# Questions tagged [optimization]

For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.

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### What is the difference between root relaxation and LP relaxation

(I apologize. I saw this question but, I do not know these may be the same or not.) I am trying to solve a MIP problem and have an issue about that. The problem's LP relaxation has the objective ...
630 views

### How can I estimate the monetary savings of a operation research application?

Developing operation research applications for industry clients is often very costly since it is in my experience often a custom special development for the client. The cost of developing a running ...
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### Is Multidisciplinary Design Optimization / Collaborative Optimization used anywhere outside of the Mechanical Engineering context?

I recently stumbled across the concept of Multidisciplinary Design Optimization (MDO), sometimes referred to as Multi-Disciplinary Optimization or Multidisciplinary Systems Design Optimization (MSDO), ...
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### Pyomo add constraint error: Rule failed when generation expression for constraint

I am trying to solve a model with Pyomo and struggling with indexing. Below is a simple problem instance, where you can also see the error. The message is straightforward and self-explanatory but ...
78 views

### Linearity of an optimization problem which comprises the product of variables with constant values from a non-linear function

In a mathematical integer optimization problem, if the objective function is represented as $\sum x_k \cdot M_k$, where $M_k$ is a non-linear function whose value is known and just plugged in to the ...
365 views

### Best ways to use machine learning / AI as an OR scientist

I have come across GUROBI's webinar "Mathematical optimization and machine learning". In essence, Mathematical Optimization (MO) and Machine Learning (ML) are different but complementary technologies....
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### Simplex - Network flow problem : Arc from 1 to P with infinite capacity

The Network - Maximum flow problem below aims to find the maximum flow using simplex method : With the LP as follow : LP : \begin{Bmatrix} Z(Max) = \sum_{i=1}^{m} fi \\ Af =0 \end{Bmatrix} ...
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### Is there a name for this variation of the assignment problem?

I'm given two matrices: $A$, an $n\times n$ adjacency matrix of a graph. The graph is unweighted, undirected and has no self-edges or multi-edges. $X$, an $n\times n$ symmetric matrix of edge ...
195 views

### PuLP Transport Problem - How to add outcomes of decision variables together

I am working on a rail scheduling problem that moves product from a production plant to a storage facility to satisfy demand. I am new to PuLP so finding this difficult to understand why this isn't ...
84 views

### Clustering a large ride-matching problem

Background: We are solving a large scale vehicle to person ride-matching problem. The problem is essentially simple (match every person with a vehicle, if possible), yet the problem size is quite ...
3k views

### What are Operations Research applications for 'good causes'?

I am looking for applications of OR for good causes, possibly with some literature. I intend a good cause loosely defined in the sense that the scope is that of improving the well-being of others, e.g....
109 views

### Interpretability Vs Accuracy in Operations Research and Management Science Community

This question might be somewhat general and not completely relevant to this forum but I think here is the most relevant place to ask the question. Currently, deep learning, RL and generally black-...
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### Maximum Flow Problem : Can someone refer me to accessible valuable resources

Can anyone please refer/suggest me some accessible papers, works, books, websites, documentation related to The Maximum Flow Problem.
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### Optimal power flow vs. economic dispatch

What is the difference between the two common optimization models for electricity systems, optimal power flow (OPF) and economic dispatch (ED)? I've heard people say that ED is just a multi-period ...
167 views

### Cplex : The cutting stock problem

The problem below aims to minimize the cutting leftovers from each cut : A company manufactures desks for kids gardens and primary schools, colleges and high schools. The leg of these deks all have ...
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### Weapon Target Assignment Problem + Time Windows

So I am very familiar with the WTAP it the static case. What I am wondering, is there a formulation that has "time windows" as well? Let's say you have some weapons and some targets, you know the ...
94 views

### What kind of scheduling problem is this?

I am trying to develop algorithm to solve following basic version of the problem. 1) I would like to know what this problem is called in literature so that I can look it up 2) What are efficient ...
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### Combining Two Different Queues

I am trying to create an optimization model for a problem that involves two different types of queues. Given Poisson demand (for both), there is a queue with constant service time and another queue ...
122 views

### Minimizing $x_1/x_2$ over a simplex in the positive orthant

I need to solve the following problem \begin{align}\min&\quad x_1/x_2\\\text{s.t.}&\quad Ax \leq b\\&\quad x > 0\end{align} where $A$ is a positive matrix. The best thing I can think ...
145 views

### Heuristic Search Planning Tree Leading to Worse TSP Solutions than Naive Greedy

I'm doing a Traveling Salesman Problem (TSP) homework for a coursera optimization course. My first attempt was a regular naive greedy approach, from each point, moving to the closest node (that hadn't ...
160 views

### Modeling Linear Program to decide if an inequality is facet

Suppose you have a set of points $v_1,\ldots,v_n$, which are the vertices of the polytope $P=\operatorname{conv}\{v_1,\ldots,v_n\}$ and a linear inequality $a^\top v \leq b$. What would be a linear ...
2k views

### Does there exist an aggregation of videos on optimization?

Is there a website or otherwise maintained list of talks regarding mathematical optimization? This would be a big help for the community it seems. I'm most interested in those relating to integer ...
84 views

### How to convert non-normal probabilistic constraints to deterministic ones for mathematical modelling?

I am working on a chance-constrained optimisation model that takes into account uncertainty. I am aware of how to convert constraints that are of a probabilistic nature into the equivalent ...
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### Analytically finding the maximizer of a trace optimization problem

$A \in \mathbb{R}^{m \times n}$ is an arbitrary data matrix. Moreover, $w \in \mathbb{R}^m$ is a data vector which is a probability vector, i.e., $w\succeq 0, \sum_{i=1}^m w_i = 1$. I have a ...