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The next important step in a RM process is the allocation of inventory (hotel rooms) among different market segments. The ratio of discounted versus full priced rooms is not fixed during the reservation period; rather, it is “tweaked” appropriately as the date of stay approaches. The opportunity cost of selling a discounted room instead of a full priced one has to be measured in order to make the best decision. Thus, when a customer approaches the hotel for a discounted price, the manager needs to evaluate this scenario with the expected revenue from another customer who might come at a later date, willing to pay a higher price for the same room. The manager would accept the request only if the discounted price now is more than the expected price at which the room might be booked by the second customer. The key word here is “expected”. RM systems use complicated mathematical algorithms to arrive at this decision using techniques such as Littlewoods and Expectation Maximization, referred to as the EM algorithm.
To explain these techniques, let us consider a simple two class scenario. A hotel has two price categories of rooms, say $60 and $100. Since the pricing is different for the two rooms, these rooms are each targeted at a different customer set. Based on the historical preference pattern of customers in each segment, it would be possible to estimate the number of customers who would be willing to buy these rooms at the given price, with a reasonable “variance”. The term variance refers to a tolerance level. For example, an average 50 customers may be willing to pay $100 for some rooms, but it could also mean that the actual number of customers who turn up for the $100 room could be 60 (or even 40) with some probability, or 80 (or 30) with a lesser probability. In statistical terms, this sort of pattern for the different customer segments is said to mimic a normal distribution.
Using the past data and applying statistical know-how, we can actually estimate an “expectation” of revenue by quantifying the probability of a specific demand value and the actual revenue. In the same example, let us assume that this hotel has 100 rooms, which are similar, but priced at the time of booking. If the booking is done fairly closely to the actual date of stay, the customers may need to pay $100, whereas, they might have paid only $60 had they booked in advance. Remember that, on an average, 50 persons are willing to pay $100 for this room. Obviously, many more than 50 (say, 120) are willing to $60 for the same room. We can use the Littlewoods rule to actually estimate the number of rooms that must be protected for those customers who are willing to pay $100. If we protect too many rooms, some rooms may go vacant thereby resulting in a loss of potential revenue of at least $60 per room. On the other hand if we protect too few rooms for $100 customers, we lose the opportunity of $40 per room on that number of rooms. The Littlewoods rule guides us to arrive at an optimal number of rooms that would maximize the expectation of revenues.
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