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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 ...
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 ...
10
votes
2answers
167 views

In an integer program, how can I “activate” a constraint only if a decision variable has a certain value?

Suppose we have the constraint $$a_1x_1 + \cdots + a_nx_n \gtreqless b,$$ where $a_i$ and $b$ are constants and $x_i$ are decision variables. Suppose also that we want the constraint to hold if $y=1$ (...
11
votes
4answers
406 views

Single reference for Mixed Integer Programming formulations to linearize, handle logical constraints and disjunctive constraints, do Big M, etc?

Is there a single crisp and accessible reference which covers how to generate Mixed Integer Programming formulations to linearize products, handle logical constraints and disjunctive constraints, do ...
15
votes
4answers
578 views

When to use indicator constraints versus big-M approaches in solving (mixed-)integer programs

Various optimization modeling languages and solvers allow for both indicator constraints (see for example here, here and here) and traditional binary variable and big-M approaches can be used to model ...
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 ...
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 ...
12
votes
1answer
419 views

How to formulate maximum function in a constraint?

How to formulate (linearize) a maximum function in a constraint? Suppose $C = \max \{c_1, c_2\}$, where both $c_1$ and $c_2$ are variables. If the objective function is minimizing $C$, then it can be ...
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 $x y$?
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 ...
16
votes
6answers
2k views

List of Implementations for common OR problems

For the TSP there famously is the concord solver (http://www.math.uwaterloo.ca/tsp/concorde.html) which is argubly the fastest exact solver for the TSP. There are many other problems that also show ...
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 ...
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 ...
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 ...
12
votes
2answers
388 views

Expressing a chain of boolean ORs using ILP

How to express a chain of OR operations in an ILP in which each expression is a less than or equal constraint and the left hand side variable in all inequalities is always the same? All the variables ...
14
votes
4answers
249 views

CPLEX non-convex Quadratic Programming algorithms

CPLEX solves non-convex quadratic problems to global optimality with a global optimality option (in version 12). The relevant pages are this and this. I benchmarked many solvers, and see that CPLEX ...
10
votes
4answers
161 views

How to linearize a constraint with a maximum of binary variables times some coefficient in the right-hand-side

I have the following constraint that I'd like to linearize: $P$ is a given set $b_p \in \{0,1\} , \forall p \in P$ a binary variable associated with each element of $P$ $c_p \in \mathbb{R}^+$, a ...
9
votes
1answer
109 views

Comparison of Algebraic modelling languages and general programming languages

Some optimization software/frameworks (commercial or open-source) such as AMPL, GAMS, Cplex, ... have a specific Algebraic modelling language. Some of them have another type of programming that uses ...
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 $xy$?
14
votes
1answer
443 views

Estimation of the size of Branch-and-Bound trees using ML

A short background: A paper [1] published in 2006 intends to show that the time needed to solve mixed-integer programming problems by branch and bound can be roughly predicted early in the solution ...
14
votes
2answers
278 views

How does a warm start work in LP/MIP?

Can someone explain how warm starts/ MIP starts work? How do solvers like CPLEX/GUROBI use warm start with the Simplex algorithm? I am interested in understanding how the entire warm start ...
12
votes
3answers
1k views

What is the purpose of libraries like Pyomo and Google OR tools?

I'm new to the OR world, and trying to learn the various tools available. I originally thought that Pyomo and Google OR tools were open source alternatives to commercial solvers like Gurobi or CPLEX. ...
6
votes
5answers
2k views

Algorithms vs LP or MIP

Is there a way of writing an algorithm with if-, while-statements to find an optimal solution without using linear-programming (LP)/MIP? If so, what would the benefits be against the LP/MIP? Is it ...
4
votes
0answers
61 views

Conditional constraint formulation [duplicate]

How can I create constraints to make sure $x=1$ if $k\geq 0$ and $x=0$ if $k<0$, where $x\in \{0,1\}$ and $k\in \mathbb{R}$? Here is my attempt: \begin{equation}\label{cons:1} \begin{aligned} ...
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 ...
17
votes
6answers
489 views

