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42
votes
10answers
6k views

Are there any COVID-19 (coronavirus) related optimization problems with input datasets that we can “crowd solve”?

Is anyone aware of a medicine/vaccine related challenges with a good problem definition and some available input datasets, ideally related to COVID-19? What kind of constraint solving challenges would ...
41
votes
8answers
3k views

Great Unsolved Problems in O.R

More than 10 years ago, there was during an INFORMS annual meeting a session dedicated to “Great Unsolved Problems in O.R.” (you can find a small report of that session on this webpage). Which are ...
37
votes
9answers
3k views

Are there any OR challenges that are similar to kaggle's competitions?

I am looking for previous OR challenges. My goal is : Applying my knowledge while solving problems suggested in those competitions; and/or If possible, reading solutions posted by participants. I ...
37
votes
7answers
901 views

Optimization Problem Libraries

Can someone please make a list of optimization problem libraries so that the community can add to and refine it? I know a few off the top of my head.
36
votes
9answers
1k views

Counter-intuitive results in OR

When teaching introductory OR courses I have often found that presenting counter-intuitive or paradox-like results is a great eye-opener for the students. I use these examples and results as a ...
35
votes
9answers
5k views

What are the reasons OR industry projects fail?

You probably have done some OR projects within the industry or - if you are in academia - for the industry. I'm wondering if you've seen some patterns of why such projects fail (or at least do not ...
34
votes
8answers
817 views

Why is the programming code of many algorithms not public in the OR community?

In recent years, a huge number of scholars in AI and ML community are using Python to develop their algorithms and then publishing their papers and codes in GitHub. This provides an opportunity for ...
34
votes
6answers
706 views

Where can I find open source LP solvers?

I'm familiar with COIN-OR and have also used a couple packages in R to solve LPs. Today I found out Google has their own open source optimization software, and it got me wondering what other open ...
33
votes
13answers
8k views

Are Python and Julia used for optimization in industry?

I am giving a small computer exercise that aims at teaching students the basics of a modelling language to model small optimization problems. So far I have been using the modelling language GAMS as ...
33
votes
10answers
4k views

Machine learning and operations research projects

Can someone give me some suggestions for projects that use both machine learning/deep learning and operations research to solve business problems? Background: I am a student in OR and I am learning ...
33
votes
1answer
837 views

What are common and not so common abbreviations in Operations Research?

Many abbreviations are used in Operations Research. For example, we have abbreviations for problem classes (LP, MIP), solution methods (IPM), and specific problems (TSP, VRP). Which abbreviations are ...
32
votes
6answers
2k views

How to determine the correct level of detail when modelling?

"All models are wrong, but some are useful" - George E. P. Box I usually work on what one could call operational problems. There I usually do not have too much trouble figuring out the level of ...
31
votes
8answers
743 views

Modeling floor function exactly

Suppose we want to enforce a constraint $$ y=\lfloor{x}\rfloor $$ where $x$ is some continuous variable. One option is to use $$ x-1\leq{y}\leq{x},\quad y\in\mathbb{Z}, $$ which fails on the edge case ...
30
votes
2answers
4k views

Make a living as a math programming freelancer?

I would like to know how the (job) market for operations research works. My dream would be to work as a freelancer in the area of math programming. I have a PHD and several years of proven experience ...
29
votes
2answers
296 views

When are Decision Diagrams the right way to model and solve a problem?

Decision Diagrams are a relatively new approach to solving difficult combinatorial optimization problems. See http://www.andrew.cmu.edu/user/vanhoeve/mdd/ for some information on this approach. Are ...
28
votes
4answers
503 views

Why are integer minimax problems hard?

