Real Life Examples of Optimization in Economics

Question

I am trying to find some real life ("non trivial") examples of optimization related to economics.

So far, most of the examples that I come across are from introductory economics textbooks involving some basic example about farmers choosing between different crops to grow based on expected harvest and market price; or some similar example of a factory in which two different machines manufacture different types of items at different speeds, and again based on expected consumer demand, the manager at the factory is expected to decide how much of each machine's workload should be assigned to which type of item. Sometimes, there might be some constraints that need to be taken into consideration. Generally, these problems I come across can be solved using algebraic manipulation or through linear programming.

I posted an example of one of these problems below:

Although these types of problems are great examples to familiarize one's self with economics and optimization, the context of these problems generally appear as "too simple", and instantly one begins to think that these are big oversimplifications of real world economics problems - and such oversimplified problems likely have little relevance in the real world. I am trying to look for some examples of optimization problems in economics in more realistic situations such as in banks, investment firms, resource allocation in national budgets, etc.

Can someone please suggest some more realistic and complex examples of optimization problems within an economics context? Perhaps some real life examples involving allocation of resources in markets, investment risks, non-convex objective functions with many complicated constraints, etc. ?

It would be ideal if the references for these problems could be provided as well that fully explain the environment and context in which these optimization problems appear.

Can someone please suggest something?

Thanks!

Answer 1

Optimization problems

Some of the problems you mention do not seem that simple to me, e.g., "farmers choosing between different crops to grow based on expected harvest and market price" can be mathematically quite difficult depending on the distribution.

In case you want a though one, have a look at the paper Economics and computer science of a radio spectrum reallocation, it has an entire section on "Feasibility Checking."

Unfortunately any example will have to 'thread the needle':

• it cannot be too simple mathematically,
• it should be detailed enough to be considered real-life,
• and it should be simple enough that you can explain it in a relatively short amount of time to non-experts.

It is unlikely that any example will meet all of the above conditions.

Optimization in economics

Interestingly, while economists frequently rely on the assumption that optimization occurs in their models, in my experience they rarely face difficult "real-life" optimization problems themselves.* Difficult optimization problems are handled by algorithms and people who specialize in these difficult algorithms tend to be computer scientists.

What applied mathematical economists (usually) do is they choose a model that fits the available data best. (In a sense this is also an optimization problem that involves minimizing the sum of least squares or some similar indicator.) Then they study the parameters of the model (or pass it on to others who will study it) and try to see if there is anything policymakers (government agencies, CEOs, etc.) can learn from it; are there bottlenecks in a process somewhere, are there areas that require more attention, and so on.

Aren't there any better examples though

Above I tried to show that while it is present to some degree, mathematical difficulty is not the main issue that applied economists focus on. The reason is that in order to "optimize" something you usually need to learn about the thing. Some of the big challenges of "Real Life Examples of Optimization in Economics" are

1. Getting high quality data in a well structured form.

What exactly are the constraints of your problem, what probabilistic distributions are you facing, and what are the parameters of your goal function? Part of the task is translating the real life situation into a mathematical model and estimating its parameters.

2. Setting a clear objective function.

Is there an actual clear cut objective function, or are there simply nebulous general objectives? E.g., we want to improve short-term profitability while maintaining brand-loyalty and laying foundations for future growth? Even maximizing public welfare requires that you make extremely reductionist assumptions. Part of the task is translating the non-mathematical goals into an optimizable function.

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*Yes, in theoretical papers the optimization problem can be difficult, e.g., most multi-actor multi-stage games with non-finite action sets will be quite difficult to solve, but I don't think these qualify as real life. Though I always liked the von Neumann quote

"If people do not believe that mathematics is simple, it is only because they do not realize how complicated life is."

Answer 2

So one thing to keep in mind is that the "simple" examples you're looking at are very much real-world. Any particular optimization decision needs to be simple enough for the people making it to understand what they're doing.

Where the complexity comes from is the further interaction between the simple elements. If what feed to use to get the cheapest source of nutrition for his cattle were the only choice the farmer had to make it would, indeed, be extremely simple. But it's not.

For example, when getting a herd through the winter, the temperature of their drinking water has a significant effect on how many calories they burn to stay warm. So where's the breakover point between spending more on feed vs on heating the water supply? Does the quality of their bedding have a similar impact? Does the salt content of their food affect their water intake such that balancing these equations becomes fiendishly difficult? Is there a third, cheaper feed he should be using to make up the raw caloric deficit for cold weather that won't affect the nutritional balance?

So it's not that any of the individual optimizations are that difficult (though they may take specialized knowledge of the domain in question) its that the complexity exponentiates with every addition to the things you're optimizing for.

A good example can be found in "I, Pencil", by Leonard Read, wherein he analyzes the optimization tree for producing the "correct" number of pencils.

