# Operations Research, a modern perspective

*This post is written for non-experts, and more precisely industrialists who want to know more about operations research and for young colleagues who contemplate starting a career in the field. I give my current opinion on why operations research matters, how it brings value to society. I conclude with the main scientific challenges.*

## Why Operations Research

The ecological transition may be the greatest challenge of our generation. The latest IPCC report emphasizes the need to act on two fronts simultaneously to curb global warming: adopting a more frugal lifestyle and improving our production methods. The latter is painless for the end consumer, as it involves producing the same goods and services more efficiently. As long as they are economically feasible, environmentally-focused policies based on technology are thus more widely accepted. It is important to implement them as effectively as possible.

When discussing environmental technologies, public debate often centers on renewable energy or low-carbon transportation. However, better decisions can also be made with existing technology. Take home delivery, for example. Investing in electric vehicles can reduce emissions. Better organization of delivery routes can also decrease the distance traveled to make the same deliveries, thereby reducing emissions as well. Yet, manually constructing efficient vehicle routes is challenging. Even with the best techniques, manually created solutions result in routes that are, on average, 13% longer than the optimal solution. To improve this, decision-support algorithms are needed. These algorithms can reduce emissions and costs by optimizing the use of available resources. They represent the mathematical and industrial version of waste reduction.

Operations research is the mathematical discipline that provides such decision-support tools. A typical outcome of an operations research project in industry is the ability to produce more cost-effectively and with fewer resources, without changing production means or technology. Advances in the field and greater data accessibility have increased the potential applications of operations research. These methods are currently underutilized outside of network industries and represent a significant source of economic and environmental value.

## Main drivers of performance in Operations Research

In Operations Research, the most critical factor for success is **modeling**. This involves translating the optimization of an industrial process into a mathematical problem. The most sophisticated algorithms are futile if they don’t address the correct problem. But this reality takes a particular flavor in Operations Research. Manual optimization of industrial processes is arduous. Over time, companies have developed numerous heuristics to streamline these processes, such as “visit each client every two days” or “truck routes should not serve more than three clients.” Initially, these rules were adopted to simplify the planner’s task, not out of industrial necessity, and over time they have become sacrosanct. However, with the advent of computing power and sophisticated algorithms for optimizing industrial processes, these rules can become obsolete and even detrimental. They restrict optimization, leading to reduced performance. Essentially, *altering the rules of the game often yields greater benefits than improving gameplay within the existing framework*.

Beyond modeling, the next pivotal element for enhancing performance is **combinatorial optimization**. Specifically, the development of combinatorial optimization algorithms that are scalable. Optimization, a branch of applied mathematics, is dedicated to minimizing functions. In essence, it seeks the optimal solutions that meet a specific goal while adhering to certain constraints. In the context of industrial processes, optimization typically involves the allocation of resources like vehicles and machinery. These resources are often non-splittable, leading to binary or integer variables. For example, a plane either operates a flight or it doesn’t; there’s no such thing as half a plane on a flight. Combinatorial optimization deals with these integer variables. When it comes to industrial processes, *performance is largely driven by economies of scale*. For instance, a company delivering parcels in a city will face inefficiencies if only a few clients are spread out. However, with a higher number of clients, particularly in the same area, the delivery process becomes more efficient, allowing for reduced marginal costs. Thus, after a process is modeled, the primary profit lever is the reduction of marginal costs. Achieving these economies of scale necessitates algorithms that can take a holistic view of the process—algorithms that perform well even as the scale of operations grows. Creating combinatorial algorithms that can handle large-scale applications is a significant mathematical challenge, both theoretically and practically. This complexity is why *operations research scholars have concentrated on combinatorial optimization for the past seven decades*.

Finally, the last driver of performance is **data**. As the saying goes *garbage in, garbage out*. Data on industrial processes used to be scarce. Two decades of digitalization of industrial processes have changed the game. However, if data is now abundant, it is sometimes incomplete and often inherently random, which makes **machine learning** the suitable discipline for managing uncertainty in their analysis and processing.