Problems that have a minimax-type structure are notoriously hard to solve. For example, the $p$-median problem from facility location (choose $p$ facilities to minimize demand-weighted distance to ...
27
votes
5answers
2k views

Optimization terminology: “Exact” v. “Approximate”

In optimization literature, I frequently see solution methods termed "exact" or "approximate". (I use the term "method" here because I suspect exactness, or its lack, is a function of both algorithm ...
27
votes
2answers
2k views

How to linearize the product of two binary variables?

Suppose we have two binary variables $x$ and $y$. How can we linearize the product $xy$?
27
votes
4answers
303 views

How to avoid having your optimization models rusting?

When designing optimization models for external organizations, I have witnessed the following: We design an optimization model for a given problem. We fine-tune it based on a portfolio of ...
27
votes
3answers
391 views

What are best practices to make optimization user interfaces intuitive for the user?

For many operations research applications a user will often be in charge of making the final decision and will use the optimization algorithms software as a part of their planning flow. Therefore, ...
26
votes
4answers
2k views

“Best practices” for formulating MIPs

Often there are many alternatives ways for formulating a MIP. For example: The model contains inequality constraints that must hold with equality in an optimal solution. The model contains ...
26
votes
3answers
3k views

How to select a Constraint Programming Solver

I would like to clarify that I am absolutely not an expert when it comes to constraint programming (I happen to use it when it seems to be the right tool for the right job). It is my understanding ...
26
votes
6answers
1k views

Statistical tests for benchmark comparison

Suppose that you have two algorithms for solving an optimization model, and you want to benchmark their performance over a large set of instances (with only one performance metric, for example, the ...
25
votes
7answers
8k views

MATLAB vs. Python in industry

I am a beginning PhD student in math, and I would like to focus on optimization. I am learning programming for the first time, and I have written out some rudimentary optimization algorithms in both ...
25
votes
6answers
3k views

How can I deal with non-operations research managers?

I am doing an internship in a company. The aim is to solve scheduling problems in the industry (a variant of the resource-constrained project scheduling problem). By the end of the internship, they ...
25
votes
5answers
6k views

Which GPUs to get for Mathematical Optimization (if any)?

The Machine Learning community has largely benefited from modern GPUs and several large companies are investing in new dedicated hardware. Unfortunately, academic and commercial mathematical ...
25
votes
3answers
319 views

Feeding known lower bounds to solvers

Given an optimization problem that aims at minimizing some objective function, a lower bound that is valid for all optimal solutions, and your solver of choice: For what theoretical and/or practical (...
25
votes
4answers
518 views

Stochastic programming MIP solvers

I am aware that Benders Decomposition is readily available in CPLEX and in SCIP; but are there any (free) solvers that provide off the shelf stochastic programming MIP algorithms or a nice to work ...
25
votes
1answer
279 views

The rationale to improve MTZ?

Currently I need to solve a quite specific problem involving symmetric TSP as a sub-problem (i.e., a Hamiltonian cycle is a necessary condition for optimizing some problem-specific variables that ...
24
votes
15answers
1k views

Recommended books/materials for practical applications of Operations Research in industry

I have a Masters' degree in Mathematics. I've very fair understanding of methods and techniques of Operations Research. I am looking for a good book/material where I can see a lot of examples on Math ...
24
votes
1answer
2k views

How to linearize the product of a binary and a non-negative continuous variable?

Suppose we have a binary variable $x$ and a non-negative continuous variable $y$. How can we linearize the product $x y$?
24
votes
2answers
268 views

How do you keep track of the latest publications in OR

It seems the most common answer to this question is: we periodically scan the websites of our favorite OR journals This approach however has several problems: you are likely to miss articles. you ...
23
votes
9answers
3k views

What are Operations Research applications for 'good causes'?

I am looking for applications of OR for good causes, possibly with some literature. I intend a good cause loosely defined in the sense that the scope is that of improving the well-being of others, e.g....
23
votes
5answers
4k views

Cubic programming and beyond?

