# Questions tagged [mixed-integer-programming]

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

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### In a routing and scheduling problem with break consideration, How can I determine whether a node is met before a break or after it?

I'm working on a routing and scheduling problem in the home care services context. I consider a break as a dummy patient, so routing and scheduling are also implemented for the break node (with some ...
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### How to reduce an LP problem already in its standard form?

Suppose we have a feasible LP problem in its standard form. From Ax=b we can directly determine some of its variables and thus we can reduce the problem. For example, from two constraints: x+y+z=2 and ...
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### Order fulfilment with constraints on factory production capacity and truckload

I have about 300 orders, where each order consists of different products that comes from a city (in total I have about 30 cities and around 100 products from all orders). My job is to allocate the ...
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1 vote
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### Why the column generation algorithm remains stuck at the same solution?

I was trying to solve a MILP by a column generation algorithm, and I noticed that the algorithm was stuck at the same solution, I tried to diversify the pool of initial columns, but the problem I ...
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1 vote
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### Help with Mathematical Formulation for VRP with Specific Constraints

I am currently working on a Vehicle Routing Problem (VRP) with a set of specific constraints. I have a total of 19 nodes, each representing a customer location, and a depot. There are also 7 pickers ...
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### In Benders Decomposition, do you add an optimality cut together with a feasibility cut?

in the process of implementing my first BD algorithm, I am unsure how to proceed in the case that the subproblem is unbounded. Obviously, it means you get an extreme ray that you can add to the RMP as ...
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1 vote
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### Non-Linear objective function due to piecewise component

I have the following objective function: $\sum_{n}(1-prob_{n})(1+x_n)$ Where $x$ is my decision variable. $prob_{n}$ is a piecewise function that can look like: $prob_{n} =$ \begin{cases} 0.5, ...
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1 vote
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### Why did the CONSENFOLP callback assertion fail when the problem has a primal feasible solution?

I am working on the problem that I am willing to use SCIP's conshdlr callback to check how the constraints might be added to the model. I am using the following ...
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1 vote
118 views

### Constraints to avoid disjointed solutions in a MIP

Given an directed graph $G= (N,E)$, where $N$ is the set of nodes and $E$ is the set of all edges, each associated with a direction. $G$ is a connected graph but not necessarily a complete graph. A ...
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1 vote
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### MILP - Find out model size

Ucame across a paper today and this paper mentioned that the model size is $O(\mid I\mid\cdot\mid T \mid)$. I am also sitting on a MILP problem right now. Does my model size also amount to this size ...
113 views

### Team Orienteering Problem with Time Windows infeasible using CP-SAT solver in Google OR-Tool

I am developing a TOPTW where there are a set of N nodes. Each node i is associated with a visit time, which is also the score Si. The starting point and the end point of each tour is fixed, which is ...
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1 vote
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### MIP constraints with chronological ordering

I am using a MIP formulation to decide which dates and locations (i.e. stops) should be chosen for a route that maximizes the total revenue over all chosen stops. My decision variable $X$ is the ...
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### ILP constraint conditional on a value of a variable

If $X_{ijklm}$ are Boolean Variables, where $i,j,k,l,m$ range from $1$ to $n$, then write an ILP constraint to ensure that for each value of $k$, either all the $jth$ variables are set to $0$ or all ...
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1 vote
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### Setting constant values in constraints depending on actual values of variables

We have a set of constraints in an ILP of the following form : $\gamma (X_{11} + X_{12} + X_{13}) \leq C_1$ where $X_{ij} \in \{0,1\}$ and the value of $\gamma$ is going to depend on the actual value ...
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### Is Benders decomposition and the L-shaped method the same algorithm?

I've been studying the Benders decomposition method to solve stochastic integer problems. I've also stumbled across papers using a so called L-shaped-algorithm which also divides into master problem ...
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### is it possible to improve the solution process of an MILP?

I am trying to optimize a charging station for EVs in matlab with intlinprog, which is connected to a PV-Modul, to an system storage systeme and to the network grid. I am using different Storage ...
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### Runtime of LP vs MILP

I was wondering how the run time of an LP and an MILP model compare to each other. I found out that MIPs are NP-hard, where as LPs aren't, but it don't really understand what it means. Does that mean ...
377 views

### Scheduling to minimize total "wait to start" time

I have a scheduling problem I am trying to work through. As I was outlining the problem, I realized it is probably of a known problem type, but I am unsure of what keywords to search for or what ...
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1 vote
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### Modeling of a special form of the precedence constraint

There exists a scheduling problem in which some tasks should be processed on some resources. Additionally, each task needs to be assigned to a specific position on each resource. Let the decision ...
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### Cplex seems to terminate early as optimal when starting solution polishing

I occasionally see this slightly strange thing happen with cplex where it jumps from a MIP gap of, say 5%, to then reporting the status as optimal. This happens when it starts solution polishing after ...
1 vote
77 views

### Finding a maximum violated infeasible subset

Given a binary optimization problem of the following form: \begin{align} min\; &cx&\\ &Dx \leq e&\\ &\sum_{i\in S} x_i \leq r(S) &\forall S\in \mathbb{S}\\ &x_i binary &...
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