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Load and profit: does the algorithm make any sense?

Arnaudus

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on: February 26, 2008, 08:11:51 pm
Hi all,

First, sorry if the topic has been already debated, I'm quite new to the game.

I played in two extreme situations: a more or less saturated market at the end of the last round, and a completely free market now. And I've been really surprised by the behavior of the load/profit algorithm, and its relationship with the ticket price. With the beginning of the new round, I could play with these parameters on a completely empty marker, which is better to understand the behavior of the simulation. And I found strange things, some of them can be discussed, but others look as real bugs.

Experiment done on the route LYS-CDG before any competition, my plane is the default BAE-146-100, 94 seats.

A) The function load = f(ticket price) is a negative exponential, truncated at 100% load. That means a sharp angle at the optimal price. The load obviously varies with the frequency of the flight. I guess it's really easy to reverse-engineer the exponential by a non-linear regression, I was too lazy to do that.

B) I then considered the function passengers=F(ticket price)... and big big surprise: it also depends on the frequency. For instance, when the ticket price is at 600€, the load is 82% (77 passengers) when the frequency is 1, and... 26% (49 passengers!!!!!) when the frequency is 2. In other words, if your flights are more frequent, less passengers will travel every day! In my opinion, this does not make sense at all, one would expect exactly the opposite (when flights are more frequent, it is easier to travel because you have less schedule constraints).

From there, everything converges to show why we have such an unrealistic bias towards low frequencies: in any case, whatever the route, whatever the competition, you'll achieve the optimal profit/flight by 1) putting the frequency as low as possible (direct consequence of point B) and 2) setting the price ticket at the maximum price leading to a load of 100% (consequence of the sharp angle described in A). All other fees (leasing price for planes, misc fees...) mainly scale with the number of flights, so they won't impact the profit/flight. The only exception is the gate rental price, which keeps constant whatever the frequency of your flights; however, this effect  is not strong enough to compensate the huge "frequency" effect on the number of passengers. There are some more complicated features (for instant, the load slightly influences the costs), but they are far too small to change the big picture.

I really think these weaknesses in the simulation algorithm directly lead to a game where the only optimal strategy is to run 0.5 or 1-frequency flights loaded at 100%, and to decrease the price in order to get these 100% in case of competition. The consequences are crystal clear: on competitive routes, the prices will drop down to a few euros; and all companies will run a lot of flights to a lot of destinations, instead of having high frequencies in important routes. Of course, some players will claim that they play in a different way, but actually they just play poorly, and they could earn much more money with the optimal strategy.

Of course, there can be long discussions claiming that it's not a bug, it's a feature, it regulates competition, blah blah blah. The fact is that it is completely anti-intuitive, and probably all beginners spend a lot of time before understanding that the game is strongly biased towards this strategy.

In my opinion, the game would be much more interesting if several strategies were viable, depending on the competition, on the route, on the size of the company, etc. I think the "passenger number bug" should be fixed, to get at least as many passengers a day with a fixed ticket price, whatever the frequency of the flights; and the load function should be smoother (a negative sigmoid for instance, with an asymptote at 100% --100% load is actually non-reachable. This would lead to very interesting strategies, in which the best profit might be achieved with intermediate loads and intermediate prices, etc.

Hope it helps.


AirHanoverInternational

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Reply #1 on: February 26, 2008, 08:51:33 pm
I never calculated like that but I have to agree that there should be at least the same number in pax you move each day regardless to the freq as long as you are the only one to serve that route :roll:
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Scandalian Airlines

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Reply #2 on: February 26, 2008, 09:03:48 pm
Quote from: "AirHanoverInternational"
I never calculated like that but I have to agree that there should be at least the same number in pax you move each day regardless to the freq as long as you are the only one to serve that route :roll:


And as I've said before, a 1.0 should be double that of a 0.5, it's pretty reasonable to think that if a person want to travel to a place, he bloody well wants to get back as well :)
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pseudoswede

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Reply #3 on: February 26, 2008, 09:03:49 pm
You bring up an excellent point. I think the biggest problem would be programming the algorithm to reflect it.