Deploying OR solutions and shipping projects

My background is a bachelor in mathematics. I learned basics OR on my own using the following : Introduction to Operations Research by F. Hillier and G. Lieberman Integer programming by l. Wolsey How ...
11
votes
4answers
263 views

Good resources for solving techniques (Metaheuristics, MILP, CP etc)

I want some resources (tutorials, online courses, lecture notes, articles, books, etc.) to learn the different techniques to solve OR problems (metaheuristics, CP, MILP, etc). It would be better if ...
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 ...
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?
17
votes
6answers
1k views

Infeasibility in mathematical optimization models

Sometimes, when solving mathematical optimization models (especially MIPs), they may be infeasible. Is there any comprehensive method to deal with the infeasibility conditions? (especially in complex ...
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 ...
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 ...
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 ...
18
votes
3answers
185 views

Variable bounds in column generation

Consider the set covering problem \[ \begin{align} \min&\ \sum_{j=1}^nc_jx_j\\ s.t.:&\ \sum_{j=1}^na_{ij}x_j\geq 1,\quad \forall i=1,\dots,m\\ &\ 0\leq x_j \leq 1 \end{align} \] ...
15
votes
4answers
421 views

Case Studies and Real Problems for Teaching Optimization and Modelling

It is that dreadful time of the year when I am prepping classes and over the last few terms I came to the realization that I need to significantly beef up the practice-oriented content of my lectures. ...
12
votes
2answers
236 views

How to choose an architecture for an OR web app and how to learn the tech stack associated?

After carefully reading the answers to my previous post I decided to opt for developing and deploying an app as a web service. I watched a talk on optimization apps. It suggests using the following ...
11
votes
2answers
193 views

OR Software Forums

A list of OR Software forums would be nice. Can someone import the list of OR Software forums from the (now) read-only OR Exchange at https://www.or-exchange.org/questions/9068/or-software-forums ? ...
7
votes
2answers
188 views

Simplex-Implementations in professional Solvers

Which non-textbook variants (primal/dual, revised) and techniques (e.g. steepest-edge) do professional solvers like Xpress, CPLEX, CLP use, to get the best out of the simplex algorithm? This ...
5
votes
2answers
261 views

Linear and Integer programming materials

I was wondering if you could refer me to some online video/text resources to learn linear and integer programming. I am intending to work in the field of data science. I greatly appreciate your kind ...
29
votes
8answers
547 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 ...
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 ...
16
votes
3answers
279 views

What is the connection of Operations Research and Reinforcement Learning?

I know that Markov Chains and Markov Decision Processes have been studied in the OR community too. But, I was wondering what is the relationship of Operations Research (OR) and Reinforcement Learning (...
15
votes
4answers
537 views

Optimization models for portfolio optimization

What are the mainstream models for portfolio optimization? We have Markowitz mean-variance model and CVaR-based models (e.g., max return subject to a CVaR constraint). What else is out there in terms ...
14
votes
2answers
285 views

references on the empirical study on the practice of OR

I am looking for (introductory) references on the empirical studies on the practice of OR. I mean literature that looks at questions like: Which methods are used in practice? How do people ...
11
votes
3answers
213 views

Is my approach to my internship project good? Optimal allocation of product across stores, constrained optimization

Context: I am a CS student currently in a non-CS internship (logistics, supply chain). My manager wants to leverage my knowledge of programming to build a program to solve the following problem: As ...
11
votes
3answers
172 views

When should I use dual Simplex over primal Simplex?

In Gurobi the user can change the method parameter in order to force Gurobi to use a particular method for solving MIPs. The user can, amongst others, choose ...
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 ...
17
votes
5answers
2k views

How to find an internship in OR/Optimization?

I am a master student in operations research with a specialization in operations research. To get my degree, I need to have a 6-month internship (from March to September). I am preparing my CV and I ...
15
votes
1answer
180 views

What is the “big-M” method? And are there two of them?

I’ve seen the "big-$M$ method" referred to in different ways. What is the "big-$M$ method" and why does it seem to mean two different things?

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