# Questions tagged [terminology]

For questions about the definition or meaning of terms used within Operations Research. Do not use this tag for questions about notation.

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### 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 ...
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### 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 ...
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### 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 ...
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### Dual bounds of integer programming problems

I often read in papers when branch-and-X algorithms are used to solve mixed integer programming problems, that the lower bound (in the minimization case) obtained from solving a linear programming ...
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### Has the expressibility of 'non-integrality testing' as extension to MILP been studied before?

It turns out that extending MILP with any of the constraints $y=\lfloor x\rfloor$, $y=\lceil x\rceil$, $0 < x$, or $x\notin \mathbb{Z}$ is 'equally hard'. (see my answer here, and below) ...
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### Polyhedra, Polyhedron, Polytopes and Polygon

About Polyhedra, Polyhedron, Polytopes and Polygon, what do they mean in the context of linear programming and what is the difference between them?
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### What is quadratization?

In the context of discrete optimization, what exactly does it mean to "quadratize" a function? The term seems to be used mainly by operations researchers, in my experience.
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### Geometric programming: Why are the constraints defined to be less than/equal to 1?

In a simple convex optimisation problem, the standard form is given by \begin{align}\min_{\bf x}&\qquad f({\bf x})\\\text{s.t.}&\qquad g_i({\bf x})\le 0,\quad i=1,\cdots,m\\&\qquad h_j({\...
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### "Partial" Lagrangian Dual in LP

Consider the optimization problem \begin{align}\label{opt-lp}\tag{Primal} \begin{array}{cl} \underset{x \in \mathbb{R}^n}{\text{minimize}} & c^\top x \\ \text{subject to} & Ax = a \\ & Bx =...
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### Difference between "Optimization" and "Constrained Optimization"?

(Another OR noob question) As I'm trying to learn about OR and Optimization methods for work, I'm having a hard time understanding the difference between "Optimization" and "Constrained Optimization"...
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### Name for this ILP problem type

I am considering automating testing of down-stream testing of packages that depend on other packages. There are test sets $T_1,\ ..., T_n$ which can be tested or not tested, which each have a time ...
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### What's the name of a finite-capacity bin packing problem trying to minimize the weight of the heaviest bin?

I have a fixed number of bins which are themselves weightless. Each bin can hold only a fixed amount of weight. Not all bins have the same capacity. I also have a fixed number of objects each of which ...
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### Is a mathematical programming problem with no objective function an optimization problem?

I have a "mathematical programming" (MP) problem that does not have an objective function. Namely, I want to find a vector that satisfies all constraints (no optimization involved, right?). ...
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### What is the definition for an integer-friendly constraint?

I have seen some papers claiming that their proposed model is integer-friendly. I would like to get more information about what type of constraints we can call integer-friendly. Probably, it can be ...
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### Terminology for continuous planning, real-time planning, non-disruptive replanning, overconstrained planning, backup planning etc

In the past 14 years, when dealing with enterprise planning challenges, I've encountered multiple challenges of "repeated planning" and "planning agility" in general. At some point,...
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### Combined arc capacity constraints in network flows

Consider the network flow polyhedron for a directed graph $G = (N, A)$. Along with the standard flow-balance and single-arc capacity constraints, we are faced with additional constraints which enforce ...
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### What is the name of the graph where any edge is part of a cycle?

I wonder if there is a special category for this kind of graphs, I am thinking of a bidirectional graph but it would also be interesting in the cases when it is undirected. I am thinking of something ...
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### What is the meaning of monotone hazard rate (MHR) distribution?

It might be somewhat irrelevant to this forum but I think that many people here are familiar with this concept. I have seen that many papers assume that customers' valuation ($F$) is a monotone hazard ...
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### Does the facility layout problem with zero and one matrices have a specific name?

I have an facility layout problem where the flow between any two departments is either zero or one. Also the distance between each location pair has the same nature (zero or one). I am curious whether ...
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### Defining multiple constraints compactly where some index combinations are not defined

My question is about how usual/strange defining constraints compactly can be (in a scientific document). Formally, I define constraints f_{i,j,k}(x) \leq 0, \quad \forall i \in [I], \ \forall j \in [...
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### Logical / combinatorial Benders Decomposition vs Cutting plane method

Is there a difference between logical and combinatorial Benders Decomposition and the cutting plane method? My understanding is that for all of these techniques, there is a MIP and based on solutions ...
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### 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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### 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 ...