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37
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 ...
36
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 ...
34
votes
7answers
646 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.
32
votes
8answers
603 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 ...
32
votes
6answers
571 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 ...
31
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 ...
30
votes
10answers
3k 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 ...
30
votes
6answers
617 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 ...
29
votes
8answers
546 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 ...
29
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 ...
28
votes
2answers
248 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 ...
27
votes
4answers
228 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 ...
26
votes
1answer
532 views

What are 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 ...
25
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 ...
25
votes
4answers
1k 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 ...
25
votes
5answers
5k 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
4answers
271 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
221 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
6answers
788 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 ...
24
votes
2answers
402 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 $xy$?
24
votes
2answers
239 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
4answers
344 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
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
5answers
3k 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}\\ ...
22
votes
5answers
1k 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 ...
22
votes
4answers
259 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 ...
22
votes
4answers
235 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 ...
22
votes
3answers
197 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 (...
22
votes
2answers
543 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 ...
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 ...
21
votes
7answers
387 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?
21
votes
5answers
777 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 ...
21
votes
5answers
1k views

Examples of machine learning applied to operations research?

Can someone give me a few examples, if they exist, of problems in operations research that could be solved using machine learning. I am aware that machine learning examples are data-driven and do not ...
21
votes
3answers
334 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 ...
21
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 ...
21
votes
3answers
835 views

How to (graphically) present computational results?

I am interested in evaluating and demonstrating various aspects of the performance of general solvers for mathematical optimization problems (in particular MILPs). I assume that I have a good testset ...
21
votes
1answer
272 views

Polynomially solvable problems with exponential extension complexity

The maximum matching problem is solvable in polynomial time using Edmonds' blossom algorithm. However, unlike for example the spanning tree polytope, it has been proven fairly recently that the ...
20
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 ...
20
votes
1answer
317 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 $x y$?
20
votes
1answer
138 views

Real-world examples of supply chain contracts?

Does anyone know of any real-world examples in which supply chain contracts, of the type introduced by Pasternack (1985) and reviewed by Cachon (2003), are actually used in practice? I'm talking about ...
19
votes
12answers
558 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 ...
19
votes
7answers
5k views

Are programming languages necessary/useful for operations research practitioner?

This semester I will start teaching Programming in Python to Master students in Supply Chain Management. I would like to start the first lesson with "Why learning programming languages will be useful ...
19
votes
5answers
1k views

Ordered list of OR journals

Is there any compact resource that includes a list of all academic journals in the OR/MS space, ranked by journal importance? Although there are some helpful features offered by publisher websites ...
19
votes
4answers
206 views

How can I remember the rules for taking the dual of a linear program (LP)?

When taking the dual of a linear program (LP), is there a trick/easy way to remember the rules for the directions of the inequalities, signs of the variables, etc.? A trick with a catchy name, perhaps?...
19
votes
3answers
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 ...
19
votes
2answers
426 views

Why is it important to choose big-M carefully and what are the consequences of doing it badly?

The question here discusses the two different use of "big-M method", where one of them is the big-M in logical constraints and linearization in (mixed-)integer programming problems (that's what I'm ...
19
votes
4answers
895 views

Linearize or approximate a square root constraint

I encounter a nonlinear constraint that contains the square root of a sum of integer variables. Of course one could use nonlinear solvers and techniques; but I like linear programming. Are there any ...
19
votes
5answers
220 views

Tightness of an LP relaxation without using objective function

How can we measure the tightness of a linear programming relaxation for a mixed integer linear program without using the objective value? I would like to get a measure in terms of the feasible set and ...
19
votes
3answers
1k views

Are valid inequalities worth the effort given modern solvers?

In Laurence Wolsey's Integer Programming[1], he presents a well-known procedure for deriving valid inequalities (VI) suitable for integer and mixed integer linear problems (see Section 8.3, and also ...
18
votes
8answers
5k views

How to innovate in OR

I am a graduate student in OR and I want to build one or two independent projects that go beyond academic projects in my university. I would like to target average people and/or those in the industry ...

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