Questions tagged [reference-request]

For questions asking for references from the literature or textbooks on specific topics.

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Methods to solve integer linear inequalities with products of two variables

I'm interested in solving the following system of equations over the integers: \begin{align*} x_l^3 &\le x_l^1x_l^2 & \text{ for } l = 1,\ldots,s \\ A x &\le b \\ 0 &\le x \end{align*} ...
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5 votes
1 answer
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Modulo Integer Programming, $m$ equations $n$ variables

I am following 'Application of Number Theory to Numerical Analysis', and there is a section by G.H. Bradley called 'Modulo Optimization Problems and Integer Linear Programming'. There he explains that ...
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6 votes
2 answers
357 views

Fleet Management: How to allocate vehicles between departments

Assume that I have data about a regular big company (not a salesman problem). data contains of every department's (marketing, finance, production, etc.) vehicle size, GPS track values, duration of ...
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3 votes
0 answers
34 views

Complexity of the ellipsoid method in general convex problems

The ellipsoid method is often mentioned in relation to the complexity of solving linear programs. Is the method however polynomial in the general non-linear convex cases? Preferably I would like a ...
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3 votes
1 answer
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studies to determine how much customers can wait to get outputs from a real time optimization model

I am building a web-based tool that needs to take input from the user and run an optimization model on a server and display results back on the webpage. Currently it is a MIP formulation solved using ...
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8 votes
3 answers
416 views

How to tackle this VRP variant?

I am currently working on the following problem, which is a variation of a vehicle routing problem. I am looking for different ideas to tackle it. Problem description A set of nodes with a given ...
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7 votes
3 answers
366 views

Combining Multiple Cost Values in Shortest Path Problem

I am trying to solve a shortest path problem through Dijkstra's algorithm. However in my case, cost between nodes (nodes $i$ and $j$) are more than one- two nodes are compared based on two different ...
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  • 179
10 votes
2 answers
223 views

The First Ever Linear Programming Problems

I have heard that Linear Programming was first used by: Dantzig to solve problems involving US military logistics in the Second World War Kantorovich to solve problems involving transportation of ...
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4 votes
0 answers
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Understanding Optimal Transport Problems

I am trying to better understand the origins of Optimal Transport Problems such as Monge's Problem. For instance, I came across the following references: https://www.math.ucdavis.edu/~qlxia/Research/...
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3 votes
0 answers
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Departure process of M/G/1 queue with hyper-exponential service times

I am working on two queues in tandem; the first queue is M/G/1 with hyper-exponential service times and the second queue has exponential service times. I want to know if the second queue can be ...
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  • 131
2 votes
1 answer
82 views

Traveling Salesman Reference

Can anyone recommend a reference which shows the amount of time required for the Traveling Salesman Problem (TSP) to be solved using brute force as the number of cities increase? I have informally ...
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4 votes
2 answers
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is there any recommended "rolling horizon in optimization" literature for beginners?

I am relatively new to optimization and mathematical programming. I am looking for literature on rolling horizon. When I search for it on the internet, I find many articles like: Lukas Glomb et al. ...
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8 votes
3 answers
240 views

Difference between "Online Optimization" and "Stochastic Optimization"/"Robust Optimization"?

I just came across the notion of Online optimization (I got a look on Wikipedia page and some other webpages), but it was not enough for me and I am looking for a more elaborated comparison, namely in ...
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1 vote
0 answers
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Reference of Optimization in the Bible : Moses and Coins

A few days ago, I was reading some articles/stackexchange posts on the "history and origins of optimization". Somewhere, there was an interesting reference to a biblical/old testament story ...
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6 votes
2 answers
204 views

I'm looking for materials to share with undergrads who want to consider a career or masters degree in OR

My daughter is a math major at a good liberal arts school. It doesn't seem like they have any OR courses or talk much about it as a career choice (either for a job or going to grad school in OR.) And,...
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2 votes
1 answer
91 views

What is the role of computation lower bounds for exact methods, heuristics, and hybrid of exact and heuristics?

