Questions tagged [optimization]
For questions involving mathematical problems that aim to minimize or maximize some objective function, possibly subject to one or more constraints.
895
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How to Set Up an Optimization Problem Like the 0/1 Knapsack
I'd like some help in understanding and setting up (what may be) an optimization problem that has some similarities to the 0/1 knapsack problem. In this problem the items are a given number of words (...
- 101
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3
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160
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Quantifying a measure of standard deviation in MILP
I am trying to set up a MILP for production scheduling. The specific details I'm not sure are important but in general a plant has M machines running N parts, each part requiring W workers. The model ...
- 33
2
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1
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64
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use Forecast distribution width in inventory optimization
I have a demand forecast that gives me a distribution for future demand, for each time period in percentiles (e.g. demand for period 1 will be between 6 and 25 (zero and 100th percentiles, and i know ...
- 83
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63
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Looking for an efficient way to solve a fractional problem (affine function over euclidean norm )
While working on optimization issues I encountered the following problem:
$$\left\{\begin{array}{ll}
{\displaystyle \sup_{z\in\mathbb{R}^{m}}} &\frac{ \langle c,z \rangle + \rho}{ \left\|B z\...
- 131
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1
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43
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How to implement tiered pricing based on weight or cube volume or order amount total into objective function with Guro i py
I am working on an optimization project here and my objective is to come out with the optimal amount of each item to buy at certain vendors that can minimize the cost while meeting the demand(already ...
1
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1
answer
21
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Array of string in OPL
how to make 2d array of strings in Cplex
//indics
{string} cluster=...;
setof(string) darkstore =...;
setof(string)demandpoint =...;
//data
cluster={chav,sree};
demandpoint=[{tsnami,adholokam,...
1
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2
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60
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Fixing binary variables in an Binary Integer Program
I have a Binary Integer Program with two binary decision variables and additionally have an expected solution. At the time of execution of this program I expect the parameters to change slightly. I am ...
- 372
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147
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Manual Benders Algorithm on CPLEX
I am using a manual Benders implementation for a problem. For that, I need to store certain variables since I need to transfer them to sub or master problems. However, as the size of the problem gets ...
- 333
1
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1
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57
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What's the suitable optimization model for solving the given model?
Given the following model, what's the suitable optimization model for it?
$X_{i,j}^N$ is a Matrix. (is known, and $N$ stands for Normalized. It means, $X_{i,j}^N$ is normalized version of $X_{i,j}$; ...
- 123
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2
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58
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Reformulate this constraint optimization problem such that I do not have to divide 2 variables?
I have a constraint optimization problem as follows:
I need to assign $m$ tasks to $n$ days, with $n \geq m$.
Each day can host 0 to $m$ tasks.
Each task either belongs to type $A$ or $B$.
I want to ...
- 21
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113
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How to perform clustering of a large number of nodes?
I have a clustering problem with around 400-500 nodes. The edge between any two nodes has a weight (between 0 and 1, 0: can be considered as there is no edge/connection between these two nodes) as ...
- 2,179
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3
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111
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Optimization solver that satisfies variable values within set membership
Is there a solver that can handle an AMPL model of this sort:
...
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52
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Gurobi-Python, unmet demand of customers
I would like to capture the unmet demand by modeling the following constraint with two decision variables. where $QU_{wc}$ is the unmet demand and $QW_{wc}$ the shipped amount of products. I model the ...
- 69
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1
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55
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Converting a piecewise function to a linear equation as a constraint
The value of one of the variable of my model (alpha_1) is given by a piecewise function. Each element of the piecewise depends on the value of some other binary decision variables (X1, x2, x3).
I'd ...
- 67
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2
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86
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Modelling with Gurobi-Python a Supply Chain Problem
I would like to write the following simple model in GurobiPy, which is part of many terms that's belongs to the objective function, I assumed that I have three suppliers are selected and three ...
- 69
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37
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Multi-Scenario Gurobi Python Output
I have an lp and am trying to solve multiple scenarios at once. One of my scenarios is infeasible though this is not the issue.
For some reason, when I print m.status, both solutions have a status of ...
- 83
2
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1
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77
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GUI Optimization tool for business users
We are looking for a tool that can be used by business users where they can do the followings:
use a simple data modeler to create the classes of data and populate the data instances
simple option to ...
