# Questions tagged [mixed-integer-programming]

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

635 questions
Filter by
Sorted by
Tagged with
36 views

### Determining the number of nodes within a cycle for an MILP problem

I have a MILP problem that requires knowing the number of nodes within a cycle (there will be multiple depending on inputs). I believe this will involve tracing nodes/values within cycles using the ...
72 views

### Docplex : How can I get the objective value of the relaxation of an MILP?

I want to solve a relaxed version of a MILP; I am using docplex.mp. I found LinearRelaxer in docplex.mp.relax_linear , however I keep getting this error message: model model1: found 1 un-relaxable ...
169 views

### Additional resources for this type of problem formulation

I'm working on a problem with the following formulation: \begin{align} \min&\quad\sum_{i \in N} \sum_{j \in J} V_{ij}x_{ij} \\ \text{s.t.}&\quad \sum_j x_{ij} = 1 \quad \forall i \in N\\ &...
76 views

### Transfer an integer model to binary

I have a minimization problem with integer variables and would like to transform it to binary variables. The problem is, that my objective is to minimize the overall waiting time, which consists of ...
237 views

### Practical, Short example of Mixed Integer Conic Program

Mixed Integer Conic Programs is a family of Mixed Integer Programs which are convex in all non integer variables. I am giving presentation on Mixed Integer technology. A large part of the presentation ...
1 vote
82 views

### Converting quadratic constrains to linear constraint [closed]

I try to convert a quadratic constraint to a linear one: $$w_j = \sum w_\text{j,i} \\ w_\text{j,i} = \frac{w_j}{D} \times u \\ w_j,D,u \in \mathbb{N} \\$$ The values for $w_j$ and $D$ are constant ...
79 views

### gurobi bigM constraint vs. epsilon

I am new to mathematical programming and I am trying to implement case specific constrains in Gurobi with Python. I am wondering about how I can implement my constraints in the fastest or most common ...
107 views

### Multiprocessor Scheduling Problem: How to modify some constraints after variable changing?

I am thinking about classic problems concerning partitions as the Multiprocessor Scheduling Problem (or Bin Packing or Number Partitioning): Given $n$ tasks, with times $\{t_i\}_{i\in I_n}$, and $m$ ...
206 views

### Approximate Speed-Up With Increasing Cores?

First off: I totally understand if "it depends" is the only feasible solution. I'm running a large (to me) MIP using Gurobi in R on my local machine. (~2M binary decision variables, ~15K ...
1 vote
87 views

### Relaxing a relation between variables if one of them reaches its maximal value

I am trying to formulate an optimization problem that can be described as a set of tanks $T$ where each tank $t$ has a maximum capacity of $\overline{r}_{t}$. I want to fill all tanks as much as ...
53 views

159 views

### Solving a MIP by Relaxation

I have tried to understand the method of relaxing an integer program. I am in the process of implementing and solving a MIP for the FJSSP. For this I use the python-MIP package to solve it. From my ...
62 views

### WIP Inventory Level Constraint?

I'm modeling a continuous-time, two-stage manufacturing process with an MIP. There are about 100 finished-goods SKUs, and each of those belongs to about 25 different semi-finished categories in a ...
389 views

I have tried to convert the following constraint into SOCP form but can't figure it out. My issue is that whenever I create the norm, the other side has to be square rooted which invalidates the SOCP ...
124 views

### crew scheduling problem with shift priority hard constraints

I am working on a crew scheduling problem formulated as a MIP binary optimization where each employee is represented by a binary variable $X_{ids}$ s.t. $i \in I$ is $i$th employee, $d \in D$ is the ...
260 views

84 views

### How to bundle pairs of trips?

I have a database of real-time optional trip demands. Each with a load that needs to be delivered from a departure point to a destination: ...
43 views

### MIP gives out zero as best solution when trying to optimize MIP model for flexible job-hop

I have implemented an existing MIP Model into python with the python-mip solver and somehow I only get '0' as a solution to my minimization problem. What could be the problem? I am fairly new to LP ...
57 views

### Determining constraint relevance in crew scheduling problem

I am working on a crew scheduling problem formulated as a MIP binary optimization where each employee is represented by a binary variable $X_{ids}$ s.t. $i \in I$ is $i$th employee, $d \in D$ is the ...
1 vote
113 views

### How to get negative shadow price for minimization problem in Gurobi?

I am currently working on a scheduling problem (MIP) to minimize cost, and my idea is to first generate a set of discrete initial solutions, and build an LP model with the discrete initial solution to ...
### Robust way to implement $(x=0) \Rightarrow (y=0)$, with $x$ nonnegative and $y$ binary
I am formulating a MILP in which there is a continuous variable x and a binary variable $y$. In the program formulation there are the following constraints: $Ay\leq x \leq By$ (with $0\leq A\leq B$). ...