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The earliest [[Revenue Management]] model is known as ''Littlewood’s rule''.
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==The two class model==
Littlewood proposed the first static single resource quantity based RM model.<ref>Pak, K. and N. Piersma (2002). Airline Revenue Management: An overview of OR Techniques 1982-2001. Rotterdam, Erasmus university</ref> It was a solution method for the seat inventory problem for a single leg flight with two fare classes. Those two fare classes have a fare of <math>R_{1}</math> and <math>R_{2}</math>, whereby <math>R_{1}> R_{2}</math>. The total capacity is <math>C</math> and demand for class <math>j</math> is indicated with <math>D_{j}</math>.  
The demand is distributed via a [[Distribution (mathematics)|distribution]] that is indicated with <math>F_{j}( )</math>. The demand for class 2 comes before demand for class 1. The question now is how much demand for class 2 should be accepted so that the optimal mix of passengers is achieved and the highest revenue is obtained. Littlewood suggests closing down class 2 when the certain revenue from selling another low fare seat is exceeded by the expected revenue of selling the same seat at the higher fare.<ref>Littlewood, K. (1972). "Forecasting and Control of Passenger Bookins." AGIFORS Symposium Proc. 12</ref> In formula form this means: accept demand for class 2 as long as:
 
:<math>R_{2}\ge R_{1} * \text{Prob}( D_{1}>x ) </math>
 
where<br />
:<math>R_{2}</math> is the value of the lower valued segment
:<math>R_{1}</math> is the value of the higher valued segment
:<math>D_{1}</math> is the demand for the higher valued segment and
:<math>x</math> is the capacity left
 
This suggests that there is an optimal protection limit <math>y_{1}^{\star}</math>. If the capacity left is less than this limit demand for class 2 is rejected. If a [[continuous distribution]] <math>F_{j}(x)</math> is used to model the demand, then <math>y_{1}^\star</math> can be calculated using what is called ''Littlewood’s rule'':
 
:<math>y_{1}^{\star} = F_{1}^{-1}(1-\frac{R_{2}}{R_{1}})</math>
 
This gives the optimal protection limit, in terms of the division of the marginal revenue of both classes.
 
Alternatively bid prices can be calculated via
 
:<math>\pi(x) = R_{1} * \text{Prob}( D_{1}>x )</math>
 
Littlewood's model is limited to two classes. P. Belobaba developed a model based on this rule called [[Expected marginal seat revenue]], abbreviated as EMSR, which is an <math>n</math>-class model <ref>Belobaba, P. P. (1987). Air Travel Demand and Airline Seat Inventory Management. Flight Transportation Laboratory. Cambridge, MIT. PhD</ref>
 
==References==
<!--- See [[Wikipedia:Footnotes]] on how to create references using <ref></ref> tags which will then appear here automatically -->
{{Reflist}}
 
==See also==
* [[Yield management]]
* [[Expected marginal seat revenue]]
 
{{DEFAULTSORT:Littlewood's Rule}}
[[Category:Pricing]]

Latest revision as of 21:40, 28 December 2014

Today, there are several other types of web development and blogging software available to design and host your website blogs online and that too in minutes, if not hours. What I advise you do next is save the backup data file to a remote place like a CD-ROM, external disk drive if you have one or a provider such as Dropbox. The effect is to promote older posts by moving them back onto the front page and into the rss feed. If you're using Wordpress and want to make your blog a "dofollow" blog, meaning that links from your blog pass on the benefits of Google pagerank, you can install one of the many dofollow plugins available. provided by Word - Press Automatic Upgrade, so whenever you need to update the new version does not, it automatically creates no webmaster.

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