# All Questions

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8answers
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### 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 ...
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 ...
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.
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $xy$?
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 ...
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 ...
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. ...
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}\\ ...
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 ...
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 ...
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 ...
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 (...
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 ...
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 ...
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?
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 $x y$?
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 ...
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 ...
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 ...
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 ...
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?...
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 ...
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 ...
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 ...
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 ...
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 ...
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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