- 121
2
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0
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142
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Distributed optimization with coupled inequality constraints
Consider the optimization problem:
\begin{equation}
\begin{array}{l}
\min_{(x,y)\in \mathbb{R}^2_{+}} \quad x_{1}a_{1} + x_2a_{2}
\\ \text {subject to } \quad\;
y_{2} \ge \frac{1}{{x}_2},
\\ \quad \...
- 215
3
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2
answers
120
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How to find the maximizing number of expected delivered units of a probabilistic minimum cost flow problem?
I am a Bitcoin / Lightning Network open source developer and researcher and new here but very active on the sister site. In the context of my research I discovered the field of operations research ...
- 131
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1
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68
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Meaning difference between SUMMATION and not in the MIP model
I'm asking you a question because I was confused about MIP while reading the paper.
This paper is about dual crane optimization.
In the MIP model of the paper, equations (7) and (8) are used to model ...
- 1
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71
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Cplex solution and dual of a problem
I have the following problem:
I took its dual as follows:
However, when I solve it on CPLEX, I somehow do not get the same objective value. Do you think there is something wrong?
Also, do you know ...
- 333
2
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1
answer
68
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Nonlinear fractional objective function
Could you please teach me when an optimization model with fractional terms in the objective function can be linearized or solved optimally?
I only know that if the objective function has a single ...
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32
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Budgeted uncertainty on the RHS
Suppose we consider budgeted uncertainty (Bertsimas and Sim, 2002) for the following scenario. We have a binary decision variable $x_{i,j}$, where $i \in I$ and $j \in J$ (two sets). We then have the ...
- 372
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76
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Converting continuous variable dict to binary variables in python docplex
I am solving a problem using linear relaxation at the initial phase. Hence, I need continuous variables at the beginning. Then I need to convert some continuous variables to binary and solve the same ...
- 333
2
votes
1
answer
106
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Formulation of nonlinear nonconvex optimization problem and finding appropiate solver
Consider the notation and objective below for this sequential resource allocation problem:
Allocation channels $i \in (1, 2)$
Spend/Cost timestep i channel j: $C_{i, j}$
Total resource: $B$
Horizon: $...
2
votes
3
answers
150
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Identifying the minimum number of required machines to schedule jobs
I am relatively new to the topic of optimization. I am currently trying to address the following problem:
We are given a set of jobs, say $J$ with release times, deadlines and duration. Jobs can be ...
- 372
2
votes
0
answers
25
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Recoverable Robustness for an optimization problem
I am relatively new to the concept of recoverable robustness. I am researching the robust version of an optimization problem. I currently have methods to address the problem with perfect knowledge. ...
- 372
1
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1
answer
92
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Mixed Integer Programming - How to model objective function with variables that depends on the solution? [duplicate]
I am modelling an optimization problem that is described as follows:
I would like to maximize audience for scheduling matches. There are n eligible teams and n/2 different slots.
Teams will only play ...
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55
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Is it useful to consider metaheuristics for power flow optimization involving binary variables?
I want to optimize the power flow in a low voltage grid, with respect to customer requests for electric vehicle (EV) charging, but also avoid grid overload (basically, the formulation can be seen in ...
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1
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178
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Software for optimization problem
I want to solve the following optimization problem
min $\|x\|_{\infty}$ such that $Ax \ge b, x \ge 0$
where $A$ is a matrix with integer coefficients and $b$ is a vector with integer coefficients.
...
- 173
2
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0
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82
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Using Optimization Algorithms to "Guess" the Dataset used to Train a Model?
There is a field of modelling called "Survival Analysis" (https://en.wikipedia.org/wiki/Survival_analysis), in which the objective is to model the effect of different "characteristics&...
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43
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Cost function for Routing Tasks between differently skilled workers
I am trying to come with a optimization framework & cost function for the following problem:
I have a stream of tasks coming in (volume of tasks upfront is unknown). Each task has a priority ...
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2
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1
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65
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Separation oracle gives optimisation
Suppose I want to minimize a linear function $f$ over a convex set $K$ and I have only access to a separation oracle, that is, given a point, the oracle returns yes if the point is in $K$ and ...
- 121
3
votes
3
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145
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Summation of maximization terms in CPLEX
I have a problem in the following type:
$$\sum_{i∈I}{\max_{j∈J}c_{ij}\cdot x_{j}}$$
For each objective, in a set of $x$ variables, the goal is to select the one with the highest cost coefficient. ...