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(when flights are more frequent, it is easier to travel because you have less schedule constraints)


I'm going to disagree, but I don't have time right now to formulate a proper response. I'll chew on it for a few hours.
             
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Reply #4 on: February 26, 2008, 09:52:10 pm
Quote from: "pseudoswede"
You bring up an excellent point. I think the biggest problem would be programming the algorithm to reflect it.

Quote

(when flights are more frequent, it is easier to travel because you have less schedule constraints)


I'm going to disagree, but I don't have time right now to formulate a proper response. I'll chew on it for a few hours.


I would help you out a bit, seeing that you have helped me a lot ;)

Not all travelers value the flexibility of schedule. Out of the several large marketing segment, only business travelers really care about how many flights you have and what time they are at. They are the one that needs the flexibility to suit their meeting schedules. If you look into the other segments like leisure guests and tour group, the time and frequency doesn't make that big a deal to them. It is the price that matter the most.

That being said, increased frequecy does not translate into increased pax.

Imagine when you notice an airline running 10 freq of a route in a day, and you want to book a ticket. You see on their website that all their flights are quite empty, with few seated booked. What would be your conclusion? The airline would be lowering the ticket price for that route sooner or later to get more pax on it, right? So why not wait for a bit? And when enough people "wait for a bit", the airlines will lower the fare to optimize the profit. Thus, the pax would be paying lower prices.
For the opposite angle, if you need a ticket, but the route is only served by 1 airline with 1 freq a week, and the flight is nearly full, you would pay whatever they charge you.

That being said, pax could be willing to pay higher when their is less capacity on the route.

Make sense?
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travismb99

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Reply #5 on: February 27, 2008, 01:38:39 am
The problem is that this question of frequency vs. cost is route-specific, depending on the individual dynamics of each market - something which is problematic, at best, to program into a game.

For example, there is massive frequency in US business corridors - LGA-DCA, OAK-LAX. In these cases, it is undoubtedly actually true that increased frequency results in more customers, because there is a huge market for same-day business travel between these major centers. If Airline A offered only five flights XXX-YYY vs. Airline B's 20, it is likely that a given business customer would choose Airline B, even if Airline B was more expensive (to a point) because the schedule flexibility is a value quotient.

On these flights, load factors can be absolutely abysmal - I've seen numbers for the US Airways Shuttle (BOS-LGA-DCA) around 60-70%. Yet these flights are obscenely profitable because of the fare premiums which the airline can demand.

But on the flip side, on a more leisure-oriented route like CMH-MCO, where pricing sensitivity is far greater and fare-induced traffic more important, then frequency becomes less of a draw and it becomes all about having the lowest fare. A given leisure customer from AAA-BBB would likely choose Airline X's two flights over Airline Z's eight flights, because scheduling flexibility is much greater for leisure traffic.

On such flights, load factor is of great import, because just one or two seats can make the difference between an unprofitable flight and a marginally profitable one. A 90-percent-full flight JFK-MCO might just barely be covering its costs.

How you get all those individual market dynamics into a game... I don't know if you can.
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Reply #6 on: February 27, 2008, 03:30:56 am
The one qualm I have about this is  the competition factor.  Someone charges a fare that is one euro less than what your fare is.  You go from 100% LF and 50k euros of profit, down to 13% and under 10k Euros.  I thought this was supposed to be fixed already, but this kept happening to me in the last round.  Would 2-3X frequencies affect that as well?  In any event, I am adopting the 1x frequency model this go around; it's more realistic.  What airline runs 2,3,4 frequencies with one aircraft?
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Reply #7 on: February 27, 2008, 03:33:58 am
Actually, the game correlates reasonably well in regards to which routes are profitable and how frequency plays in.  it may need a little extra boost [which will be reflected in multiworlds] over what it presently has for frequency bonuses [+ up to 5% going up to + up to 7.5%, condering even up to 10%, but unsure if you take into effect how it compounds out through the other demand modifiers].

