Questions tagged [modeling]

For questions related to the process of converting a real-world problem into a mathematical model. Can include questions related to linearization, logical constraints, tightness of formulations, and so on.

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2
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1answer
103 views

Best way to add dummy to transportation problem? Zero cost will be always chosen first?

I know that an unbalanced transportation problem could be made a balanced transportation problem by adding a dummy node which equals the difference between demand and supply. In literature, dummy ...
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0answers
32 views

Probabilistic model

Given that the demand for a commodity typically occurs every day from 7:00am to 2:00pm after which this commodity is no longer demanded and can only be disposed of at a cost to the seller. Given that ...
7
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1answer
128 views

How can I strengthen a family of constraints in the presence of a clique constraint?

Suppose $x_i$ are binary variables, $y_j$ are arbitrary variables, $a_j$ and $b$ are constants, and I have the following linear constraints: \begin{align} x_i + \sum_j a_j y_j &\le b &&\...
4
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1answer
104 views

Problems modeling a constraint in network design problem

I'm working on a network design problem where the objective is to minimise the network design cost. Given a graph G = (V, E) and a set of point-to-point demands K, the task is to route the demands and ...
5
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1answer
109 views

How to partition a graph with optimal number of groups?

I have a graph with $N=12$ nodes. Some nodes may not have any edge between them. every edge has a weight. How to find the optimal partitioning of the graph so that total weight in the system is ...
13
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2answers
372 views

Column generation for TSP

For teaching purposes, I would like to solve the Travelling Salesman Problem with a column generation approach. In the academic literature, an approach is proposed (for example here), where columns ...
2
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1answer
48 views

Model definition in pyomo to solve online optimization problem

I am trying to model the attached online optmization problem in pyomo. Eventually, I am going to use the octeract solver to find the matrix soluions of W and G. I would like to ask advice about ...
7
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1answer
231 views

Effect of 'unused' variables on the result and runtime of optimization algorithms

I have a general question about the effect of 'unused' variables on the result and runtime of optimization algorithms. I try to explain my question by giving an example. Let's say I have 2 type of ...
6
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1answer
152 views

How to model this multi-commodity flow problem with a twist?

Problem description I am working on a variation of the multicommodity flow problem on a graph $G=(V,E)$. I have requests $r_{uv}$ for pairs of nodes $(u,v), u\in V, v\in V$, which means that $r_{uv}$ ...
3
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1answer
64 views

Obtaining linear relaxation objective value from MILP model coded in Pyomo

I would like to seek some advice on modeling the following: I am currently using Pyomo to generate my MILP model in Pyomo. It seems that it is not possible to cast the integer and binary variables to ...
3
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2answers
121 views

Setting up Branching Priority for GUROBI in Pyomo

I am currently experimenting with GUROBI and would appreciate some kind advice on the following: In Pyomo: Setting variable branching priorities, there was a response to doing so for CPLEX, hence I ...
2
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1answer
63 views

Finding the minimum of a group of timings

I would like to seek some modeling advice on the following: Say for instance I have 5 nodes representing workstations of the operation of 5 jobs, and that I have less than 5 vehicles. Say I have two ...
5
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2answers
393 views

How to minimize the number of breaks in sports scheduling?

I have the following sports scheduling problem. For $n$ teams and $m$ rounds, I define the binary decision variable $$ x_{i,j,s} = \text{1 if team $i$ plays at home against team $j$ at round $s$, 0 ...
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1answer
248 views

How to mathematically formulate the optimization problem?

I have a system with $S$ service points. There are also $U$ users in the system. We have $$U>S>G$$ One group can have maximum $M$ service points, but there is no restrictions on the number of ...
5
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1answer
207 views

How to set a limit for a switch to 0 of a variable for 2 variables combined

I have a follow up question to another question of mine How to set a limit for a switch to 0 of a variable about counting the number of switches to 0 of one decision variable. Now I would like to ask ...
2
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2answers
93 views

How to deal with a decision variable in the objective function that depends on if-else conditions involving other decision variables?

