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I have some information against each company we deal with. For e.g. number of employees, business volume, average salary, etc. Which technique can I use to rank each company against the others? Thanks!

Abha
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    Rank according to which overall criterion? Some composite concept of "size"? Of "efficiency"? Other? – Alecos Papadopoulos Jan 05 '15 at 10:20
  • Need to incorporate all the metrics - size, efficiency, reach, etc. – Abha Jan 05 '15 at 10:38
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    Again, to obtain what? Assume that you have your composite measure and firm A has rank #1. How would you call this firm? The "biggest"? The "smallest"? The "leanest"? The "most profitable"? The "best"? And "best" in what sense? – Alecos Papadopoulos Jan 05 '15 at 10:43
  • @Scortchi: the discussion talks about assigning arbitrary weights. However, I am looking for a slightly more sophisticated method. Can I back my weights through some technique and not just "business knowledge"? – Abha Jan 05 '15 at 10:55
  • @Scortchi The OP would certainly benefit to read the thread you linked to. – Alecos Papadopoulos Jan 05 '15 at 10:55
  • @AlecosPapadopoulos The intent is to obtain a ranking in terms of the most profitable corporates. As in profitable to our business – Abha Jan 05 '15 at 10:59
  • Abha: Do you actually *have* data on profitability? - that would change the nature of the question completely. If not I suggest you read whuber's answer to the linked question carefully, as well as thinking over @Alecos's comments - what could you use *but* "business knowledge" to rank companies? – Scortchi - Reinstate Monica Jan 05 '15 at 11:08
  • @Scortchi i do have some measure of profitability - actually viability is a better word for the data i have. While business knowledge is crucial, i would like to ensure that no factor is gaining excessive importance just because we (as the business) think it is important. Likewise, wud like to ensure no factor is ignored or given less importance – Abha Jan 05 '15 at 11:10
  • @Abha: Then it sounds like multiple regression - with profitability, viability, or whatever as the response & no. employees, business volume, &c. as the predictors - is what you want. – Scortchi - Reinstate Monica Jan 05 '15 at 11:14

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If you want to compare and rank companies (or any other subjects, for that matter) across a set of parameters (criteria), I suggest using some weighting scheme that assigns each parameter $p$ some weight $w$ (level of importance, if you will) on some arbitrary scale, such as 0-1 or 1-10. Then a total numeric rank $R$ of a company $C$ could be represented by the following formula:

\begin{align*} R_C = w_1 * p_1 + \ldots + w_n * p_n, \end{align*} where $n$ is the number of considered parameters (criteria).

I believe that this is a rather standard approach, at least, to the best of my knowledge. It is simple, easy to implement and might be good enough for various situations. However, some particular circumstances might require the need in some special, more sophisticated weighting scheme.

Aleksandr Blekh
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    And what would your $R_c$ represent? What would it tell us about each company? Moreover, to provide an answer saying "just create a linear combination of the various parameters" simply says "don't start the effort by trying a non-linear combination". – Alecos Papadopoulos Jan 05 '15 at 10:47
  • @AlecosPapadopoulos: $R_C$ would represent exactly what the OP asked about - an aggregate metric for each company. Obviously, this is the simplest linear weighting scheme. As I mentioned, if needed, a more sophisticated (and even non-linear) schemes could be used. However, based on the [Occam's razor](http://en.wikipedia.org/wiki/Occam%27s_razor)'s principle, I believe that in many cases, this solution might be good enough. "Simplicity is the ultimate sophistication" (Leonardo da Vinci). – Aleksandr Blekh Jan 05 '15 at 10:58
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    A metric indicating what? – Alecos Papadopoulos Jan 05 '15 at 10:58
  • @AlecosPapadopoulos: A metric, indicating an aggregate representation of a set of (company's) features, weighted by their importance, according to goals of the measurement. – Aleksandr Blekh Jan 05 '15 at 11:02