# Questions tagged [mixed-integer-programming]

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

390 questions
Filter by
Sorted by
Tagged with
66 views

### Is it known that any boolean function is equivalent, in some sense, to a system of linear inequalities?

I cannot believe that below is a "fresh result" in mathematical programming as my rather intensive literature search did not bring references to any similar assertions. I will appreciate any ...
375 views

### How to visit a subset of network nodes in a single trip?

I have a connected network where I want to visit a set of destinations which may require visiting intermediate nodes as well because there may be no direct edge between source and destination nodes. I ...
73 views

### MILP modelling on minimal disturbance of right-hand-side to make a linear system infeasible

I try to model the following problem: given $z\in\{0,1\}^m$ and a linear system $Ax\le b(z), x\in\Bbb R^n, A\in\Bbb R^{d\times n}, b(z)\in\Bbb R^{d}$, where $b(z)$ means that some entries of $b$ are ...
225 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 ...
51 views

### Electricity market clearing price using fixed-MIP formulation?

Dual information of electricity markets clearing problem is required to calculate the marginal clearing price. As most electricity market problems are based on MIP (and dual information of MIP is not ...
86 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 &&\...
98 views

252 views

### How to model y = floor(x)?

I went through the answers to this question: Modeling floor function exactly, but I still do not get how to model y = floor(x). Is that question answered and I just ...
149 views

### Oscillations with (online) mixed-integer optimization problem

I have the following mixed-integer optimization problem: \begin{aligned} \max_{x,y} \quad & \sum_i x_i - \|wx\|_2 \\ \text{s.t.} \quad & \sum_i x_i \leq A \\ \quad & x \leq x_{\max} y \\ ...
45 views

### What will be an efficient heuristic approach for this optimization problem [closed]

I am looking for a heuristic approach to this optimization problem. How to mathematically formulate the optimization problem? RobPratt suggested an mathematical formulation for this problem which is ...
189 views

### Mixed-integer optimization with bilinear constraint

So I have an optimization problem of the following form: \begin{aligned} \max_{x,y} \quad & \sum_i x_i \\ \text{s.t.} \quad & \sum_i x_iy_i \leq a \\ \quad & x_{\min} \leq x \leq x_{\max} ...
120 views

### Linearizing a Max Function in the constraint - not working

I have a minimization function which is in its simplest form looks like below. I am including the index of the variables. ...
156 views

79 views

### How to linearise this nonlinear constraint?

I have a constraint in the form $\sum_{n=1}^{N}x_{m,n}\omega_{m,n}\ge (t_u-1)\beta_u, \forall u, u=1,2,\cdots, U$ where $x_{m,n}$ is binary variable $t_u$ and $\beta_u$ are continuous optimization ...
74 views

### MILP formulation for “if (a>=b) then c=1, 0 otherwise”

I need to build a MILP (Mixed integer linear programming) constraint form this if-else statement. In my formulation a and b are two continuous variables and c is boolean. if (a >= b) then c = 1, 0 ...
88 views

### How can I linearise this nonlinear proportional relation constraint?

My optimisation problem has a constraint in the form \begin{array}{*{35}{l}} \text{}\hspace{16.5mm}\text{ C4:} \hspace{2mm}\sum_{u=1}^U d_{u,1}L_{u}:\sum_{u=1}^U d_{u,2}L_{u}:\cdots:\...
1k views

### How does a solver generally know whether a solution is optimal?

I was wondering how does the solver for a MILP determine whether a solution is optimal. I am having a hard time to believe that the solver actually tries all solutions, since in some cases I have over ...
43 views

### How can we understand which solution approach is suitable for our mathematical problem?

I'm looking for a solution approach for my MIP model, but I couldn't find any specific books about this issue whose solution approach is suitable for my model. There are a lot of exact, heuristic or ...
148 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 ...
109 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 ...
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 ...