Mathematical analysis of e-shop

[Rachnog]

Hi,

I'm ukrainian student, studying applied mathematics in Kiev.

 

I have an online store and some statistics data on it's work. Also I've learned a bit about optimization problems and operation reasearch.

 

I want to know how to apply mathematics to work with an online store? Maybe apply machine learning algorithms to handle existing statistics? Or maybe I can use some optimization techniques? I am a novice at all these things, I have only theoretical knowledge and know how to program the methods but don't know anything about their application in business.

I would be grateful for some links, books or just advice

Reagrds,

Alex Rachnog

Edited March 6, 2014 by Rachnog

[studiot]

Business calculations are mostly about artificial rules (mostly to do with tax), not natural mathematical ones.

 

There is some mathematical theory, such as linear programming, applicable to large scale operations such as oil refineries but not, I would have thought to an e-shop.

 

As regards the handling of statistics, many programs such as Excel, Mathematica, MathCad, have lots of built-in statistical functions, and there are some dedicated statistical ones such as SPSS.

There are also a number of business 'management' programs that can analyse and present data, but the best of these are usually accounting packages which already include the necessary tax rules.

 

Sorry I know nothing about Ukranian tax rules, but it is good to welcome and support someone making business, not war.

[imatfaal]

The most sophisticated pricing mechanism in shops and auctions use Game Theory to set prices/organise bidding at an optimum level. I have seen this in action for a tender process for land sale in NYC and the results were spectacular (I signed the sales contract which at the time was the highest ever per square foot in Manhattan and described by Donald Trump as ridiculous!) . You could also read up about the UK Govt 3g sale - which used a similar process for selling bandwidth for mobile phones and ended up making vastly more than expected. IIRC it is a UK don from Warwick who ran the 3g auction

[studiot]

One thing to observe is the relationship between time and money.

 

The 'value' of money depends, in part, on when it occurs.

 

You should look up concepts like

 

Net Present Value (NPV)

 

Discounted Cash Flow (DCF)

 

Pricing policy may dpend upon game theory but also upon time and perishability of the product.

So it's OK to play games with real estate that will still have a value next week or next month if unsold, but not with fresh fish that will have no value, or even negative value (disposal costs) next week if unsold.

Edited March 6, 2014 by studiot

[imatfaal]

..

Pricing policy may dpend upon game theory but also upon time and perishability of the product.

So it's OK to play games with real estate that will still have a value next week or next month if unsold, but not with fresh fish that will have no value, or even negative vlaue (disposal costs) next week if unsold.

Agree with the top bit but the point of perishable goods is just incorrect (environmental issues aside) - would you rather sell ten truffles at a ten thousands pounds each and dispose of your other 9990 or flood the small specialist market and sell 10,000 at a fiver each? pq curves only work for freely enterable and transparent markets. You set your sale price at that which maximises overall profit not that which sells the greatest quantity in many many markets - competition often changes the price quantity point to a maximal level but few markets obey the rules.

[studiot]

 

Agree with the top bit but the point of perishable goods is just incorrect

 

Consider these examples.

 

1) I buy 10 fish for $1 each and offer them for sale at a fish market, where all unsold fish must be disposed of at the end of the day's trading at 5c per fish. What price should I charge?

 

As I understand game theory it says that I should start offering them cheaply and increase the price as I begin to sell them. This minimises the potential loss if I do not sell any.

 

However this is the obverse of the practice enacted by most market traders I have seen who start dear and cut prices at the end of the day.

 

2) I buy 10 fancy boxed dolls for $1 each and sell them at one of those 'one day only' auctions. Here traders habitually offer the first below cost and bid each one up to hope to sell the last one at $15 or $20.

Edited March 6, 2014 by studiot

[imatfaal]

 

Consider these examples.

 

1) I buy 10 fish for $1 each and offer them for sale at a fish market, where all unsold fish must be disposed of at the end of the day's trading at 5c per fish. What price should I charge?

