Current Issues of Interest

Question

What are some current issue of interest in Operations Research? I am interested in current topics that experts in the field are interested in researching.

Answer 1

This is an attempt at an answer, based on my current understanding:

Background:

Operations Research is an interdisciplinary field. You go from business administration and economics to theoretical computer science and mathematics.

In practice, you observe a real-world situation, model it, solve the model (or develop a method for solving general instances), and then implement the solution to the model in the real world, evaluate and repeat.

In each of these steps, there is active research.

1) If you work mostly empirically, and research how actors solve these problems in the real world, you go into behavioral OR or case studies that would be published in journals like "INFORMS Journal of applied analytics". An example of such a study would be:

We formulate the omni-channel fulfillment problem as an online optimization problem. We propose a novel algorithm for this problem based on the primal–dual schema. Our algorithm is robust: It does not require explicit demand forecasts. This is an important practical advantage in the apparel-retail setting, where demand is volatile and unpredictable. We provide a performance analysis establishing that our algorithm admits optimal performance guarantees in the face of adversarial demand. We describe a large-scale implementation of our algorithm at Urban Outfitters, Inc. This implementation processes on average 18,000 customer orders a day and as many as 100,000 orders on peak demand days. The system has resulted in substantial savings relative to an incumbent industry-standard fulfillment optimization implementation through optimal order-fulfillment decisions that simultaneously increase turn and lower shipping costs.

https://doi.org/10.1287/inte.2019.1013

Scientists working in that area are often organized by the field of business, that they are interested in. (e.g. warehousing...)

2) When only improving solution methods you get into mathematics, and journals like "Mathematical Programming". Here look at the most abstracted problems and try to prove general abstract results.

An example would be:

We show that the classical LP relaxation of the asymmetric traveling salesman path problem (ATSPP) has constant integrality ratio. If $\rho_{\rm ATSP}$ and $\rho_{\rm ATSPP}$ denote the integrality ratios for the asymmetric TSP and its path version, then $\rho_{\rm ATSPP}\le4\rho_{\rm ATSP}-3$. We prove an even better bound for node-weighted instances: if the integrality ratio for ATSP on node-weighted instances is $\rho_{\rm ATSP}^{\textrm N\,\,W}$, then the integrality ratio for ATSPP on node-weighted instances is at most $2\rho_{\rm ATSP}^{\textrm N\,\,W}-1$. Moreover, we show that for ATSP node-weighted instances and unweighted digraph instances are almost equivalent. From this we deduce a lower bound of $2$ on the integrality ratio of unweighted digraph instances.

https://doi.org/10.1007/s10107-019-01450-8

Scientists working in that area are often organized around the kind of mathematics they use. (e.g. polyhedral theory)

3) There is obviously a lot of stuff in between very relevant to practice, and high applicability; and purely theoretic results for very abstract models. And often a single paper might cover both a new real-world example and contain novel methods. Much of that work transfers ideas from one of the extremes in the direction of the other.

If there is a trend in better models for practice, there will be a tendency to find common mathematical features and find a more abstract model. Then people will work on the more abstract model and improve the understanding of these models.

If there is a big new result in theory, or a new method, people will try to extend it so that it can be applied to real-world problems.

Actual answer (kind of): On the more mathematical side you often have big open questions, like: What is the best possible approximation ratio for the asymmetric traveling salesperson problem?

Note: very rarely does someone just solve a long open problem. Rather there are small improvements for special cases like: if all distances for the TSP are 1 or 2 we have a new algorithm that has an approximation ratio of 1.28953 instead of 1.3. Aka, don't be intimidated by the weird cult of genius in mathematics.

On the more applied side, you are more or less driven by the real world. The best way to look at what is happening in your area of interest is literature reviews.

TL;DR: Here https://doi.org/10.1016/J.SORMS.2016.05.002 is a literature review of literature reviews in OR. It contains more than 300 literature reviews, and they typically contain a section with suggestions for future research.

Good luck, stay curious and research these operations;)

Answer 2

On the solving side, some hot topics include:

• presolving techniques

• GPU-powered algorithms

• algorithms designed for problems that consume a lot of memory

• algorithms for distributed architectures

• decompositions

• quantum computing optimisation algorithms

• large-scale factorisation algorithms/implementation

• domain reduction techniques

• automatic differentiation algorithms, especially for spatially challenging problems and gray-box problems

• improving numerical stability, either by using non-floating point numbers, or by using specialised hardware, or both

• graph manipulation algorithms/implementations