Many of the high frequency trunk routes have suppressed prices [due to massive capacity generated by high frequency and fierce competition] whereas many of the infrequent, smaller regional routes are highly profitable due to tight capacity offerings.  Supply side ecomics.  If you control supply [as you do], and you're the sole provider of XXX-ZZZ, you can charge a greater ticket premium for reasonably low service [given enough demand] in frequency and/or plane size.  If you're in fierce competition, unless you're a premium provider [say all biz/first or something], you're dragged down to within some reasonable parity with your competition.  just watch articles on the pricing behaviours regarding airline fuel surcharges in the US or elsewhere.  Generally when one big player makes a move in a given direction, the rest of the big players hop on and mimic it.

A 777, fully loaded, flying JFK-LAX [big airport to big airport, high frequency], might if it's lucky make only $200 profit for an airline [As i recall this data is based on AmAirlines actually].  Other routes are where the real money is made for an airline.  

You're right travis, BOS-LGA-DCA is highly profitable, fairly frequent, but at the same time it's a tiny plane.  you have to fly a 50-60 seater two-to-three times as often as you would a 737 to achieve the same capacity.

One last comment, the biggest money makers tend to be biz class and first class [the more price affluent customers], we're hoping to implement classes sometime post-multiworlds, as i've got most all of it figured out in my head. i just need to get to the point where it's not counter-productive to work it all out on the game.


Quote from: "Steeler83"
The one qualm I have about this is  the competition factor.  Someone charges a fare that is one euro less than what your fare is.  You go from 100% LF and 50k euros of profit, down to 13% and under 10k Euros.  I thought this was supposed to be fixed already, but this kept happening to me in the last round.  Would 2-3X frequencies affect that as well?  In any event, I am adopting the 1x frequency model this go around; it's more realistic.  What airline runs 2,3,4 frequencies with one aircraft?


It depends on the type of plane.  little regionals may spend all day bopping between only two or three cities, big jets tend to cycle through differently.  Turn-time plays a big role in this [is my understanding a least].
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travismb99

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Reply #8 on: February 27, 2008, 04:03:36 am
Quote from: "Air Elbonia"
You're right travis, BOS-LGA-DCA is highly profitable, fairly frequent, but at the same time it's a tiny plane.  you have to fly a 50-60 seater two-to-three times as often as you would a 737 to achieve the same capacity.

No, that's not true at all. US Airways uses exclusively Airbus A319 aircraft on its BOS-LGA-DCA-BOS routes, in a 126-seat configuration (12F/114Y).

Delta uses 134-seat all-Y MD-80 aircraft on its BOS-LGA-DCA Shuttle.
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Air Elbonia

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Reply #9 on: February 27, 2008, 04:13:01 am
touché.
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travismb99

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Reply #10 on: February 27, 2008, 04:14:05 am
Which makes the 60-70 percent load factors that much more stunning. Half-empty A319s making gigabucks for US :P
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air1

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Reply #11 on: February 27, 2008, 04:17:24 am
Something should be done about long haul routes, it isn't very realistic.  International routes are the most profitable for airlines (in the real world), here they aren't so much.  I just looked up a ticket from O'Hare to Narita... around $1,500 for economy class, $12,000 first class round trip on a B777.

I tried running a B747 on the same route and my average price was ~e600 (cant remember exactly), one way.

Edit- just looked up O'Hare -d-> Hong Kong... $27,000


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Reply #12 on: February 27, 2008, 04:22:04 am
I was disappointed with that last round- I saved up and bought a 707-320B, then found it only made as much as my 737-200's.
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Arnaudus

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Reply #13 on: February 27, 2008, 10:29:17 am
Quote
That being said, pax could be willing to pay higher when their is less capacity on the route.


