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Questions tagged [mixed-integer-programming]

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

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Better formulation of bilinear terms

I am working on an optimization problem where I need to formulate a constraint that represents the total sales value under specific conditions. The challenge lies in creating an expression that ...
Lemma's user avatar
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Cost function value of relaxed ILP after rounding is less than or equal to the optimal one

I have a minimization problem for which I am having some misunderstandings and confusions with regard to some results I am getting for an ILP and its LP relaxation. In the ILP I have two decision ...
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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 ...
Apurba Saha's user avatar
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Extracting a sequence as a decision variable from a matrix (PuLP)

I am solving a sequencing problem x[i][j], i.e. a binary matrix indicating that product i is followed by ...
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Workforce scheduling optimization using ML model output

I am working on a workforce scheduling problem where we want to come up with an intelligent way to identify a set of shift candidates that is just enough to cover all labor demand but also flexible ...
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Using docplex with mpmath

In Python 3.10, is it possible to use docplex along with mpmath (https://mpmath.org/), e.g., to compute expressions in constraints and objectives with arbitrary precision?
Stencil's user avatar
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Travelling Salesman problem and Vehicle routing problems

Can someone explain to me why are we doing the $x_{ij}=1$ and and the constraint $U_j \geq u_i+1-n(1-x_{ij})$ Also do you have any books or sources in mind from where I could learn in more detail from ...
uni_lad's user avatar
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Formulation for data insight

There is an interesting data insight question that I want to solve using mathematical programming. I aim to find the combination of features that has the highest impact on the target indicators. We ...
Ying's user avatar
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Production scheduling

I'm formulating a scheduling problem with the following decision variables: $$X_t \space \text{is power sold to market in time period t} \\ Y_t \space \text{is power used for production in time period ...
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Distributed coloring of nodes of sensor ntwork

I have the same graph coloring problem as in Coloring of nodes of a sensor network @RobPratt and @prubin have proposed some very good solutions. This time I am or interested in distributed coloring ...
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In routing problems, when is it ever necessary to include both 1) subtour elimination constraints, AND 2) elementary paths constraint?

In many routing problems, it is fairly common to include a constraint that ensures all vehicles follow an elementary path, meaning that no vertices are repeated. However, when an elementary path is ...
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MILP: Linearization / approximation of mean and variance

My question- What is the standard practice to linearize / approximate computations of mean and variance using MILP solvers? Edit: referencing comments, an idea was proposed to set an upper limit and ...
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Joint, two-sided chance constraint of MILP reformulation of a logical constrain

I reformulated the logical constraint $x = \min\{y,z\}$ as this MILP problem $$ \begin{array}{ll} x &\leq y \\ x &\leq z \\ x &\geq y-M(1-w) \\ x &\geq z-Mw \end{array} $$ in which $...
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Optimize revenue function with log part

I am working on an optimization problem where I aim to maximize revenue. My current model has the following objective function: $$ Sales(P_i) * log(P_i - const_i))$$ where $P_i$ represents the price ...
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is it possible to improve the solution process of an MILP?

I am trying to optimize a charging station for EVs in matlab with intlinprog, which is connected to a PV-Modul, to an system storage systeme and to the network grid. I am using different Storage ...
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How to linearize such a constraint?

My original content was like this: Assuming that server $k$ can only allocate corresponding computing functions to MU $i$ after receiving their tasks. Let $$ y_{i,k,t} = \begin{cases} 1 & \text{if ...
Yunqi Li's user avatar
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Resource selection problem with non-linear objective function

I have an optimisation problem to solve but I can't model it correctly. Any insight is welcome :) It has been a few years since my optimisation classes in university, and while I have forgotten a lot ...
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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 ...
Abde's user avatar
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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 ...
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Creating a simple class in python for doing simulation of MDP

I am currently learning Python and doing object-oriented programming. I am trying to create a simulation for MDP. My problem statement is: "I have four stages of process. Each stage has two ...
Margi Shah's user avatar
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CPLEX returns no solution with deterministic time limit

I'm working with CPLEX using the python API (Docplex). If I set the time limit in seconds with model.set_time_limit(60) the solver returns the best integer feasible ...
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Products distribution planning model

I have a problem of planning the distribution of products for a month. I have different unique products. A Mandate is provided for each product, and the Mandated quantity for each product is to be ...
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Lower bound very bad. How to improve?

I have the following MILP: \begin{alignat}{2} \nonumber \mbox{minimize } \quad & \phi = \sum_{i=1}^{m-1} \sum_{f=1}^{F} \sum_{\underset{\bar{f} \neq f}{\bar{f}=1}}^F \sum_{h \in H} \left( D_{f \...
Angelo Aliano Filho's user avatar
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Check VRP instance is feasibility

Beforehand, this is a very long thread, in case you want to know in advance, to see if this thread's interests match with yours, this thread concerns fast ways of determining whether a VRP instance is ...
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Problems with a MILP

I need some advice, any hints will be appreciated. I have a MILP and I am using Gurobi to solve it. I have a feasible integer solution. When I use mipstart, after ...
Angelo Aliano Filho's user avatar
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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 ...
Jack's user avatar
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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 ...
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