To pull an example, a pencil is made partly of wood. To get the wood, you need lumberjacks. How many lumberjacks to cut how many trees? How much coffee do you need to get them out of bed and working in the morning? How much bacon? How many eggs? How many axes are required for them to chop with? Oh dear... Axes take steel... How many miners to mine the ore? How many pickaxes, how many carts, how many smelters, how many forges? How many cargo containers to move the ore from the mine to the smelter, the steel from the smelter to the forge, the axes from the forge to the lumberjack camp? How much additional steel to build the cargo vehicles? How much diesel to power them? I could go on...

Each step, viewed individually, seems quite simple to sort out. And it is. Business managers and entrepreneurs do it all the time. But as you zoom out you see that the output of one optimization affects the input of another, which affects a third, and a fourth, and the whole thing turns into a big, continuous feedback loop and then you might as well be looking at multivariable calculus.

That essay, and a few others like it, do a good job of showing where the complexity comes from and just how crazily-interconnected it all gets.

If you're looking for actual math in your examples, your best bet is probably to wander over and talk to the Finance folks since converting real-world optimization problems into math and then solving them is pretty much what they do for a living. But even there, you'll notice that they try to chop them into manageable chunks because how much torture you put yourself through to push your accuracy past the third or fourth decimal place is also a thing you should be optimizing.

Answer 3

One could use simple games of resource management, this way the scope is fairly finite. I do research in digital games and economics, which students tend to be interested in. Some relevant papers are linked below.

How massive multiplayer online games incorporate principles of economics, Joshua H. Barnett & Leanna Archambault, 2014

The Diablo 3 Economy: An Agent Based Approach, Makram El-Shagi & Gregor von Schweinitz, 2014

Standard Economic Models in Nonstandard Settings–StarCraft: Brood War, BS Weber, 2018 This paper is about Cobb-Douglass and Tit-for-Tat in a resource management game of conflict.

Deployment of Causal Effect Estimation in Live Games of Dota 2, AH Christiansen, E Gensby, and BS Weber 2021 This one is about IV, control function approach, and we actually test if people prefer unbiased predictors to biased ones in a small pilot group. They do!

Answer 4

The NFL uses optimization when scheduling.

In 2013, the NFL began using Gurobi’s mathematical optimization solver to tackle this incredibly complex scheduling problem. With mathematical optimization, NFL planners can generate and analyze more than 50,000 feasible schedules despite adding more constraints to the process every year. Now – instead of spending months manually creating a single feasible schedule – the NFL planners can focus on evaluating and comparing completed schedules to determine which should be selected as the final schedule.

Whitepaper

Answer 5

I am currently working on a software solution that aims at calculating orders for retail distribution centers.

As context, we all shop at supermarkets and drugstores (so-called "points of sale", POS). These POS get their supply typically from large distribution centers (DCs), which are also part of the retailer. These DCs, in turn, place orders for product at consumer packaged goods (CPG) companies, wholesalers, or other suppliers.

The order calculation at the retailer's DC is highly complex.

• First off, the main input is a forecast of the stores' demand, which in itself is very hard to forecast (stores' demand to the DC is governed by end consumer demand at stores, which is hard to forecast in itself, and which then gets filtered through order optimization at the store... and then overwritten by the store manager, because he feels like it).

• Second, the objective function is highly fuzzy. Ideally, we would optimize total costs or margin. But while we know purchasing prices (and rebate structures, and time-varying purchasing prices because of promotions, are complex in themselves) and sales prices, we only have the vaguest inkling of handling costs at the DC, or of the costs of stockouts. Sure, we are not selling the product we are out of because of an order that was too low - but (a) how much demand are we losing (we are not seeing it!), and (b) at what point does the end customer stop coming to our store?

  Retailers typically then work with proxy objectives, like minimum service levels (which, again, depend on forecasts, so they are hard to pin down), ranges of coverage or other KPIs.

• Third, the constraints are complicated. You can only order in specific units of measure, like cartons, layers or full pallets. You may be able to mix products on a pallet - or not. If you can mix, there are stackability constraints. Trucks must be full, because of agreements with the suppliers. (See above on nobody knowing the true costs of half-full trucks, so we need to fall back to such agreements.) Except that some suppliers will happily send you just five pallets, by using a 3rd party logistics provider. Except that if they do so, they cannot guarantee delivery by a particular date, because they need to take account of when that 3rd party logistics provider has a truck going your way - so we have a chicken-and-egg problem in calculating order amounts.

Also, I haven't mentioned shelf lives, the generally horrendous quality of the data in IT systems, budgets, contractually agreed minimum order values across a whole quarter or a year, multiple sources of supply (you can get your apples from different farmers' cooperatives), substitution effects (supplier A may be out of apples, but supplier B can sell you some, except that you don't have anything else to order from B but that half truck of apples, so what do you fill that truck up with?). Nor direct end consumer demand facing the DC, because that DC may fulfill your online orders. Except that maybe today it's fulfilled out of a different DC for some reason. Which we may need to keep in mind in tomorrow's forecasting run: clean the historical time series.

Bottom line: there is a huge amount of economic optimization going on just to make sure your local supermarket is stocked, or your online order can be fulfilled. Most of it is incredibly complex, and there is an art to knowing where to push for exactness and where to use approximations (and what kind).