I'm struggling with this question for weeks: What is the main difference between the role of computation lower bounds for exact methods, heuristics, and hybrid of exact and heuristics? I try to answer ...
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17 votes
6 answers
2k views

Breakthroughs in Operations Research since 2010

Recently I saw the following question Breakthroughs in mathematics in 2021 by Johnny Cage on mathoverflow, which inspired me to ask the following question: "As specialised operations researchers ...
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3 votes
0 answers
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What is the general name (e.g. facility location problem) for this problem (if any)?

I would like to know if there is a general name for the following problem: We will open several facilities. Each facility has an associated facility type. There exists a given number of facility ...
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3 votes
0 answers
46 views

Indeterminacy Reduction for MINLP

I am considering a Mixed Interger NonLinear Program (MINLP), and using a solver to obtain admissible solutions. Is there a general method to reduce indeterminacy of solutions (e.g. by adding ...
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3 votes
1 answer
50 views

Goal Programming -- Best practice for standardizing magnitude of deviations across goals?

A certain goal program I've been working on has three goals that each operate at different scales. Two of the goals stay between 0-10, so any deviation from the goal is generally only a couple of &...
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6 votes
2 answers
216 views

Multi-commodity Network Flow: Convert a node-arc solution to an arc-path solution

For a logistics optimization problem I am working on, the most natural expression of the problem is using a node-arc formulation of the MCNF. It is solved using an LP/MIP solver like CPLEX/Gurobi. ...
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  • 109
2 votes
0 answers
42 views

Importance of Polynomial Time Approximation algorithm for special case [closed]

I am an MSc student, searching for an interesting topic in operations research for NP-hard problems. I need your opinion and recommendation about: "Searching a polynomial time approximation ...
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3 votes
0 answers
100 views

Sources of Min-Cost Flow Models That Utilize Binary Variables for Transportation Networks

I am looking for articles that include min-cost flow models with binary variables for flow transportation like gas networks, traffic systems, heating systems. Is there any specific place(like OR ...
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2 votes
0 answers
61 views

Designing Multi Floor Architectural Layouts

Architectural layouts define the position and shape of rooms in 3D space, where windows and water pipes are and as well as how humans travel between rooms (among other things). There is a lot of ...
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3 votes
1 answer
64 views

optimizing quadratic form over bounded polytope

As a followup to this question, I am looking for references for the problem of maximizing $x^TQx$, where $Q$ is positive definite, subject to linear equality and inequality constraints bounding all ...
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2 votes
1 answer
107 views

What are some good references for understanding the conjugate gradient method?

Are there any good references that provide an intuitive, motivated, or visual explanation of the conjugate gradient method?
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2 votes
1 answer
52 views

Elevator Traffic (Queueing Theory) Papers

I am about to start my final year thesis. The topic would be related to the queueing theory, specifically for the elevator traffic systems. I would need to do some literature review before going ...
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5 votes
0 answers
41 views

Constant-factor approximation algorithms for max-min number partitioning

In the k-way number partitioning problem, the input is a set of numbers and the goal is to partition them into $k$ parts in an optimal way. The most well-studied optimization objective is to minimize ...
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6 votes
1 answer
111 views

In which time complexity operates the Savings algorithm for the TSP?

In which time complexity operates the Savings algorithm from Clarke and Wright for the TSP? I mean the parallel version of Savings. I think it is in $\mathcal O(|V|\log|V|)$ with V as vertex/node ...
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  • 659
5 votes
1 answer
122 views

What are (some of) the best resources for shift scheduling/rostering?

Shift scheduling/rostering is obviously very widely researched, with tons of papers around it. I found the review papers by Van den Bergh et al. [1] and Ernst et al. [2], but am looking for something ...
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  • 3,034
12 votes
5 answers
1k views

Is Hillier F. Introductory to Operations Research a good book for a data analyst interested in Operation Research field?

Is Hillier F. Introduction to Operations Research a good book for a data analyst? I was particularly interested in Operations Research especially when I was reading about the history about this area: ...
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4 votes
1 answer
113 views

Maximizing sum of step functions under single linear constraint

I am trying to efficiently solve the following optimization problem: \begin{align}\max_{b \in \mathbb{R}_+^D}&\quad\sum_{n=1}^{N}\operatorname H(b^T w^{(n)} - c^{(n)}) \\\text{s.t.}&\quad\sum_{...
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7 votes
2 answers
378 views

Is there a ranking of heuristics for the travelling salesman problem?