When it comes to the tangible benefits of optimizing industrial processes, the hierarchy of impact generally begins with modeling, followed by combinatorial optimization, and finally, machine learning. Applied mathematics and computer science scholars who work on Operations Research tend to focus on the methodological aspects, which lie on the optimization and on the learning side. Modeling is more an art than a scientific discipline. While a comprehensive understanding of mathematical tools is essential, it’s not the sole requirement for proficiency. True expertise in modeling also demands an appreciation for economic significance and a well-honed ability to engage with industry professionals. This engagement is crucial for speaking their language, and being able to challenge the rules of the games to unlock value.

## Today’s Top Challenges in Operations Research

Two elements have profoundly changed the operations research landscape during the last decades. First process digitalization have made data abundant and algorithm much easier to integrate in workflows. Second, dramatic progress have been made on combinatorial optimization. Indeed, given the hierarchy of benefits previously outlined, it comes as no surprise that the operations research community has focused on building algorithms that scales, even if this means simplifying the objective. And it has been widely successful in this endeavor. Consider for instance mixed integer linear programming (MILP), which could be described as the Swiss knife of combinatorial optimization. On the same computer, the 2015 version of a well-known solver is 780 thousands times faster than the 1991 version. If we factor the hardware improvements, we get a 450 billion times speed-up. Problems with millions of variables and constraints are now routinely solved in the industry. As a result, *efficient off the shelf algorithms are now available* for static and deterministic Operations Research problems. **Operations research is therefore now widely applicable in the industry, and still underused**. One brake to the adoption is that these algorithms require appropriate modeling for being efficient. For instance, many MILP formulations can model the same problem, some efficiently solved by MILP solvers, some not. Hence, there are many low-hanging fruits, i.e., industrial processes that can be optimized over three months projects. But grabbing them may require an expert at the early modeling stage.

While operations research tools were getting more and more efficient, industrial needs have been evolving. First, the COVID era has underlined the need for *resilience* especially in supply chain. From a scientific perspective, this requires handling risks coming from random events that may affect the process. Practically, information on this randomness is available in the now abundant data on industrial processes. Statistical challenge must be address to exploit these data to manage the risks inherent to industrial processes. Second, the *ecological transition* introduce several additional challenges. First, they introduce new combinatorial optimization challenge. For instance, operating a multimodal supply chain requires synchronizing trains arrival and truck departures. Second, they introduce additional randomness, such as the uncertainty on sun and wind power. This reinforces the need to exploit data to manage uncertainty when optimizing processes.

Hence, we believe that the main scientific challenge for operations research is to develop a new generation of **scalable and data driven optimization algorithms that make industrial processes more efficient and resilient**. While *combinatorial optimization* is the appropriate scientific discipline to address the scalability aspects, *machine learning* is the appropriate one to handle the data driven aspect. And a series of scientific work have shown that these combinatorial and statistical aspects must be dealt with simultaneously, as we otherwise end-up with a statistically intractable machine learning problem followed by a computationally intractable optimization problem.

## My methodological research

Following the diagnostics above, most of my methodological research is focused on developing algorithms that merge machine learning and combinatorial optimization tools to handle data driven problem. This has pushed me to work on *contextual stochastic optimization*: Given a context that contains all the information available on a process, how to take the best decision. Practically, this requires building a policy that maps a context to a decision. To build such a policy, I chain a neural network, which handles the statistical aspects, with a combinatorial optimization algorithm. The neural network therefore outputs the parameters of a combinatorial optimization algorithm, and the combinatorial algorithm outputs the decision. Two scientific challenges must be addressed and are the focus of my research. First, adequate architectures must be identified for the neural network and the combinatorial optimization. Second, such an approach can be efficient only if we develop efficient algorithms to learn from data the right parametrization of the neural network. Efficient algorithms must train the neural network in an integrated way, i.e., by minimizing the error on the decisions and not on the parameters.