Favorite Operations Research Problems in the Wild
Every year or so, I come across some verbally formulated “problems”* which can actually be modeled as some form of Operations Research** (OR).
These problems might or might not have prior, but neither I nor the “problem owners” had any prior mapping of these problems to mathematical models. But when formulated as one, its benefits were obvious.
I have five examples for you. Examples are from different parts of finance, logistics, energy and something I don’t know about. Here they are.
Liquidity Planning for a Bank
Banks perform in a highly regulated AND competitive landscape. They are subject to detailed rules about how they should limit many items in their balance sheet.
One of the highly challenging operations is to maintain their liquidity in a well balanced manner. If their liquidity levels are unnecessarily high, they are practically losing profit from not putting the money to work (e.g. loans). But if liquidity slides to dangerously low levels, they have to replenish quickly and usually at a significant cost. There are some strict and well defined rules such as Liquidity Coverage Ratio (LCR).
Treasury have some short term options to fine tune their liquidity levels such as deposit levels and issuing short term bonds. Each option is subject to some sort of dynamics (e.g. availability, price, replenishment rate). Also don’t forget that time component is also a factor. It has to account for future event (e.g. some previously known large outflow).
Our objective was to minimize the cost of maintaining liquidity levels at a “sweet spot” while accounting for future shocks and uncertainties for the next X months. The result is a beautiful stochastic dynamic programming model laying out a strategy for each option. It can be run for different scenarios and results are easily comparable. To the best of my knowledge, they are still running the model to guide their decisions.
Energy Optimization for a Production Facility
I particularly enjoyed building the model of this one because it is an instant money saver with no effect on the production plan. This facility requires several pressure levels of steam (from very high to high, medium and low) and electricity to utilize their machines. Steam is derived from natural gas and water.
Some machines may use electricity or steam interchangeably. Facility also has several “cogeneration plants” (i.e. electricity production using steam or natural gas). Both electricity and natural gas costs are variable but short- term deterministic. In short, we want to minimize total energy costs given a production plan and machine constraints.
Even though there are additional intricacies such as transmission between buildings and pre-purchased electricity, they can be represented in the model.
The model was built around the recent heyday of energy prices. My part was finished after the model is built; but later in a published article, monthly reported savings were substantial (>USD 100K). The best part is these savings were possible with no tradeoff at all.
Fair Value Portfolio Hedging for a Bank
OR is used in finance a lot. OR is also used in portfolio selection a lot. But it is usually optimizing on assets, derivatives or entities of similar nature. For a bank it can be the hedging of loans with derivatives.
Ever since a long time, a bank’s most basic functions are being a place to securely deposit your money and a place to borrow from. Banks invest their customers’ money in investment instruments such as bonds, loans etc. The cautionary tale is maturity mismatch.
Maturity of deposits are usually short term (e.g. < 90 days) and loans can be really long term (e.g. >5 years). Deposits also frequently replenish and it is a fine balance. Using Swaps to hedge risks from time (actually more like interest and currency) is a frequently used way. Though, swap market might not always offer perfectly fitting contracts. So, you need to make the best of what you have.
The objective is to minimize interest rate risk, given a huge portfolio of loans (>100k) and a selection of candidate swaps (~100). Interest rate risk is calculated with a basic simulation of how would valuations change if there is a shock to the interest rate market curve. We want to minimize excess movement to either side (i.e. positive and negative value changes) with our portfolio.
It is only one side of the coin. But, handling the other side (deposits vs swaps) is far easier and it usually does not require an optimization model.
Supply Chain of Second Hand Cars
This one started as a simulation but ended up as an MIP model. Problem owners already have had a network of “inventory” points, distribution centers and demand from all over the country. They also beautifully constructed a logistics daisy chain.
Their problem was they were rapidly expanding and they would like to know more about tactical decisions (e.g. how their network load will be affected, where they should hire more trucks to carry cars and personnel depending on future expansions) and strategic decisions (e.g. where they should build a distribution center next).
We managed to build a model which conforms to their supply chain requirements and aims to minimize total costs (e.g. total mileage, number of personnel, trucks etc). To the best of my knowledge, it is still in use in an advanced form.
The Most Peculiar Assignment Problem
This last one is not important to me because it was a difficult model to solve or it required special expertise. Because it was confidential.
Some friends were working on a project for a partner or customer. At some point, some of their calculations were taking too long. Since it was a confidential project, they had to conceal the background and anonymize variables and constraints. They couldn’t tell me anything about the problem except the working mechanics. Their only requirement was that they needed to find a solution for any instance “under two hours”.
It turned out to be an easy assignment problem and with a simple solver every instance was solved in an instant. The part which gave me the most joy is to find a solution fitting for the problem with really significant savings. It felt like using “cheat code” in a game. The fact that the problem was a bit cryptic due to confidentiality was also fun.
Conclusion
OR and its prominent techniques such as LP, MIP etc. have more applications than we are used to see. To be honest, I am not a distinguished modeller, mathematician, programmer. I count myself as lucky to encounter such cases. But, as in one occasion, von Neumann swooped in to save Danzig from Hotelling’s criticism***: “If you have an application that satisfies the axioms, well use it. If it does not, then don’t”.
This is the last (?) post of my impromptu miniseries about OR in practice. My purpose was to assess whether a product business on OR is viable rather than consulting. I just wanted to finish with a personal touch. You can read previous posts in the publication.
Footnotes
\*: When I write “problem”, it usually means a mathematical modeling problem.
\**: I must say that OR is not limited to these applications and it encapsulates a much broader setting. Though, here I assume these problems here that can be solved with MILP, MINLP, stochastic programming etc. fall under OR’s domain.
\***: It is a story I like a lot. See here on page 4.