Nice theory, but it does not work, IMHO. I think it's a mistake to consider that passengers know the size of the planes, the number of competitors, the price of all seats etc. on a given route. They know how much a trip costs, in average, on this route, and they check if the proposed price is reasonable or not. Most of them don't care about the size of the plane, and at least in Europe, it is completely impossible to know if the plane is fully booked or not; this information is not available when you order a ticket, and even partially hidden afterwards (with some companies, you can chose your seat among a selection of seats, not all of them). For instance, it happened to me once to pay an expensive ticket, assuming that the plane was full, and we were 10 in a 150 seats aircraft. Too bad :-)

In any case, if your suggestion was true, real airlines would tend to decrease the frequency of flights, to fill them as much as possible with high ticket price. It's not the case, at least in Europe: you often end up in 50% loaded planes running 4 times a day. I'm really convinced that high frequencies brings you extra passengers, because all experienced travelers have already missed a plane, and know how painful it is to wait for 24 hours because your company runs only a daily trip. High frequency is a service, as much as free meals or good coffee.

Quote
Actually, the game correlates reasonably well in regards to which routes are profitable and how frequency plays in.


I can't agree, definitely. OK, I am not experienced in this game, and I wouldn't dare being too harsh with the developers, but I really feel that one should avoid the reaction: "I don't want to change anything, so I will find any reasons explaining why this bug is actually a feature of the game". I won't explain again the pax number bug, but my feeling is that the algorithm does not need fine tuning, it needs to be reconsidered from scratch.  Here is a list of unexpected behaviors:

* When you don't have any competitors on a route, the optimal strategy is to run only one flight with 100% load and high ticket price. This shouldn't be, in real world, you should have an optimal frequency, with an intermediate ticket price, and an intermediate load.
* When you are in a saturated market, the optimal strategy is to run low-frequency flights to hundred of destinations, and you earn more money in going to ridiculously small airports. This shouldn't be. In the real world, you should never make profit, even with small planes, between two very small airports: such flights simply do not exist (with a few exceptions, for instance if you are lucky enough to travel to a hub for a low-cost company), you always need a transfer through a bigger airport in this case.
* When you look at the schedule of large airports, you can see only small frequency flights run by the same company. This shouldn't be. Just go to any big airport, and you will see that most routes are 3, 4, 5, up to 10 frequency routes.
* On highly competitive routes, competition is so harsh that the price drops and the route is basically "screwed up". This shouldn't be. In the real world, companies are competing, but the average ticket price remains reasonable (keep in mind that the 1€ tickets are not average prices, most passengers on this routes pay much more than that, and in the few cases where a low-cost company tries to break the market, it is almost never on highly competitive routes: it is rather done to attract people to a small countryside airport).

I acknowledge that it is possible to play the game as it is today. It is probably even possible to have fun doing that. However, it is not a good simulation, and experienced players might tend to be conservative because they know how to play. For instance, there is a post asking "why are you stupid enough to run 2-frequency routes?" in this forum, and I think the right answer is "because most players still think this game is a simulation, and they behave as if they were managing a real airline in the real world".


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Reply #14 on: February 27, 2008, 06:25:08 pm
Quote from: "Arnaudus"
Quote
That being said, pax could be willing to pay higher when their is less capacity on the route.