I'm modeling an optimization problem in which a decision variable $x_1$ in the objective function depends on if-else conditions involving decision variables $x_2$ and $x_3$, as the following equation, ...
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0answers
44 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....
5
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1answer
191 views

How to set a limit for a switch to 0 of a variable

I would like to know how to define a constraint to set a limit for switching to 0 for a decision variable? So I have a linear variable $x(t)$ which quantifies the modulation degree of a heating device....
12
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6answers
889 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 ...
3
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1answer
44 views

Control & Experimental Group Selection Methodology using STDEV and T-Test?

I would like to know if my methodology was 'correct': I am trying to conduct an experiment on my stores. I would like to find out the effect of a marketing campaign on the number of transactions. Only ...
1
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2answers
160 views

add constraints to the problem

Take a single source capacitated FLP (facility location problem). As we know the linear formulation to this problem is: \begin{align} & && \text{min} \; \sum_{j \in J} a_{ij} \; ...
3
votes
3answers
658 views

Model if-else statement

I need to build a if-else constraint for this statement, where $x_P$ and $x_I$ are decision variables, and $C$ is a constant: if $x_P \ge C$ then $x_I = x_P - C$ else $x_I = 0$. Any help is greatly ...
4
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1answer
316 views

Indicator function in math programming

Let $x$ be an integer variable that takes the values $1$, $2$ or $3$. Let $y_1$ and $y_2$ be binary variables. I want to express the two following logical constraints: if $x=2$ then $y_1=1$ if $x=3$ ...
2
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2answers
107 views

Trouble with optional nodes in a VRP model using Gurobi for python

I am currently working on a VRP problem where the vehicles are electric. This means that I have range restrictions, and charging stations as nodes which are optional to visit. In my model I have the ...
2
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1answer
59 views

How does the RCPSP's precedence constraint work?

In [1] the authors define the RCPSP (resource-constrained project scheduling problem) as follows: minimize $$ \sum_{t} t x_{n t} $$ subject to $$ \begin{array}{c} \sum_{t} x_{j t}=1, \quad j \in J, \\ ...
7
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0answers
276 views

OR-TOOLS : delivery node with multiple possible pickup nodes

I am using ortools to model a VRP with pickup and delivery constraints, where pickups can be done at different nodes. For example, if node A has a demand, it must be picked at node B or C. Here is how ...
8
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2answers
150 views

Does dispersion really matter?

Context: Given a counting process $\{N(t),\,t\ge 0\}$ which tracks the number of events (arrivals) by time $t$, the index of dispersion (for counts) is the variance-to-mean ratio of the cumulative ...
1
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1answer
46 views

Can I define constraints in Pyomo as a list?

I would like to define the following constraint in Pyomo $$W^\top{\bf 1}\le\hat w=\begin{bmatrix}\hat{w}_1&\hat{w}_2&\ldots&\hat{w}_N\end{bmatrix}^\top$$ where $W$ is a $2\times4$ matrix. ...
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0answers
23 views

Correct way to define constraints in Pyomo

Can I know if the constraint below can be defined as follows in Pyomo for convex optimization. W and G are arrays of dimension M x N. ...
2
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2answers
75 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 ...
3
votes
2answers
312 views

How can I express this max-min in CPLEX?

Initially, I had the below objective function $\max \sum_{u=1}^{U}\sum_{c=1}^{C}x_{u,c}d_{u,c}$ where $x_{u,c}$ are optimization variables I modelled this in CPLEX as ...
3
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0answers
71 views

How to linearize a max min objective function?

Let us suppose that I have a $\max \min$ objective function that only depends on one set of variables: $\underset{x}\max \underset{y}\min dy$ Associated with the linear set of constraints and right ...
1
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1answer
121 views

MILP constrained by the minimum number of satisfied constraints

I have an MILP where we have $$ t_k = \sum_i P_i\cdot C_{ik} : P_i\ \in \{0,1\}, C_{ik} \in I^+ $$ and our model is constrained by the number of times $t_k$ is bigger than a certain value $T_k$. $$ \...
2
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0answers
29 views

How to use NEOS without using Pyomo

I am new to modelling language and specifically NEOS server. I aim to solve MINLP using Baron, through the NEOS server. So, far I have been able to write model file, data file and command file as ...
3
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0answers
40 views

How to formulate a storage component?

