# 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 to say to Gurobi solver with Python API to start from a given solution?

I have a binary linear program, where all my variables are binary. So, I have implemented the problem on python with Gurobi solver. I have implemented also a heuristic to find a near-optimal solution. ...
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### Has the expressibility of 'non-integrality testing' as extension to MILP been studied before?

It turns out that extending MILP with any of the constraints $y=\lfloor x\rfloor$, $y=\lceil x\rceil$, $0 < x$, or $x\notin \mathbb{Z}$ is 'equally hard'. (see my answer here, and below) ...
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### If variable falls below a certain value, include difference to set value in objective

I think its easiest to describe my goal first and continue with my implementation and the resulting problems! My goal: Using Pyomo as interface and Gurobi as solver, if a variable $x_{i,t}$ falls ...
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### Network design problem with rounded capacity constraints

I have a network design problem with complicating capacity constraints which I'm trying to model through a Mixed Integer Programming formulation. The problem is defined on a directed, incomplete graph ...
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### Why does the getTime() function from cplex concert returns wrong value?

I am running a MILP formulation (implemented in C++) with the Cplex Concert Technology 12.10, and I am trying to get the total elapsed time. So till the moment, I have tried three approaches: Be ...
47 views

### Capacitated Facility Location problem with a dynamic set up cost

I am trying to solve a Capacitated Facility Location Problem (CFLP) with a dynamic setup cost in R. The problem statement is this: I have the transport cost The ...
251 views

### Is it possible to identify all possible Irreducible Infeasible Sets (IIS) for an infeasible Integer Linear Programming problem? (ILP)?

For an Integer Linear Programming problem (ILP), an irreducible infeasible set (IIS) is an infeasible subset of constraints, variable bounds, and integer restrictions that becomes feasible if any ...
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### Rule of thumb for introducing known constraints in Mixed Integer problem when they grow the formula

When encoding a problem into a Mixed Integer formula one faces a trade-off between embedding domain knowledge which might require new helper variables to express the constraints thereby growing the ...
29 views

### How can I 2 terms in the objective function with sigma over each term in pywraplp library in OR tools

I am having 2 terms in my objective function based on the below objective function. Please guide me on how can I formalize it in OR tools? I tried the below way but it only considers the second term ...
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### Inventory positioning Model in GAMS

I have plotted a problem in GAMS expecting to get the route and inventory level I should put in DC but it's not shown the result. ...
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### How to linearize the product of two integer variables?

Given two integer variables $L_x \leq x \leq U_x$ and $L_y \leq y \leq U_y$, how can we linearize the product $x \cdot y$?
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### Is there any open source solver for MILP that can output the top N best results instead of the global best?

I am working on an MILP problem, and the project needs to output the top N best results rather than the global best. I am looking for an open source solver which has a callback function. Can anyone ...
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### Linearize product of $x\cdot y \text{ with } x,y \in \{-1,0,1\}$ for MILP

I have a problem where I have many products between variables drawn out of $\{-1,0,1\}$. Could you suggest a linearization in terms of variables in $\{-1,0,1\}$ or $B_1 - B_2$ where $B_i \in \{0,1\}$ ...
582 views

### Linear Programming: Integer and non-integer decision variables

I am looking for an answer to a question I can't quite get behind. I am given the following mathematical optimization problem: \begin{align}\min&\quad\sum_{t\in T}s_t\cdot z_t+h_t\cdot i_t+p_t\...
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### Docplex : model is infeasible

I have implemented a model in cplex and even if I give it an initial feasible solution of a heuristic programmed elsewhere, it gives me the error "the model is infeasible". Please if someone ...
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### KPIs in Docplex?

I want to add a KPI to calculate the percentage of occupancy of vehicles: the total travel time of occupied arcs (where the capacity of a vehicle is non-zero) over the total travel time. How can I ...
53 views

### How to build a contiguous path?

In my (simplified) problem I have a grid. Given an origin cell, I'd like to find a minimum-length path on this grid that connects to one or more target cells. My idea is to use a series of binary ...
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### Convex Optimization with Variable Dependency / no unmet demand carry forward

I'm running into an issue with a Linear Optimization Problem. The ultimate goal is to come back with an optimal production quantity (prod_qty) across several items ...
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### why in coding constraints you don't get the right answer?

From "A new unrelated parallel machine scheduling problem with tool changes to minimize the total energy consumption" Zhang et al. 2020 paper. A scheduling problem that schedules $n$ jobs on ...
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### Using OR-Tools with .NET and GUROBI

We want to model our MILP problem with Google OR-Tools in .NET, and solve it using GUROBI (solver may change in the next 1-2 years). However, we couldn't find the correct syntax to call GUROBI. https:/...
160 views

### What methods are used to solve multi-objective optimization problem with non-linear objective functions and integer decision variables?

Case 1: NLP When either the objective function or at least one of the constraints or both are non-linear it is a NLP. We use generalized reduced gradient or Quadratic Programming to solve NLP. However,...
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### Boolean constraining another boolean

like the title suggest, I am trying to constraint a boolean with another boolean, if that makes sense. x and y are both booleans, where y=1 when ...
259 views

### Issue in solving a large scale MIQP problem

I am solving a large scale MIQP optimisation problem at each step of a model predictive control problem. The problem description is as below. \begin{align} \min_{u} \quad (x_{k}&-x_\text{ref})^{T}...
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### Problem with Piecewise constraint in Gurobi

I am facing a problem in my model with piecewise constraints that is making my one of the decision variables equal to zero for every value. My objective function is: \begin{equation} \min \sum_{t=...
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### How to compare the optimality gaps between a commercial solver and Benders

Suppose I have a mixed-integer-linear programming model where the objective is maximization. I solve my model in two different ways. First, I call CPLEX (a commercial solver), and then implement ...
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### Mathematical model complexity Vs Time Complexity of the model

As far as I know, when we talk about the term of complexity, it referred to the time complexity of the model in which how long does it take to solve a specific mathematical program by a specific ...
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### Is Apple's M1 suitable for Operations Research?

I am curious about the performance of Apple's M1 chip solving optimizations models, MIP, LP, and in solutions approach as benders or columns generations. I read that is a spectacular cpu to perform ...
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### How to return the last upper bound docplex?

I try to solve a model in docplex(python) the model was stopped after a specific time limit. I want when the model stop return the best upper bound was found.
323 views

### Mixed-Integer Linear Programming With Free Variables

In the classic Mixed-Integer Linear Programming (MILP), the variables are fixed to be either integer or real. I am interested in the following MILP variant, where only one thing different from the ...
89 views

I am solving an OR scheduling problem where I assign the patient to (day,OR) tuple in Master Problem. Once the assignment is made, a subproblem can be solved for each (day,OR) tuple independently ...