## The Whole and the Parts – Feedback Loops with Delay

In my previous post on feedback loops I promised to look at their limitations.  I’ll start that in this post, but think I should say a little more about what they are good for first.  In the example of a thermostat in your house, the temperature is maintained at roughly the temperature at which you set it, within some range.  If you set the temperature at 68 degrees Fahrenheit, and the house is currently at 50 degrees Fahrenheit, it may take a while for the temperature to get up to 68 degrees.  The furnace may be on at full blast, but it still takes a while to heat up your house.  Once your house has warmed up to 68 degrees, the thermostat will kick the furnace off and on repeatedly, with the effect that the house stays roughly at 68 degrees.  By and large, the thermostat brings the temperature to an equilibrium and maintains that equilibrium at the set temperature, at least in that particular place in the house where the thermometer is located that’s used by the thermostat as its sensor.

When there is no thermostat as such, there are more actions you need to take to keep the temperature where you want it.  There is still a feedback loop, but in the absence of  a thermostat, you are an active part of the feedback loop.   A well-known example of this is a shower driven by two faucets, a hot water faucet and a cold water faucet.  If the temperature of the water coming out of the shower head is too cold, you turn up the hot water faucet (or turn down the cold water faucet); if the water is too hot, you turn up the cold water faucet (or turn down the hot water faucet).  Since the faucets control the volume as well as the temperature of the water, you are actually engaged in a fairly involved dance with the two faucets to get the whole thing come out the way you want it.  Involved or not, most of us have a track record of being able to handle this and handle it well.

Real-life feedback systems have some delay built in.  When you sense that the system is “away” from the desired range, and you start the action to correct, it will take some time for that action to take effect.  You might wish for it to respond right away, but it can’t.  The delay has an impact on the operation of the feedback system, and the impact is sometimes unintended.  To see this clearly, we’ll use an example where the delay is substantial.  One such example is hotel capacity in a city.  Let’s simplify and say that Pacific City currently has 2000 hotel rooms, and that it takes exactly a year to build a new hotel with 100 more rooms.  Let’s also assume all hotel rooms are the same and are in equally desirable locations.  Of course our assumptions are unrealistic, but even as unrealistic as they are, we can see something interesting from looking at the behavior of this feedback system.  How is it a feedback system?  Well, assume that there currently is a demand for 3000 hotel rooms in Pacific City.  That is, 3000 customers are willing to rent rooms in Pacific City at current prices.  Of course, 1000 customers will have to be turned away.  Room rates may go up, and deals and discounts will dry up.  But if the capacity is only 2000 rooms, one way or the other, 1000 customers are going elsewhere, are coming later, or won’t be coming at all.  A perceptive entrepreneur, let’s call her Jane, may see an opportunity for making money, and starts building a new hotel with 100 rooms.  Jane is part of the feedback loop, as much as the people raising room prices.   Jane makes her decision today, based on today’s capacity and demand, but she can’t conjure up extra capacity instantly – it will take her a year to see the extra capacity materialize.  In the mean time, if the hig demand continues, prices will rise, and customers will be turned away.  Next month, a slightly less perceptive entrepeneur, Josephine, will see even higher prices, and will see a high demand and a capacity of only 2000 rooms, and will decide to build a new hotel, with another 100 rooms.  But Josephine’s rooms don’t come on line immediately either, they take her a year to build.  A month later, there is still a capacity of 2000 rooms, more people turned away, prices going up, and newspaper articles are starting to appear, complaining about lack of hotel capacity, disappointed tourists, the need for building more hotels.  Jessica reads the newspaper, agrees with the analysis, and proceeds to build a hotel, for 100 extra rooms, to be ready in a year.  Next month, the peak season is at hand, the capacity is still at 2000 rooms, 4000 customers are expected, prices are high, hotel owners are making very decent profits, the restaurants are doing well, the tourist-oriented businesses are going great guns, the city collects lots of money in entertainment taxes.  But they can all see that lots of money is ‘left on the table’ since hotel capacity is still the limiting factor.  Even with the high hotel room rates, 2000 people had to be turned away.  The situation is starting to get obvious to lots of entrepreneurs – and also to people who never were entrepreneurs but see an opportunity to become one.  So, Jana, Jesse, Joey, Jason, Jonah and Justin each jump into the fray and start build a hotel, for 100 rooms each.  Of course, their hotel, too, will take a year to build.  The building business is booming, more construction workers are brought in from other cities.  People from all over hear about the bustling business in Pacific City, and how it is poised to really support more tourists.  Pacific City clearly is the place to be, and demand for hotel rooms rises, even though it no longer is the peak season.  Space and zoning are becoming a problem in Pacific City, but not in Pacific Suburb right next to Pacific City.  John, Jerry, Jay, Jan, Joy, Jill, Joseph and Janae start building hotels in Pacific Suburb where there is space, and zoning laws more permissive – the hotels they start have 200 rooms each, and the building employs many people.  Even though no  new tourists have come to Pacific Suburb yet, the place is bustling just from the building activity alone.

Each player is part of a feedback loop.  Their actions are reasonable, based on best available data.  A year to build a hotel is quite quick actually, the players really couldn’t be expected to react to the need in a more responsive way.  But you can see what is coming down the pike.  When the new hotel room capacity starts to come on line, and the demand is steady, the situation does actually improve.  Fewer potential customers have to be turned away, prices come down a bit from their high levels, which may boost demand even more.  But extra capacity keeps coming on line, not driven by current demand, but by the picture of the demand as it existed a year ago.  A few months later, total capacity is well above the demand of 3000, assuming that is still the demand.  Hotel rooms will remain empty, occupancy rates go way down, and some hotels will start offering discounts or lowering the prices well below what they used to be.   For the hotels that are only 80% built, the business prospects are quickly deteriorating, but it still makes economic sense for the entrepreneur to finish the hotel, and it makes sense for the lending banks to supply money for the hotel to be finished, as an unfinished hotel is a total economic loss for sure.  Pacific City and Pacific Suburb may now have a long period of overcapacity.

A feedback system with delay is vulnerable to overshoot, is vulnerable to cycles of boom and bust, is vulnerable to all the parts acting in their best interest and with the best of intentions, and yet resulting in a whole that nobody asked for, that nobody wanted, that few foresaw.  In a feedback system with delay, the logic of the whole is different from the logic of the parts.