# 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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### My Professor couldn't complete the model for this optimization problem. how do i model this problem?

(Edit: there was a slight translation error, to be clear, we tried this since the start with Binary variables (IP), even then we couldn't crack it) I'm an undergraduate in Industrial Engineering and ...
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### Avoid double counting in objective function for a maintenance scheduling problem

I have a problem to do with machine maintenance scheduling which I have formulated as a MIP where I have a binary variable $x_{ijt}$ which is 1 if the maintenance job j is scheduled on the same ...
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### PULP: Optimization Assignment of Bicycle production per month

Q1. If bicycles of types A and H are produced, then bicycles of type C can be produced with 20% shorter working hours, while selling profit of bicycles type H can be 20% higher. Q2: If bicycles of ...
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### Inconsistencies in modeling a binary variable that indicates a switch

this is a follow-up question to this post here and to @RobPratt's answer. I have implemented the whole thing, and now it happened that on day 1 the machine did not run and was only used for the first ...
517 views

### Model a > 0 implies b = 1, where a is unbounded above

I want to model if a > 0 then b = 1, where a is an unbounded above continuous variable and ...
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### Linear condition between two continuous variables

There are two real variables $x$ and $y$. The conditions are such that: if $y\le 0$, then $x=0$ if $y>0$, then $x=y$ How to write linear equations or inequalities to satisfy both the conditions?
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### Formulation and modeling of a logistics problem: Combination of bin packing and cutting stock problem?

I'm a Data Scientist with a strong mathematical background but don't know much apart from textbook material about Operations Research. I'm dealing with a logistics problem which I don't know how to ...
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### Modeling Approach to Adjust linear Elasticity Effect in Pricing Optimization

I am working on a pricing optimization model for a product where the price depends on the competition as well as our costs. The current formulation of the model is: ...
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### How to model this constraint in a better way?

I have a resource allocation problem. There are $M$ users and $N$ resources (machines). One user can be assigned to multiple resources/machines. But maximum $B$ machines can be activated at a time for ...
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### Reformulate constraints

I have the following constraints and am wondering whether I can formulate the whole thing more narrowly and with fewer constraints. $x_{itk}$ is binary and $u_{it}, v_{itk}\in [0,1]$. $M$ is a Big-M ...
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### How to constrain variables to fit a normal distribution

Given a time series $s_t$, I would like to define for each $t$ a perturbation $e_t$ such that the set of all $e_t$ "fits" (within some range) a normal distribution with mean $\mu=0$ and a ...
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### Add second "constraint" to model a binary variable

in my model I have the binary variable $f_{ij}$ which pushes a time-dependent $j$ integer variable $D_{ij}$ to zero if $f_{ij}$ takes the value 1 and keeps the integer number if $f_{ij}$ equals 0. Yes,...
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### Is it possible to transform MIQP into MILP without introducing new variable?

I have a QP optimization problem in the form $$\min {\bf x}^T{\bf Qx}-{\bf c}^T{\bf x}$$ here $\bf Q$ is a symmetric matrix. $\bf x$ is the optimization variable, and it is binary. Is there a way to ...
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### R package cannot find PYOMO. How do I point to the correct location of where it's located?

As a quick note this is a re-post from the main StackOverflow. I am trying to use the PYOMO linear programming solver from within an R script. When I type ...
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### How to maximize the number of variables with value at least 0?

Given a matrix $A$ and a vector $b$, I would like to find a vector $x$ satisfying the set of linear constraints $A x \leq b$, and subject to that, contains as many variables as possible with ...
1 vote
87 views

### volume-weighted mean equality constraints

I have the following optimization objective function for a dynamic pricing problem: \begin{align*} sum\_profit = \sum_{i \in sales\_point} \Bigg( constant[i] + {elasticity[i]} \cdot (movement[i] + ...
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### How to model this constraint for a QP problem?

I have a system with 100 users. There are 6 resources. At any point of time, only 2 resources are made available and those resources can be shared among the users. Some users may not get any resource, ...
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### How to initialize a parameter (belonging to the first stage model) in a two stage model, taking its value from second stage model?

I am working on a two stage approach in order to reduce the complexity of a scheduling model which is an NP-hard problem. I have to implement a while loop in order to repeat solving the models in case ...
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### proper notation for union of dictionary

Traditionally, our notation has separated out a set and values associated with said set. We'll say something like the state is a tuple of $(V, f)$, where $V$ is a set of control values and $f$ is a ...
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### Converting a piecewise function to linear equations

I am trying to build a MILP model. In this model, I have a dependent variable (alpha) that its value depends on the value of some other variables (or different combination of some other variables). In ...
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### How to Group IDs Based on the Difference of Each ID’s Min and Max Value?

I have a dataset that contains IDs along with their corresponding minimum and maximum values. Here’s a sample of the data: ...
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1 vote
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### Incorporate fixed effects in pricing decisions with linear models

I have the following model the predict the log of volume: fixed_effect + day_of_week_effect + elasticity * (Price - competitor_price). I want to formulate an optimization problem that maximize my ...
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### Modelling set of binaries as SOS1

H.P. Williams states in his book "Model Building in Mathematical Programming: "An SOS1 is a set of variables (continuous or integer) within which exactly one variable must be non-zero." ...
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### Removing min operator from max objective

I am reading a paper where the authors made the following statement on page 16: I wonder why dropping the 'min' operator inside a 'max' objective function is a valid operation here. Any explanation ...
1 vote
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### Problems with Big-M Constraint

I have the following constraints for my roster optimisation problem: \begin{align} &(1-r_{i,t})\le \sum_{j=t-\chi}^{t-1}sc_{i,j}\quad &\forall i\in I, t\in \{1+\chi,\ldots,T\} \end{align} \...
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### Generalize working days constraints

I have the following constraints. The first ensures that in my shift plan there are always exactly two days off between blocks of working days and only then does the next block begin. It reads as ...
1 vote
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### How to model membership to a set using MILP?

Consider the following problem. I have two regions $X1=[a,b]$ and $X2=[b,c]$. Notice that they are disjoint except for point $b$. I have a continuous variable $x$ and two binary variables, $y_1,y_2$ ...
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### Dealing with a problem that contains a specific structure with a standard MILP solver

Suppose we have a specific formulation in which contains a special structure. For example, the formulation has a block diagonal format with some linking constraints. As far as I know, this format ...
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### Creating a decision variable that is the sum of other variables in PuLP

I'm trying to represent the following problem with PuLP: A car factory needs to maximize profit with an X amount of car models. Each car model has an individual profit and a manufacturing limit, and ...
1 vote
219 views

### Formulating a constraint to select the minimum value of an index

To provide a clear description of my problem, let me outline the scenario. I have a binary variable $\phi_{k,c}$ where $k$ is an index belonging to the set $\{1, 2, 3, ..., 9\}$. As an example, for a ...
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### Which of these formulations has the tightest linear relaxation ? (Part 2)

This is a follow up question of this question, in which it was asked to compare the "tightness" of two models: I have a sequence of binary variables $x_i$ and want to enforce consecutive $1$...
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I have a sequence of binary variables $x_i$ and want to enforce consecutive $1$'s of length at least $3$. I have $2$ formulations: Model $1$ (from here): \begin{align} x_i \le x_{i-1}+x_{i+1} \tag{1}\...
I have an optimization problem: \begin{align*} \text{ minimize } \sum_{i=1}^n H(x_i) \\ \text{ subject to } Ax \geq b, x\geq 0, x\in \mathbb{Z}^n \end{align*} where $H(n)$ is the $n$-th Harmonic ...