- 333
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1
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73
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Grid search for optimization problem
Suppose you wanted to solve the following optimization problem:
$$\inf_{a \geq 0}\sup_{b \geq 0}\dfrac{(a^2 + 1)(a + b)}{2a + b} + \dfrac{b}{a + b} - ab,$$
where $a, b$ are scalars. How would you use ...
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70
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Infeasibility Detection in Combinatorial Benders Subproblem
I am dealing with a large-scale combinatorial benders problem of the following type. Number of binary variables is low, but the number of continuous variables in the subproblem is very large.
$z$ is ...
- 333
5
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6
answers
2k
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How can I solve this algorithmic task in Python?
I am trying to solve this task:
There are three datasets: first data on offices in cities: each city has a certain number of offices and each office has its own capacity of employees. Second, data on ...
- 61
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votes
2
answers
407
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Minimize worker variance assignment problem
I have a problem, which is similar to Assignment Problem, described as follows:
The problem instance has a number of workers and a number of tasks. Any task can only be assigned to a subset of the ...
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3
votes
2
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453
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Pulp problem gets the right objective value but fails to find the minimal solution
I converted an excel solver problem to Pulp. However, while the pulp program calculates the objective function value correctly, it doesn't arrive at the right answer. I can't figure out what is wrong ...
- 39
2
votes
1
answer
83
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Updating constraint set rhs in docplex
I am trying to update the rhs of a constraint iteratively under a while loop in docplex, however, it does not work properly. As I analyze the output text file, while some constraints are updated as I ...
- 333
3
votes
1
answer
100
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Gamma uncertainty set
I am new to the concept of robust optimization. I am currently trying to use a gamma uncertainty set (Bertsimas and Sim, 2002) for the following scenario. Suppose we have a constraint of the form $\...
- 372
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1
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52
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How to mathematically model this vehicle routing with pickup and deliveries problem?
I have this problem right here
There are N passengers whose are at places 1,2,...,N respectively. The i-th passenger, who is currently at place i, wants to go to place i+N. There are K buses are ...
- 23
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3
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325
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"Re-optimize" feature in Commercial Optimization
How does the "re-optimize" feature work in commercial optimization solvers such as IBM CPLEX and Gurobi? I recently experienced a considerable performance boost by re-solving a model with ...
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GurobiPy Tutorials and hands on from beginner to advanced
What is the best way to start modelling with GurobiPy, in order to utilize it, for research purpose (i.e. more complicated problems)?
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3
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135
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Definition of a modified scheduling problem where jobs are halted based on the shifts of employees
I am looking for the name of a scheduling problem in literature with some references. Here is the variant that I have in mind.
Given a set of jobs, employees have certain shifts that they can work on ...
- 292
3
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2
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137
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Vehicle passenger assignment with capacity constraint
Problem Summary
To match passengers (the number of passengers) to capacitated vehicles such that the profit is increased. All the vehicles have the same capacity $c$. It is not important to track ...
- 33
1
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2
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118
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Is it possible to say that problem A and problem B are equivalent, and B is concave?
Based on the assumption that $f(x)$, $g_1(x)$, and $g_2(x)$ are concave and positive, we get the following optimization problem:
Problem A
\begin{align}
\max_x&\quad f(x) \\\text { subject to }&...
- 35
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1
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64
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How to enumerate disjoint sets which cover a vector space in $\mathbb{R}^n$?
My experience with OR is pretty limited, so I apologize if I'm using any sort of bespoke terminology.
I have a set of subsets ${ \{ S_1,\cdots,S_m\}}$ of $\mathbb{R}^n$, and corresponding functions $\{...
- 123
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1
answer
99
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How to rewrite this problem in a standard format?
I have an optimization problem as below
\begin{align}
\max_x&\quad x\sum_{k=1}^{K}\log\left(1+\frac{h_k}{x}\right)+{(1-x) \sum_{l=1}^L \log\left(1+\frac{g_l}{1-x}\right)}\\\text { subject to }&...
- 35
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3
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206
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Robust Optimization in Gurobi
I have a research problem where my Mixed Integer Linear Program has data that follow probability distributions. I am approaching this by creating some m instances through realizations of these random ...