Let’s say I have a drink for several customers, and I know their demand. Besides, I also have a storage tank for the drink during times when demand exceeds supply. The storage tank's size is not yet ...
2
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0answers
54 views

How to model non-zero minimum constraint?

I found following way to model a minimum constraint but in my case I need a non-zero minimum value. So in this figure, if any value of x_i is 0 then answer is 0 (assume x_i >=0) but I need non-zero ...
2
votes
1answer
63 views

Bounding box fusion with constraints

I have N bounding boxes that I want to fuse/merge given some constraints. Each bounding box has a label. Goal: The main goal is to minimize ...
0
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1answer
107 views

Assignment problem with variable tasks to be done

I'm dealing with a kind of assignment problem, in which I have a set of tasks $t$ to be executed by machines $w$, but these tasks depend on the variatns $v$ of components $m$ being selected, which is ...
0
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0answers
60 views

Excluding non-preferable solutions from a MILP

I have a model which delivers the following results (other combinations are also possible, all Xs have 50 as an upper bound): Case I $X1 = 50.0$ $X2 = 13.750$ $X3 = 50.0$ $X4 = 50.0$ Case II (obtained ...
4
votes
2answers
428 views

Modeling a constraint such that a set of binary decision variables do not equate to 1 simultaneously

I would like to seek some advice on modeling the following logical condition: I would like to ensure that a group of binary variables do not equate to 1 simultaneously, i.e., $\omega_{1}=1, \omega_{2}=...
3
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2answers
220 views

A relaxed version of job shop scheduling

I am working on a formulation for a problem that seems similar to the bin packing problem. My problem variables include items that are to be placed in bins, special events that are conditionally ...
1
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1answer
113 views

Why some decision variables don't get values in Cplex?

I use this code in the cplex and don't know why some decision variables don't get value, I attach my code below. I don't know my model is wrong or my code? I haven't error in the code but have some ...
5
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2answers
632 views

How to transform this logical if-then constraint?

Consider the binary variables $x, y, z \in \{0,1\}$. I'd like to formulate the two if-then constraints: $$ x + y \geq 2 \implies z = 0, \tag{1} $$ $$ x + y \leq 1 \implies z = 1. \tag{2} $$ Constraint ...
1
vote
1answer
108 views

Constraint programming and scheduling issues

I have a constraint problem that I need to resolve, but I did not how know to model the problem: I have 11 employees, I will name them from $a$ to $k$: $\{a,b,c,d,e,f,g,h,i,j,k\}$. I have a small ...
1
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1answer
95 views

Solving general minimum cost flow problems using only one demand and one supply node

This is a practice in using reduction. Suppose I have a solver that only allows input to a MCF that specifies only one demand and one supply node. How could I use this solver to solve general MCF ...
2
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0answers
36 views

Hardness Reduction for assigning Users to Servers

Suppose there are $x$ servers, and $y$ users. The $y$ users are to be assigned to the $x$ servers similar to classic scheduling problems. The cost of using servers is given by $c(|x|)$ which is an ...
2
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1answer
81 views

Which is better to minimize w.r.t a lower bound or an upper bound of an objective function?

Suppose there is a optimization problem that aims at minimizing an objective function $X$ but we can't develop a mathematical model for minimizing $X$. However, there are two objective functions $Y$ ...
3
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0answers
102 views

Production planning for a video game economy

I'm a software developer who likes to play a video game that has a complex economy. I realized that the type of problem I'm trying to solve mimics real life operations research problems, and I am ...
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0answers
41 views

The different behavior of the solvers to dial with MINLP problem

I have tried to solve an optimization problem (an MINLP) to minimize the number of items which need to be stored. The objective function is as follows: $$\min \quad z = \sum_{i=1}^{n} \, \color{blue} {...
5
votes
1answer
152 views

ILP Constraint to ensure exactly one constraint from a set of constraints is satisfied

Consider several Integer (0/1) ILP variables, i.e., Boolean variables, $x_i$'s. Consider an ILP constraint $x_1 + x_2 + x_3 \geq 1$ and another constraint $x_4 + x_5 + x_6 \geq 1$. I would like to ...

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