Does a ranking of TSP heuristics exist that is based on the quality of the solutions? For example a paper or another resource that compares the performance of TSP heuristics like the nearest neighbour,...
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0 votes
0 answers
153 views

Set Covering and Column Generation

I need some set covering and column generation examples in OR-Tools python. If anyone can provide or direct me to some resources that would be great..!
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3 votes
0 answers
47 views

Popup facility location

I was searching through articles for popup facility location and could not find anything devoted to it. If anyone has come across it, can someone guide me to some papers?
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3 votes
2 answers
140 views

Scheduling of planned orders while respecting certain stock levels

I am searching for the academic name of the problem of computing a valid schedule for planned order. More precisely, The problem consists of: list of orders O, available vehicle per day K, and the ...
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  • 119
3 votes
1 answer
94 views

Extreme points for capacitated flow polytope

Given a network as a directed acyclic graph with a source and sink, and non-negative edge capacities, I am interested in the extreme source-sink flows. More formally, I am interested in a ...
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  • 1,311
5 votes
0 answers
23 views

What are some references for Fluid and Diffusion models in Queuing?

In queuing theory and stochastic process, there are many papers that have applied fluid and diffusion models to approximate the original models. However, the concepts and basics of these models are ...
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  • 2,105
8 votes
2 answers
143 views

Reference for algorithms and complexity

What kind of background in algorithms and complexity theory is needed to fully understand the computational aspects of an OR paper. To be specific, I am not always sure when a paper says 'XYZ problem ...
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7 votes
1 answer
127 views

Is there any academic reference which suggests/uses dual values as initialization of Lagrangian multipliers?

The Lagrangian relaxation approach is used to generate lower (upper) bounds for minimization (maximization) problems by moving some constraints to the objective function and multiplying them by "...
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3 votes
4 answers
289 views

Book recommendations on OPL

Are there any good books that teach how to work with OPL in CPLEX? I searched but I didn't find any.
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  • 141
4 votes
3 answers
218 views

Overview of the different areas of OR and optimization

I am somewhat new to OR. I have taken up courses on Linear Programming, Game Theory and Queueing Theory and I know a bit of Dynamic Programming. Soon I shall be doing a project on OR or Optimization ...
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2 votes
2 answers
125 views

Literature for building solver portfolios

A portfolio of solvers is a collection of solvers with different configurations that share CPU time, CPU cores, and memory resources and try to get an answer as soon as possible. Solvers might also ...
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1 vote
1 answer
166 views

References to publications on representation of any boolean function as a system of linear inequalities

It is known that any boolean function may be represented, in some sense, as a system of linear inequalities. But my rather intensive literature search brought a little references. I will appreciate ...
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2 votes
1 answer
110 views

Any good resource for solving power system optimization in GAMS?

I am looking for some resources to learn the modelling tricks of GAMS in power system optimisation problems.
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5 votes
2 answers
175 views

Logic-based Benders decomposition with integer master variables

I am looking for a paper/study in which a Logic-based Benders decomposition (LLBD) framework is used when the master problem is associated with integer variables (not specifically binary). In general ...
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2 votes
0 answers
107 views

Recommendations on Operations Statistics/Analytics Approaches/Materials

I'm an operations data analyst. I was wondering if I can get recommendations on books/videos on statistical models specific to optimizing business operations through analytics and statistical modeling....
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13 votes
6 answers
964 views

Where can I find documentation on good practices for efficient formulations of a problem?

I am sort of new to mathematical optimization and have to build some fairly complicated models for my thesis. I was wondering where I could find literature to help me develop more efficient versions ...
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3 votes
2 answers
84 views

IP model for k-rooted spanning forest

I am looking for an IP model for finding a $k$-rooted minimum spanning forest on an undirected graph $G$. Given a set of roots $R$ and a set of nodes $N$ $(R\cap N=\emptyset)$, I would find a forest ...
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  • 907
8 votes
1 answer
75 views

Real-life timetabling problems in education

I am looking for papers/resources that deal with timetabling problems in education. I want the resources to cover as much information as possible: I don't have enough contact with people who are ...
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