Nice theory, but it does not work, IMHO. I think it's a mistake to consider that passengers know the size of the planes, the number of competitors, the price of all seats etc. on a given route. They know how much a trip costs, in average, on this route, and they check if the proposed price is reasonable or not. Most of them don't care about the size of the plane, and at least in Europe, it is completely impossible to know if the plane is fully booked or not; this information is not available when you order a ticket, and even partially hidden afterwards (with some companies, you can chose your seat among a selection of seats, not all of them). For instance, it happened to me once to pay an expensive ticket, assuming that the plane was full, and we were 10 in a 150 seats aircraft. Too bad :-)

In any case, if your suggestion was true, real airlines would tend to decrease the frequency of flights, to fill them as much as possible with high ticket price. It's not the case, at least in Europe: you often end up in 50% loaded planes running 4 times a day. I'm really convinced that high frequencies brings you extra passengers, because all experienced travelers have already missed a plane, and know how painful it is to wait for 24 hours because your company runs only a daily trip. High frequency is a service, as much as free meals or good coffee.


You are right, from a demanders perspective.  Whether the plane is a b1900 or a 747-4 flying a route, my view on price isn't affected much [though many fliers i know, whether plane fans or not, know the difference between a tiny turboprop and a nice mid-size jet, and it does impact their spending behaviour].  Demand perspective is a relatively fixed standpoint.  You yourself may only pay €300 for a trip between XXX-ZZZ, however. from a suppliers perspective: at €300 euros, there may be 5,000 people a day who want to travel that route.  If you put a 737/a320 on it, only once a day, you can only reasonably supply the 200-400 seats [depending on config].  You raise the price, where competition allows, to where maybe 1,000 people a day will want to fly that route [say €600 euros].  You yourself may only be willing pay €300 euros, thereby you no longer are among that group of people willing to fly that route when it's at €600.  This is supply side economics.  I'll get into other considerations which affect real life routeplanning decisions, and are planned to be implemented, but as of yet haven't made it into the game [unfortunately].

Quote
Quote
Actually, the game correlates reasonably well in regards to which routes are profitable and how frequency plays in.


I can't agree, definitely. OK, I am not experienced in this game, and I wouldn't dare being too harsh with the developers, but I really feel that one should avoid the reaction: "I don't want to change anything, so I will find any reasons explaining why this bug is actually a feature of the game". I won't explain again the pax number bug, but my feeling is that the algorithm does not need fine tuning, it needs to be reconsidered from scratch.  Here is a list of unexpected behaviors:

* When you don't have any competitors on a route, the optimal strategy is to run only one flight with 100% load and high ticket price. This shouldn't be, in real world, you should have an optimal frequency, with an intermediate ticket price, and an intermediate load.
* When you are in a saturated market, the optimal strategy is to run low-frequency flights to hundred of destinations, and you earn more money in going to ridiculously small airports. This shouldn't be. In the real world, you should never make profit, even with small planes, between two very small airports: such flights simply do not exist (with a few exceptions, for instance if you are lucky enough to travel to a hub for a low-cost company), you always need a transfer through a bigger airport in this case.


In real life, yes, you don't just fly one-way when you have a monopoly.  Optimal in real life is likely around 2-4 frequencies in that respect.  HOWEVER, in real life you have two big demand modications yet fully or properly implemented.  One, you have airline reputation [which is affected by service level you provide] and Two, you have substantial hub effect you can create for yourself out of thin air [any passengers you sell one+ stop tickets to].  

The former, will likely come in with multi-class seating [which i do hope to code in soon.]  A strong reputation won't just be made up from your aircraft's seating configuration, but also through service levels with some peak bonus established near the 2-4 frequency range.  If you're known for frequent flights, you're preferred by business where flexibility is key.  This tends to help suppress prices a little as well [as airlines are looking to fill more seats, thereby play a little more with price for the demand effect] and helps boost the leisure travelers on the route.  

