The curse of dimensionality in hotel management, and the surprising connections with Occam’s razor.

Simplicity of control should be the goal of every hotel manager, this is particularly true for Hotel Revenue Management.

revenue management, hotel management software

Consider these two numbers.

The second number is the age of the universe, the number of seconds from the Big Bang (according to this theory). An impressive number indeed, but the first number is much bigger. What does it represent? Think about it for a minute and contact us for a special prize if you guess it right.

Let’s assume that an hotel manager needs to decide which discounts to apply to children of age less than 18. This problem requires filling a table with 18 values (one for each age, from 0 to 17) of the discount to apply (a percent value, from 0% —no discount at all— to 100% — children stay for free).

When asking manager about why they selected specific discount values, answers range from “Why not?” to “We imitate what our neighbour is doing”, to “We do not know, the software required some values and we had to fill them in in some way”. Determining an optimal solution for the above problem, one leading to the maximum possible profit, is not difficult because of laziness or ignorance but because there are just too many possibilities. There are 100 possible discount values for each age, to be multiplied to get the above amazing number of different ways of filling the complete table with percent values, that is, 1 followed by 36 zeros. Even if you analyse a possible way of filling the discount table in one second, the entire life of the universe would permit to consider only a minuscule fraction of possibilities, and your professional life is less than the life of the universe.

revenue management, hotel management software

Imagine that the hotel owner or revenue manager starts considering possible discounts immediately after the Big Bang, well, after recovering from his personal big shock and after some years of evolution to create the human species. He observes the creation of stars and galaxies, and keeps trying discounts, observes the formation of the sun from dust and its ignition to create light and heat up the cold matter, and keeps trying discounts, observes the creation of planet Earth and Moon and keeps trying discounts, observe his personal life pass without excessive emotions and keeps analysing discounts.

This explosion of possibilities is known also as the “curse of dimensionality”. Smart optimization schemes can deliver optimal solutions in reasonable times despite enormous numbers of possibilities only for a selected list of special problems, which unfortunately excludes almost all complex problems of real-world interest. If hotel managers want to apply a scientific, principled manner to choose business settings, and not black magic, a much smaller number of possibilities must be considered.

For a simple example, the manager can decide among two possibilities, and set up an experiment to decide whether a 50% discount for children of all ages will improve profits w.r.t. no discount at all. Of course, a children discount may be desirable if the hotel targets families and wants to discourage couples or singles, but the decision should be based on measurable results. For example, an experiment can be done with split testing in the hotel website, or by trying the two possibilities for comparable analogous periods. Similar conclusions hold for different decisions, like for setting proper prices for each type of room and for each day depending on demand, market evolution, competition, type of customer, groups, agencies, etc., problems which are much more difficult and more crucial than deciding about children discounts.

revenue management, hotel management software

(William of Occam and friend, painting by Andrea di Bonaiuto da Firenze)

The above fact related to the impossibility of dealing in an effective manner with decisions with too many parameters is deeply rooted in the scientific approach. A good scientific theory is characterized by brevity, and concision is the source of power enabling a solid scientific theory to conquer the world. Occam’s razor (a.k.a. “law of parsimony”) is the problem-solving principle stating that in science the simplest theories must be preferred. The idea is attributed to William of Ockham (c. 1287–1347), an English Franciscan friar and philosopher. The same “law of parsimony” is at the basis of machine learning (ML) or learning from data. Because the objective of ML is to generalize for new and unseen data, if the model is too complex, the examples presented during learning will be reproduced, but learning degrades to a sort of superficial memorization of the examples, not extracting the deep underlying rules. For revenue management, a crucial aspect is to forecast demand by customers and hotel occupation levels. Data about previous months and years, together with data from similar hotels, can be precious to “machine learn” a forecast. Again, simple models with a small number of free parameters need to be used to predict the future (before it happens).


Fast food or slow food, hotel or slow hotel?

What hotel owners can learn from Eataly success.

revenue management, hotel management software

To understand the reasons for innovation and business success it is always useful to jump sideways and put your nose - and perhaps even your tongue - into fields different from hotel management.

Let's put ourselves in the shoes of an entrepreneur in the pasta sector, let's call him Mauro, who reflects on the positioning of his business. Mauro wants to open a pasta shop. If you ask why his customers should buy his spaghetti, he can answer in at least two ways: 1) calories, 2) magic and lifestyle.

If Mauro puts himself in the business of selling calories, he competes with others who sell calories. From a recent survey [1], prices for a package of good quality spaghetti range from 45 cents to about 1.45 euros. If Mauro opens a new shop, he could try to set average price, say 1 Euro, maybe a little lower to attract new customers and hope for word of mouth. At most, focusing on high-quality dough, a few tens of cents may come up.

Only a fool could hope to sell pasta at 10 euros per kilo.

Yet at least one of these madmen exists. His name is Oscar Farinetti, he founded in 2004 a new food distribution chain, Eataly, and has opened or is opening thirty stores in the capital cities of the planet. I discovered Eataly a few days ago in the center of Manhattan, and I tried to steal some of his secrets.

