# Questions tagged [mixed-integer-programming]

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

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### 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. ...
1answer
162 views

1answer
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### 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 ...
0answers
80 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 ...
1answer
89 views

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

My optimisation problem has a constraint in the form \begin{equation} \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:\...
3answers
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 ...
1answer
45 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 ...
2answers
221 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 ...
1answer
113 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 ...
2answers
632 views

### How to transform this logical if-then constraint?

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 ...
2answers
297 views

### 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 ...
1answer
99 views

1answer
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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 ...
3answers
156 views

1answer
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### Lagrangian Relaxation The Weak Lower Bound

I am applying Lagrangian Relaxation with Subgradient Optimization Method and trying to solve a MIP model. Before testing the large-scale instances, I wanted to see how it performs on small-size ones. ...
1answer
110 views

### Free solver for MINP problems

I have a mixed-integer nonlinear programming (MINP) problem. Is there a free solver for such a problem?