The latter I've also reasonably figured out, and will come in varying degrees due to the level of hub you classify your airport at.  It'll have a nice level of effective competition reduction for the formula, and will hopefully also be completed near the multiclass seating feature.  This pushes airlines to pump more frequencies and lower fares into routes into a hub city.  More capacity that's utilized [higher frequencies, lower fares tend to make greater capacity used] gets more passengers into a hub city.  More passengers in a hub city tends to make up a greater number of people willing to save some money flying the one-stop flight, effectively shifting demand from AAA-BBB into AAA-XXX and XXX-BBB.  Pooling this effect across a broader network makes for a nice boost to demand.  Add in code-sharing through alliances to that and you add another Nth percent more people to the demand of a given route. [we have some limited effect of code-sharing by an alliance within the game, however proper codesharing is... a scary thought to code at the moment.  I just can't come up with a good way to avoid double-selling tickets while offering the capability for you to book a passenger on an alliance partner's plane.]

I must say, however, that you are your route network in the eyes of many passengers, though things like orbitz are cutting that down a little it still holds true for the upper-echelon seats [first/biz].  If you serve a lot of cities, you're more likely to be favored by business travelers and you're more likely to be able to sell to some leisure travelers.  

Oh, and maybe this is an American's perspective, but I know some of the most profitable routes can be the less frequent small turboprops servicing a small airport from a big[ger] one.  They tend to have less demand, and thereby support relatively little competition for any given pair of cities direct HOWEVER, they're made profitable all around by the following facts.  One, some routes into smaller airports are subsidized by gov'ts [small factor], Two tiny little planes are cheap to acquire [i've often seen orders for 15-20 embraears or bombardiers which were announced for the same as one 787 or larger plane.]  Three, fuel burn on turboprops is a lot lighter typically, resulting in a lower break-even point.  Four, tiny planes require [usually] less experienced pilots, thereby can be flown by cheaper pilots.  On top of this, some don't even require a flight attendent, resulting in lower staffing costs thereby a lower break-even point on the route.  

Quote
* When you look at the schedule of large airports, you can see only small frequency flights run by the same company. This shouldn't be. Just go to any big airport, and you will see that most routes are 3, 4, 5, up to 10 frequency routes.


You're right, i could try to play this off as something along the lines of those 3,4,5 or 10 frequency routes are served by multiple aircraft.  I've been idly thinking about ways to improve the calculation in this respect wherein multiple planes can effectively service "one" route.  As of yet, I haven't managed to come up with effective ways to do this without a very extensive redesign of the backend.  Hopefully I can figure this out though.  I've had a few sparks, but they fizzled out in some preliminary testing.

Quote

* On highly competitive routes, competition is so harsh that the price drops and the route is basically "screwed up". This shouldn't be. In the real world, companies are competing, but the average ticket price remains reasonable (keep in mind that the 1€ tickets are not average prices, most passengers on this routes pay much more than that, and in the few cases where a low-cost company tries to break the market, it is almost never on highly competitive routes: it is rather done to attract people to a small countryside airport).


This is a very serious problem, and as soon as multiworlds is finished, i'm going to try to push forward on multi-class seating and/or hub effect [whichever is more practical to code in terms of time and my perceptions of the effect will determine which first], as well as some improvements to the edit route page to allow for swapping aircraft on a route in one page and a way to mass discount or mark up your routes to make editing a little softer on the game-play for small and large airlines.

Quote
I acknowledge that it is possible to play the game as it is today. It is probably even possible to have fun doing that. However, it is not a good simulation, and experienced players might tend to be conservative because they know how to play. For instance, there is a post asking "why are you stupid enough to run 2-frequency routes?" in this forum, and I think the right answer is "because most players still think this game is a simulation, and they behave as if they were managing a real airline in the real world".


I may quibble a few points on what else makes it a poor simulation, but generally selling your project short doesn't get you far.  Many of these are being addressed, but many are also skewed by factors which unfortunately are not yet in the game [as i've described above].  We hope to add them, to help rectify it a bit.  Time, unfortunately, is a limited resource sometimes and presently with the current active player count at approximately 2,300 accounts, we've been devoting our time towards upgrading the site to support multiple worlds.  If only i had all the time in the world, or the ability to plug my brain straight into the code... in either case, AM would have a lot more features a lot faster.
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