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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1answer
100 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
104 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 ...
2
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1answer
91 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 ...
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 ...
5
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1answer
150 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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2answers
111 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
62 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 ...
4
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2answers
386 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 ...
5
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1answer
90 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 &&\...
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2answers
92 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, ...
4
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1answer
204 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 ...
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0answers
43 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....
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 ...
4
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1answer
189 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
885 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 ...
3
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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 ...
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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} \; ...
2
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2answers
104 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, \\ ...
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1answer
247 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 ...
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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. ...
1
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1answer
45 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. ...
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
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2answers
299 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 ...
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 ...
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
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1answer
62 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 ...
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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
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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
204 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
vote
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
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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
votes
1answer
80 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 $Y$ ...
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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 ...
2
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0answers
22 views

Are there standard symbols to describe discrete event simulations (DES)

I just wonder, whether there is a good reference for the symbols used in a flow chart to describe a DES process. I am looking for something like Kendall notation, but with a reference to the symbols. ...
2
votes
1answer
49 views

Logical equivalencies to modeling an indicator decision variable in transportation problem

I am formulating a model that seeks to minimize the cost of shipping goods from factories to warehouses, where the cost of shipping is independent of the type or amount of goods being shipped (except ...
3
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0answers
51 views

Where I can study some job shop scheduling by course (video )?

I am seeking the help to know where I can study the job shop scheduling Heuristics or using solver by some course/video as I see some of books and papers hard to understand . It is hoped that the ...
6
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1answer
130 views

Formulating two non-negative variables without binary and/or big-M

There are two non-negative integer variables $q$ and $p$, where only one of them can take a positive value. To impose this relation, I write: \begin{align} q &\leq M(1 - y) \tag1 \\ p &\leq M(...
2
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1answer
149 views

Working with large models

I am working with a variant of TSP, number of nodes that I need to test are in between 2500 to 3000 nodes, I am using docplex for modelling, I have a 8 gb Ram but it gets filled with only 400 nodes. ...
3
votes
2answers
185 views

Modeling in integer programming vs modeling in constraint programming

I have some experience with linear and integer programming modeling (I read Model Building In Mathematical Programming by Williams). Now I am trying to learn how to model with constraint programming. ...
2
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0answers
61 views

Dynamic Programming problem of affecting equipment with budget constraint

I have a problem that I must formulate as a DP problem and solve. A hospital is split up into 4 sections, each section has 1 or 2 or 3 backup generators. We have to maximize the likelihood that no ...

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