It is almost inevitable in Operations Research to come across linear or quadratic programming problems. The overall structures of these problems are below: \begin{align}\begin{array}{ll} \sf{Linear}\\ ...
23
votes
6answers
1k views

How to compare two different formulations of a problem?

I somewhat know how to compare two MILP formulations of a problem that both use the same set of decision variables (as in the classical MTZ vs DFJ formulations of the TSP). I was wondering how two ...
23
votes
4answers
343 views

How to determine if a given problem seems to be a good fit to be solved using combinatorial Benders decomposition

Combinatorial Benders decomposition is a mathematical programming technique consisting into dividing a problem into a master problem and a sub problem. The master problem is solved to optimality (or ...
23
votes
4answers
488 views

What are the tradeoffs between “exact” and Reinforcement Learning methods for solving optimization problems

Exact methods, e.g., models that utilize an MIP approach with a specified objective and constraints, have advantages like the following: Using off the shelf solvers Optimality gap provability ...
22
votes
7answers
528 views

What are the main differences between Operations Research in the academic world, in the enterprise world and in the government world?

For anyone who's been on both sides of the fence: how does academic OR differ from OR in enterprises or governments?
22
votes
9answers
381 views

Reference for column generation applications

When talking about column generation algorithms, the main example is the cutting stock problem. I'm aware that variations of vehicle routing problem (VRP) can be solved using a column generation ...
22
votes
4answers
4k views

What instances can be solved today by modern solvers (pure LP)?

I have found a PowerPoint presentation in which the presentor Hall claims instances could be of the size of 108 in variables and constraints to be solved today. I assume that he meant sparse problems. ...
22
votes
4answers
2k views

Find feasible point in polynomial time in linear programming

Background A while ago my team was implementing an interior point LP solver and we came across the following conundrum: Is there a polynomial-time algorithm to find a feasible starting point in ...
22
votes
3answers
2k views

In an integer program, how I can force a binary variable to equal 1 if some condition holds?

Suppose we have a binary or continuous variable $x$, a binary variable $y$, and a constant $b$, and we want to enforce a relationship like If $x \gtreqless b$, then $y = 1$. How can we write this ...
22
votes
4answers
1k views

What is a solution?

Consider a standard optimization problem: Minimize an objective function with respect to constraints. My question is: What does the term "solution of the optimization problem" mean? At first I ...
22
votes
4answers
2k views

OR-backed serious games

A "serious game" is a game (usually a simulation) designed for a primary purpose other than pure entertainment. Games like the beer game or the fresh connection can be considered serious games serving ...
22
votes
1answer
342 views

Usages of logarithmic mean in optimization

I have recently learned about the logarithmic mean $$\frac{x-y}{\ln(x)-\ln(y)},\quad x,y > 0.$$ It is used a lot in chemical engineering optimization models e.g. see slide 15 of Developing ...
21
votes
10answers
3k views

What are Operations Research problems which occur in everyday life?

What are Operations Research problems which occur in your everyday life? Things that come to mind are for example: driving to work: shortest path problem packing your backpack for vacation: ...
21
votes
7answers
3k views

Applications of pure mathematics in operations research

This is a question that I've been thinking about for a while, as my background is mainly on pure mathematics. From a few OR papers that I've looked at, I could identify some areas of pure mathematics ...
21
votes
5answers
2k views

Validation and verification of mathematical models

Within the subject of simulation I have found some literature on validation and verification (e.g. Sargent's paper). My question is, what techniques do you use to validate and verify your mathematical ...
21
votes
5answers
377 views

Solving ATSP problem for large-scale problem

I want to solve the Asymmetric TSP for a large-scale problem for an industrial application where the company cannot buy a commercial software license. For their applications, it is very important to ...
21
votes
5answers
971 views

Solving pricing problem heuristically in column generation algorithm for VRP

In the set covering/column generation approach for the VRP (Balinski and Quandt (1964), or e.g. this tutorial), the basic idea is: Generate some routes. Solve the set covering problem using those ...

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