# Questions tagged [mixed-integer-programming]

For questions about mathematical optimization problems involving both continuous and binary or general integer variables.

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### How to mathematically formulate the optimization problem?

I have a system with $S$ service points. There are also $U$ users in the system. The service points as well as users need to be grouped in $G$ non overlapped groups. Therefore, one user/service point ...
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### How to treat a system of bilinear constraints

A model contains constraints of the following form $R(k) \leq X(k) G(k)$ where $X(k)$ binary and $G(k)$, $R(k)$ non-negative variables. The index $k$ runs from $1$ to $50$. I linearise the equations ...
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### 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 ...
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### Constraints that set values to binary variables depending on other binaries

I am trying to write a mathematical problem that involves some conditions based on binary variables. More specifically, I have a set of three binary variables $d_1$, $d_2$, $d_3$ and depending on ...
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### Modelling precedence relations

I have two tasks $i$ and $k$ with durations $d_i$ and $d_k$, where $d_i$ and $d_k$ are nonnegative variables. I would like to model that $i$ may precede $k$ or $k$ may precede $i$ and that they may ...
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### Assignment problem with batching costs

I am studying an assignment problem with batching costs, and I would like to know if there is a standard name or algorithm for this problem. I know this problem can be formulated as mixed-integer ...
121 views

### Non-linear optimization local or global solution

In an NLP, I have a constraint that I would like to formulate in a convex manner preferably without introducing binary variables and/or big M formulations if possible. The actual problem is non-convex ...
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### Strange Result from GurobiPy

I am trying to understand why GurobiPy gives me a strange result for a simple linear programming model coded as below? Why is the optimality gap is 0%? Please let me know if you spot any errors in the ...
157 views

### Index of element in MILP vector decision variable that equals 1

Consider a decision variable in a MILP constrained: $$\sum_i p_i = 1$$ $$p_i\ \in \{0, 1\}$$ Obviously one element in $p$ is 1 and all others are 0. How can I set a decision variable to the index i of ...
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### Linearize x different of y in ILP

I am surprised I couldn't find an already written answer for my question in the internet. I want to linearize $x$ different of $y$ for two nonegative integer decision variables. I am not considering ...
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### Mixed Integer Programming - How to model the dependency of two variables in an objective function

I have two variables $a$ and $b$, in which $a$ is the amount of goods and $b$ is the amount of boxes of the given sizes. So $b$ (box size + number) is dependent on a (goods quantity). If $a$ is ...
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### Mixed Integer Programming - Model Formulation for A Resource Allocation Problem

There are a number of orders, which needs to be shipped. For each order, there may be 1 to 3 route options. The problem here is to find out the best allocation (combination) of orders among these ...
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### Cutting Stock Problem : Mixed Integer Programming

I am asked to solve the following problem: The problem: You were asked to repair a farm house with sheets of plywood. You were given thirty sheets of plywood. (each size = 10ft x 10ft) The house ...
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### Coding the OR problem with cplex

I am new to using OPL. I wrote a CPLEX code for the vaccine distribution from a paper, it doesn't get an error, but it hasn't given the answer. I don't know its problem; please help me; I attached the ...
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### How can I find the optimal assignments for this MILP problem heuristically?

I have an assignment problem as follows \$ \begin{array}{*{35}{l}} \underset{d_{u,c}}{\max}\hspace{1mm}\hspace{1mm}\sum_{u=1}^{U}\sum_{c=1}^{C}d_{u,c}\omega_{u,c}\\ \text{}\text{...