Why Operations Research is awesome — An introduction

Mathematics is the language of the universe, and it is, by definition, logical. But doing mathematics isn't just logic – It is a highly creative process of utilizing the tools math gives us. In operations research, you get to be creative with the tools of mathematics to solve some really exciting problems!

Operations Research (OR) is an applied math field where mathematical tools are not just used to investigate mathematics further but rather to model, analyze, and solve problems within the OR domain.

Fig 1. Photo by NASA on Unsplash

Motivation to Understand Operations Research

Decision making of the future will be as close to fully automated as possible (think "Tony Stark" level automation). One of the research fields that investigates and furthers this transition is OR. At its core, OR is an applied mathematics field that integrates advanced analytics methods in decision support/making.

As the problems and decision environments become increasingly complex, it is essential to advance research that emphasizes the human-technology interface to avoid misconceptions. A classic horror example of the future is if a decision-maker seeks to maximize customer happiness, and the (AI-)system translates that into putting everyone in a dopamine-infused coma similar to that in "The Matrix" (which we may or may not already be in..).

But there are also more tangible issues that we struggle with today. E.g. Routing for package delivery where the total distance of the route should be minimized while still maximizing the number of delivered packages. The two objectives will, in extreme cases, either not let the drivers deliver any packages or not let them have any free time, but there are also a lot of sub-optimal instances in between. And these issues are only the tip of the iceberg, Jack. So it is crucial that future decision-makers can integrate their preferences properly to avoid these situations — and Operations Research investigates precisely this!

Fig. 2: The infinity gauntlet illustrates OR (of course!), as the toolkit that OR brings will obliviate half of the future problems. Photo by Morning Brew on Unsplash

I came upon OR as a graduate student in math and economics, where two extensions were possible to study; either OR or Financial Engineering. Compared to each other, the latter deals with decision-making in finance, trading, and risk/investment, while Operations Research does so more generally within industry and business. Although, some terminology is putting Financial engineering as a more specialized sub-category to the then broader field of OR.

What is Operations Research?

Generally, OR is concerned with obtaining extreme values of some real-world objective functions; maximum (profit, performance, utility, or yield), minimum (loss, risk, distance, or cost). It incorporates techniques from mathematical modelling, optimization, and statistical analysis while emphasizing the human-technology interface. However, one of the difficulties in answering this question is that there is a lot of overlap in scientific terminology — and sometimes terms become extremely popular, affecting the landscape of the terminology. E.g. the popularity of vague and broad terms such as AI and Big Data which both work great for marketing but does nothing for the discussion on the research. Therefore, I have tried illustrating it in terms of ORs-related fields, subfields, and the addressed problems in Fig. 3.

Fig. 3: Holistic illustration of the disciplines and problems related to operations research. Note, I am greatly limited by the 2D representation as there are multiple other connections between disciplines than shown here. E.g. probability theory and statistics being an intrinsic part of machine learning. Illustration by Alex Elkjær Vasegaard.

Operations research had its historical origin in the 17th century when game-theoretic approaches and expected values were being utilized to solve problems. The modern version of OR originated during the second world war when it became apparent that the military needed to solve some of the significant logistic and supply chain problems that come with being in war.

Back then, it was defined as "a scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control" and was coined "operational analysis" (still is in Denmark) or "quantitative management".

A future in Operations Research?

An attractive feature of OR is the applicability of the knowledge, skills, and tools in various industries. Today, OR is applied in a more or less specialized version in most businesses and industries — everything from agriculture, energy trading, production, and sales to the space industry, asset pricing, military operations, and demand forecasting. The most notable usecases are probably:

• Supply chain management
• logistics and inventory management
• Routing and pathfinding problems
• Predictive maintenance
• Scheduling and assignment problems
• Evaluation problems (multi-criteria decision-making)
• Systems engineering
• Forecasting

The common denominator in terms of tools is the four following skills, allowing you to:

• Utilize mathematical optimization methods, such as linear programming, dynamic programming, stochastic programming, etc.
• Develop solution algorithms. Often solutions are required in near real-time. That is, the optimal solution is not necessary. One 'just' wants a good enough solution. For large problems with high complexity (for example, NP-Hard problems), solution algorithms such as expert-inspired heuristics or bio-inspired genetics algorithm, ant colony optimization, or even neural networks or decision-tree-inspired gradient boosting methods. It depends on the framework of the problem and whether it is a model-based or data-based solution approach.
• Conduct extensive simulations to investigate the robustness and flexibility aspects of the derived solution approaches. Either by Monte Carlo simulation, sensitivity analysis, etc.
• Conduct extensive analysis of the problems—e.g. to identify critical paths in a network. As an example to illustrate the importance of a proper analysis, in network analysis, more specifically in traffic networks, it has been observed that by removing roads, it is possible to increase the flow of traffic. It is coined Braess's paradox, and it has also been found to trick other systems, such as electricity grids, biology, and team sports strategy. So it is vital to analyze one's solutions properly.

I hope this was informal and let you know what Operations Research is — my family, friends, and colleagues from other research areas have often been asking me to clarify the topic, I hope this aided you as well.