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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5
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0answers
211 views

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 ...
11
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3answers
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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1answer
43 views

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), ...
3
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1answer
139 views

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 ...
2
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4answers
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 ...
17
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3answers
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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0answers
80 views

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} ...
6
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1answer
329 views

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 ...
4
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1answer
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 ...
4
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1answer
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 ...
24
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9answers
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....
5
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1answer
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-...
3
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1answer
107 views

How to transform these conditional constraints to linear integer ones in a more efficient way?

The conditional constraints A and B can be transformed to a set of linear integer constraints as follows: A) $\text{if} \ x_1=0 \ \text{then} \ d_1=1 \ \text{else} \ d_1= 0\\ x_1\in {\rm I\!R}^{\geq ...
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0answers
62 views

Density Optimization by Fitting an Circle to a Field - Monte Carlo Method

Given: I have 2D non-parametric formula that provides instantaneous intensity at certain (x,y) location. Required: I want to en-circle a region where the density is high via optimization. In other ...
8
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1answer
61 views

Covering problem on a network (?)

I have this problem described in natural language, and I was wondering whether it is relatable to any known problem. I have a directed acyclic graph. Each node can host a "probe". If node $i$ hosts ...
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0answers
66 views

Ways to improve lower bounds while solving MIPs

What are the ways to improve lower bounds while solving a minimization problem (MILP)?
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2answers
187 views

Pulp: slack variable to identify & measure extent infeasible in supply problem

I am currently modelling a supply problem that attempts to optimise a rail schedule which moves products from a production plant, to a warehouse to satisfy sales. The model is working fine (thanks in ...
3
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0answers
49 views

What are the efficient ways to model this scheduling problem and ways to improve running time

There are $N - \{1 \ldots N\}$ jobs, each with processing time $p_j$, to be scheduled on $M - \{1 \ldots M\}$ machines over span of $D - \{1 \ldots D\}$ days and while working $T - \{1 \ldots E \ldots ...
4
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2answers
138 views

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.
6
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2answers
1k views

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 ...
3
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1answer
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 ...
2
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0answers
55 views

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 ...
3
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1answer
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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1answer
150 views

How do I solve this Optimization problem?

Optimization of a simple expansion problem minimise: $$ \sum_{t=1}^{5}\left[\sum_{i=1}^{2}x_{i,t}CC_i\left(\frac{1+EIC}{1+r}\right)^t+UE_t*C_{UE}\right] $$ subject to: $$ 0 \leq x_{i,t} \leq 5 \\ ...
7
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1answer
1k views

How to use the least number of colours to colour different routes of a bus route such that no two intersecting routes will have the same colour

I would like to know of a method in which if provided say 10 routes with details regarding which route intersects with which another route, we can use the least number of colours to colour the routes, ...
11
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1answer
411 views

What are the pros and cons of LocalSolver?

LocalSolver is a company which provides a global optimization solver, combining exact and heuristic techniques. The benchmarks on their website are quite impressive. For example, they claim they can ...
8
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3answers
1k views

Open source MILP solver for quick “good enough” solution

I have a problem that I have already posted elsewhere in OR.stack, but the question is focused around a large binary MILP (about 1 million decision variables). Ultimately, I am more time constrained ...
1
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1answer
36 views

Enforcing discontinuous range for a variable

I want to enforce the following ranges for a set of variables, where the ranges for each variable are discontinuous. For example, I have two sets of ranges for each variable, \begin{align}\sf LB_1 &...
4
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1answer
107 views

Mobile Sensor Placement for Optimal Coverage

I have come across the paper that deals with spatial positioning of mobile sensors to optimally detect sound source, or position mobile cellphone towers to maximize the coverage. The region $Q$ is ...
2
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1answer
167 views

Does this problem fall into any common problem definition…Knapsack maybe?

I am struggling to find a representative problem formulation for this optimization challenge. I have implemented a MILP in Matlab, but the run time is taking more then a day. My goal is to see if it ...
2
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1answer
51 views

Normalization approaches to manufacturing data

I’m hoping someone would be able to help with insight to a normalization approach, I am tasked with identifying the relative difficulty between stages in a manufacturing process. The processes can be ...
17
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3answers
959 views

TSP with revenue maximization

How to approach a travelling salesman problem with an aim to maximize revenue at each town visited in a certain number of days (total number of towns is greater than what can be visited in the given ...
21
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3answers
2k 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 ...
3
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0answers
33 views

Constraint equivalence in PuLP

I'm working on an optimization problem in PuLP and I have to enforce a daily minimum of shifts and a daily maximum of assigned shifts. I have the following constraints to ensure each day has a minimum ...
11
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2answers
121 views

Is a “multistep” or “multiphase” Newsvendor model possible?

I'm trying to address the question of how many times should I order a product from my supplier, assuming highly stochastic demand. In my mind there would be something like the Newsvendor model, but ...
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2answers
351 views

Solving a (Non-)Linear Programming Problem

Apologies for my basic question, but I am kinda new to optimization methods, and I am bumping into the optimization problem below: $\min_{x} (c_1 \cdot u_1 + c_2 \cdot u_2)\\ \mbox{subject to:}\\ ...
17
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1answer
807 views

The difference between max-min and min-max

I am solving two-stage optimization problems in the form of $$\max_{x \in X}\min_{y \in Y} f(x,y),$$ where $f(x,y)$ is the solution of a mixed integer linear program (MIP). As the constraints of the ...
2
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1answer
69 views

What is the state of the art on the Weber problem?

I'm trying to get up to speed on the Weber problem. I'm very much not an expert, unfortunately. I would really appreciate recent literature recommendations / surveys / potted histories, however ...
4
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2answers
281 views

What are the most useful evaluation metrics when comparing the performance of different model formulations

Suppose you are writing a paper about a certain new problem class. You have certain problem instances of different size (real-world as well as random) given. You developed different integer ...
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0answers
49 views

Identifying saddle point in constrained optimization

Suppose we are minimizing $f(x)$. The first order necessary condition of $x^*$ being local minmum is: $$\nabla f(x^*)= \mathbf{0}.$$ For sufficiency, we check if also $\nabla^2f(x^*) \succ 0$, i.e., ...
5
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1answer
88 views

Local minimization of a function over a line

Let $f:\mathbb{R}^n \mapsto \mathbb{R}$ be a differentiable function. Suppose $x^*$ is a local minimizer of $f$ along every line that passes through $x^*$. This means that the function $$g(\alpha) = f(...
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0answers
85 views

How do I find the extreme rays and points for a stochastic programming problem

I have the following 2 stage Stochastic Programming program: \begin{align}\min_x& \quad x+\sum_{s=1}^{3}p_sQ_s(x)\\\text{s.t.}&\quad x\in\Bbb R\\&\quad Q_s(x)=\min\left[\begin{pmatrix}1&...
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0answers
62 views

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 ...
5
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2answers
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 ...
8
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1answer
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 ...
8
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2answers
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 ...
16
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7answers
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 ...
4
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1answer
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 ...
4
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1answer
85 views

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 ...
3
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0answers
35 views

Best method to optimise the blending of different types of coal to ensure all quality parameters are met at the lowest possible price?

I am looking to optimise the blending of different types of coal for the coke making process of a steel plant. I want to take into account the statistical variation of each coal’s qualities, so for ...

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