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Questions tagged [mixed-integer-programming]

A mixed-integer programming (MIP) problem is a linear program where some of the decision variables are constrained to take integer values.

In mixed-integer programming one seeks to find the best (optimal) solution to a linear programming problem. In constrast to ordinary linear programming, however, some of the variables are allowed to take discrete values. Mixed-integer programming has many applications in practice and is often used to model "yes"/"no"-decisions via binary variables. Even though discrete decision variables allow a user to define better and often more realistic models, their introduction to a linear programming problem comes with a high computational cost.

434 questions
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Understanding "Blessing of Binary"

The theorem I am stating is Theorem 6.2 (Blessing of Binary) of the dissertation THE ROLE OF EXTREME POINTS FOR CONVEX HULL OPERATIONS, which was cited from Stochastic Dual Dynamic Integer Programming albeit with a different formalism. Let $c\in…
Sudix
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in linear programming how to relate an integer variable with a binary one

mixed integer linear programming problem of assigning operations to machines and each operation require number of operators. there is a limited number of available resource (operators). during the solution $S_i$ is determined. my question is: I…
Enas Esh
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Mutual exclusivity variables in mixed integer programming problems

I am working on a employee scheduling problems (assigning shifts to temporary workers) by modeling it as a MIP. There is a one shift per day constraint for the employees that restricts more than one shift per day. While doing that we have overnight…
SDC
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How to write if statement for 3 dimensional problem linear programming

I have a problem regarding formulating the following with math notation. My goal is that if shop i’s arrival time is lower than all the other shop’s arrival times, then shop i must be allocated to the palletspace with the lowest distance (to obtain…
Alexander Strarup
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Indicator function to an Integer linear program

I am asking a follow-up question of this problem. For simplicity, let's say we have a constraint, $I(-a_i x\leq b) \geq m$. We reformulate it as $$y_i \geq m,\,-a_i x \le b + A(1-y_i) \text{ such that } y_i \in \{0,1\}.$$ As I understood, if…
Cherryblossoms
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why the code assigns multiple jobs on same position on machines

scheduling n jobs on m machines, each job has a different processing time on each machine. all schedule has n positions indexed by l as l =0,1,...,n as position 0 for dummy job Used this mathematical model to present the problem min Cmax subject to:…
Enas Esh
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constraints formulation

This question is an extension of this. Again, I have n total fruit plantations and s number of just apple plantations. I want to place s and (n-s) plantations on an m by m grid of field. Each s apple plantation should be a minimum distance, d away…
user818406
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linear programming formulation

I want to formulate equations for this problem. I have previously looked at many examples and I am new to this. Suppose I have n total fruit plantations and s number of just apple plantations. I want to place s and (n-s) plantations on an m by m…
user818406
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Enforce constraints in nth visited node

I have a problem similar to the tsp problem where : $x_{i,j} \in \left\{0,1\right\}$, is 1 if I visit node $j$ immediately after node $i$. Now suppose that I need to enforce constraints for the n-th visited node, how would I do that in an efficient…
nikferrari
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integer programming linearization

I have two variables. $g$ is a binary variable and $s$ is a continuous variable. Goal is to linearize this $gs \geq0$ a.k.a if $s \geq 0, g = 1\:\: \text{or}\:\: s\leq0, g = 0$. How can I linearize this ?
Jinghan Yang
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Coping with $y = \text{max}\{b-x,0\}$ in constraint for MILP

Problem Description: I have a mixed integer linear optimization problem (MILP) with objective function $$\min_{x_{jt}} \sum_\omega \sum_j \sum_t y_{jt}(\omega)$$ I know $L_{jt}\le x_{jt}\le U_{jt}$ with $L_{jt}\ge 0$ and $L_{jt}\le U_{jt}$. We…
SecretAgentMan
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Finding all solutions for a system of equations with constraint on the sum of absolute values

I am looking for a fast algorithm to find all integer solutions for the following system of linear equations ($c_1,\ldots,c_n \in \mathbb{Z}$ and $r\in…
Sepehr
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