engineer can further analyse the BOM  to provide insight on component selection. Was a particular component chosen because of price or performance or a long business relationship between the product company and the component company or any combination of these? My earlier post “Electronics Engineering through Real World Examples” focused on the design aspects of a product. This post adds the product pricing issues to design considerations. The two posts should be seen to complement each other. Sometimes, a design engineer may not get a component of his choice because a similar component is already being sourced from another supplier (because of various reasons including company legacy)  and its details are already available in the internal component database maintained by the company. The two components may differ a bit in their performance, package, PCB footprint etc.  and the design engineer has to use his/her skills to workaround this issue. If you subtract the sum of BOM cost and manufacturing cost from the retail price, you can think of the remainder as the sum of marketing cost and profit per piece of the product. If you further do a little bit of study on money spent on marketing of the product and its sales volume, you can come up with a reasonable estimate of the profit earned per piece of the product. Of course, I have simplified the analysis a bit to give a reasonable understanding of the pricing methodology.  In a more complicated model, for products where technical support is required, there could be a “support cost” built into the pricing model. I will leave it to you to dig further into pricing models if you are interested.