# 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 can I direct the behaviour of a MILP Solver

I have a model involving constraints of the form $$d(i) = a \cdot W(i) + b \cdot B(i)$$ where $W(i)$ is binary and $d(i), B(i)$ are positive reals. The objective function is $\max\sum B(i)$. While ...
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### How can I model this binary logic?

I am looking for a constraint to express the following: IF W1 = 0 AND W2 = 0 THEN Y = 0 IF W1 = 0 AND W2 = 1 THEN Y = 1 IF W1 = 1 AND W2 = 0 THEN Y = 0 IF W1 = 1 AND W2 = 1 THEN Y <= 1 ...
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### How can this be expressed as a MILP constraint?

I am looking for a constraint to express the following: IF W1 = 0 AND W2 = 0 THEN Y = 1 IF W1 = 0 AND W2 = 1 THEN Y = 1 IF W1 = 1 AND W2 = 0 THEN Y = 0 IF W1 = 1 AND W2 = 1 THEN Y <= 1 ...
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### Optimising the current model

After developing the MIP model I noticed that solver is taking a lot of time to reach the solution. So, how should I approach to optimize the current model? Are there any visualization tools or any ...
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### Modelling an if-then-else logic in MIP

I was hoping to get some help in modelling the following logic as an MIP Constraint If $X_{ij}=1$ and $\text{SDV}_{ikj}=1$ for a particular index $i$, then $\text{SOC}^L_i=100$, else $\text{SOC}^L_i$...
512 views

### Check which constraints are violated (Concert - Cplex Studio 12.10 - C++)

Currently, I am working on the implementation of a formulation for an optimization problem, at the moment I already have the MIP formulation implemented in C++ using Cplex studio 12.10 with the ...
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### Open Source MILP software for Python with user-friendly API to define the optimization problem

Following the accepted answer to Assignment problem where assignments must be done sequentially I would like to write a Python script which can solve the problem defined there. It's a Mixed Integer ...
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### How is Big M calculated?

Because of excessive pollution on the Momiss River, the state of Momiss is going to build pollution control stations. Three sites (1, 2, and 3) are under consideration. Momiss is interested in ...
317 views

### Cplex is stuck after root node relaxation solution

I am solving an MIP through Benders decomposition (coded both generic and legacy callback versions), by employing Java with Cplex 12.9. For some of the instances, Cplex is stuck for two hours (time ...