 

As I understand game theory it says that I should start offering them cheaply and increase the price as I begin to sell them. This minimises the potential loss if I do not sell any.

 

However this is the obverse of the practice enacted by most market traders I have seen who start dear and cut prices at the end of the day.

 

2) I buy 10 fancy boxed dolls for $1 each and sell them at one of those 'one day only' auctions. Here traders habitually offer the first below cost and bid each one up to hope to sell the last one at $15 or $20.

 

1) I buy 10 fish for $1 each and offer them for sale at a fish market, where all unsold fish must be disposed of at the end of the day's trading at 5c per fish. What price should I charge?

 

Even basic economics would need to know what your market is - if there are only 5 people in your town that eat fish don't bother buying 10 fish if you are in an ardently catholic large town and you are the only fish-seller then buy more fish. The question does not have enough information. Without knowledge of the scenario then no answer is possible / all answers are possible. The point is that you are seeking a optimum point at which the buyer of the fish and and you as the seller both feel that they cannot do better whilst the other persons strategy remains unchanged.

 

2) I buy 10 fancy boxed dolls for $1 each and sell them at one of those 'one day only' auctions. Here traders habitually offer the first below cost and bid each one up to hope to sell the last one at $15 or $20.

 

That would be a very complex system to analyse with multiple sales and multiple parties - but in what way is this not analysable mathematical economics - which is my very point.

[studiot]

You must have had some bad fish for dinner.

 

 

The OP was very wide ranging and I'm simply trying to offer up a selection of points for consideration.

I make no claims that the my list is exhaustive.

 

As I understand game theory it is about the balance between the possible losses and the possible gains and maximising the function gains minus losses, allowing that the maximum may be zero.

 

 

The point is that you are seeking a optimum point at which the buyer of the fish and and you as the seller both feel that they cannot do better whilst the other persons strategy remains unchanged.

 

But the seller can do 'better', although that would mean the buyer doing worse.

 

Value, of course, in an imprecise term.

Edited March 6, 2014 by studiot

[imatfaal]

...

But the seller can do 'better', although that would mean the buyer doing worse.

 

...

 

The nash equilibrium sought in game theory is the point at which both parties believe that they cannot change their position for the better presuming that the other party does not change and as they know the other party's position calculated in a similar way this is not going to happen. In the long run - or with good information - the buyer will act such that the seller cannot do better because the buyer will not accept worse.

[studiot]

A good introductory text to this side of the subject of business mathematics, up to and including the Axioms of Nash, is to be found in

 

 

"An Introduction to Linear Programming and Game Theory" by Paul R Thie, published by Wiley.

Edited March 7, 2014 by studiot

[imatfaal]

Not read that one - but for the internet generation (which I think I am a little too old to claim membership of) there is a great intro/taster course on Game Theory on iTunes University

 

https://itunes.apple.com/gb/itunes-u/game-theory-video/id341651977?mt=10

 

It is by Ben Polak of Yale

[Rachnog]

Guys, thanks for the responses and links, I see what I need to learn. Also found a good book by Taha - Operation Research (http://books.google.com.ua/books/about/Operations_Research_An_Introduction_8_E.html?id=QhU5BkVRm2oC&redir_esc=y), I'm sure, it seems to be classical, but I haven't worked with it.

 

I understand that I have to do a little more fundamental economic to deeper understand subject area

[studiot]

Operational Research and Game Theory flowered in the 1940s and attracted many of the era's big names in mathematics

 

Kantarovich

 

Mathematical Methods in The Organisation and Planning of Production (Russian 1939, English 1960)

 

VonNeuman

 

The Theory of Games and Economic Behaviour

 

Nash's work appeared in papers in the early 1950s

 

Nash

 

The Bargaining problem

Econometrica 18 (1950)

 

Non-Cooperative Games

Annals of Mathematics 54 (1951)

 

Two-person Cooperative Games

Econometrica 21 (1951)