The store is located in one of the most modern, theatrical and symbolic places in New York, on the top floor of a recently completed shopping center, in the area of ​​the World Trade Center rebuilt after the collapse of the twin towers. The building is characterized by a democratic luxury where white marbles dominate, windows jump towards the sky that let blades of natural light filter through, large screens dominate like football fields. In short, one of the rare shopping centers where you do not you feel suffocated after a few minutes of stay.

I climbed there from the new subway station called the World Trade Center Transportation Hub, which opened in 2016. Trains stop in a gallery covered with an immaculate mosaic. At a close look I notice that the white mosaic tiles in relief along the walls quote extracts from the American constitution and human rights. It seemed like a clear way to say in a public space "destroy our towers but we will not change our values". Together with thousands of urban ants, you swarm upwards and into the light of the colossal square called Oculus, covered by giant eyelashes of steel and glass that open towards the sky. You notice something unusual in the middle.

revenue management, hotel management software

It is an American-sized happy machine for making pasta, which wants to be noticed from a distance and surprise. On the pasta blade there is a motto "Life is a combination of magic and pasta - Federico Fellini". The crank of the machine, like a kind of invitation, indicates the direction to take to get to the store. I follow the signal in the white gallery and I notice that on the road signs, "Eataly" is the only indication present besides the information to reach the various towers - unique among hundreds of shops. The gigantic pasta machine is the only tri-dimensional advertising object in the square. My hypothesis is that Eataly has been considered the pheromone trail, the ultimate goal, which pushes many of the human ants to enter the gallery of shops, and maybe buy some perfume, a watch or a piece of clothing during the move. It's what happens in airports, no one is there with the purpose of buying some product, the goal is the journey, but, by taking advantage of the passage of people to get to the exit gate, dozens of shops wait with hope. For Eataly, the journey undertaken, the love that moves the sky and the other stars, is that into the experience of Italian cuisine and food products. And the other shopkeepers are happy to take advantage of the flow of gastronomic pilgrims.

On the top floor of the tower, with a rare sight on the Twin Towers memorial fountain, on the orange autumn plane trees, and on the gigantic quarters of the new buildings, including the highest tower in the Western Hemisphere that replaced the twin towers, is Eataly. The New York Times described it as a "megastore" that "combines elements of a vibrant open European market, a Whole Foods style supermarket, a high-end food court and a New Age learning center" [2].

revenue management, hotel management software

It is a polymorphic combination of shops where some products are created fresh in front of visitors behind transparent glass. Seeing fresh pasta nests coming out of the machine to be rolled up by expert hands is actually magical and refers to times gone by. Some items are those of quality supermarkets, others are real pieces from food boutiques, for example olive oil in golden packaging at about 50 euros per liter. Other products are designed specifically for the American market. There are plenty of short and clear explanations on food traditions, gadgets of all kinds, books, T-shirts, flags, Italian cooking classes, altars celebrating Parma hams and speck from Tretino-Alto Adige.

The shops are strategically surrounded by various restaurants with different styles and prices that range from high-but-affordable, to prices of the kind "with what I pay for a starter I can live for a week". The place is so crowded that many people eat while standing up, devouring pizzas and sandwiches, fries and oysters, not discouraged by the objective ergonomic difficulties. There are queues but the organization is that of a precision clock, you leave the cell phone number, turn safely in the sales / education / socialization spaces, and are alerted with polite messages "ten minutes before eating", "your table is almost free, please come to the host to be seated ". Overall, the impression is that of Italian pride "based on facts", not rhetorical and exhibited but conscious and solid, in short, the exact opposite of exhibitionist masochism ("Tafazzismo" [3]) which ultimately dominates the Italian public discourse.

revenue management, hotel management software

After admiring the courage and vision of a colleague, what can we bring home for hotel owners and managers?

The Mauro hotelier in this case has at least two answers to the meaning of his business: 1) clean beds 2) a unique experience. If he sells clean beds, perhaps he will analyze the average selling price of the competitors and will try to position himself, perhaps lowering it by 5 euros compared to the neighbor (which in turn will lower them by 5 euros compared to Mauro, and so on to reach marginal costs and therefore zero profit ...). On the other hand, if he offers a unique experience, his envious neighbors will be puzzled by the excellent levels of room occupancy despite the frightening prices it applies.

What is the analogue of "magic and pasta" for Mauro hotelier? What is the analogue of fast food or slow food? How does Mauro transform his hotel from means (in competition with many other equivalent means) to ends, to the final motivation that moves the tourist? Perhaps the difference between places where "you will feel at home" and places where you will live "an experience you could never live at home"? We are talking about places that push the tourist to leave their home to come to your hotel.

To transform your hotel from means (for example to perform a job in the area) to an end, to the purpose that sets in motion the soul of the tourist, is the quantum leap that many hoteliers can do to become a bit the "Farinetti's of tourism".


[2] Tardi, Alan (24 October 2007) "Spacious Food Bazaar in the Turin Plans Manhattan Branch", The New York Times