# Questions tagged [integer-programming]

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

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110 views

### Problems finding a feasible solution in a MIP

I am using CPLEX with Julia using the package JuMP to solve a MIP problem. In a small instance, I have tested my problem but, after 10 minutes, nothing happens. I have defined the following parameters ...
276 views

### Mocking up conditional statements in LP

I would like to know how if condition statements in linear programming can be reformulated using indicator constraints, and hence solved as a mixed integer linear program. Specifically: 1. Is it ...
132 views

### How to get an extreme ray of an LP from Gurobi

I am working on a problem of form \begin{array}{l @{\quad} l} \mathrm{max}_{x, u} & p^{\top} u \\ \text{st.} & A u + a x \leq 0 \\ & x \in \{0, 1\...
143 views

### Formulation of assignment problem as Linear Optimization

In the anti-tumor treatment with radiotherapy, it is possible to irradiate the tumoral mass from different positions with different intensities. For each of these possibilities, however, one has to ...
65 views

### How to improve relative mip GAP using CPLEX in a MIP

Supose that I have an integer feasible solution for a MIP and I provide this one for CPLEX. I have tested this situation in a problem and CPLEX have reported the following: ...
164 views

### Problem solving a linear program using Excel

The exercise is as follows: ACI has decided to put an order for golf shoes twice every year and expects to receive one shipment of $960$ pallets of shoes by the beginning of January and another ...
78 views

### Integer decision variables as index

The following problem has only two integer variables; however, they appear in the index of the parameters. Appreciate it if anyone has any efficient idea to transform it into a canonical integer ...
38 views

### Finding bounds on a data sensitivity scenario ILP problem

This is a follow up to a problem I posted here: Modelling a data-sensitivity scenario as an ILP problem As a recap, I was interested in finding the minimum number of cells that need to be suppressed ...
94 views

### What kind of scheduling problem is this?

I am trying to develop algorithm to solve following basic version of the problem. 1) I would like to know what this problem is called in literature so that I can look it up 2) What are efficient ...
58 views

### Optimal Seat Allocation Problem

I have to do an operations research assignment based on optimal seat allocation. The problem goes something like this. There are 5 rooms in an office each with a separate seating capacity. We now have ...
50 views

### Flexible Job Shop with Preemption

I'm trying to solve a flexible job shop problem variant that has precedence constraints on jobs along with a few other issues. We have a MIP formulation and also a simulated annealing algorithm to ...
65 views

### Indicator function for integer variable with inequality constraint

I have $n$ integer variables $\vec{x}$ with the following integer programming problem. $$COST = \sum^{n-1}_{i = 0} a_i x_i + \sum^{n-1}_{j=0} b_j I(x_j > 0)$$ Here, $a_i, b_j \in \mathbb{R}_+$ ...
98 views

### How develop a branch and bound algorithm for integer programming with black box objective function?

The problem here described was taken from a university exercitation session. A serial production line is made of $K$ workstations: one kind product is manufactured by this line and has to be processed ...
93 views

### Condition for an integer program and its linear relaxation to have the same value

Let $A$ be a $(0,1)$-matrix where no row or column is a zero vector, and consider the following optimization programs \begin{align}(1):\min&\quad y\cdot1\\\text{s.t.}&\quad yA\ge w\\&\quad ...
38 views

### How to find all covers and minimal covers?

Consider a constraint of type $$c_1x_1+c_2x_2+\cdots+c_nx_n\leq C$$ with $x_i$ binary. We call a cover a subset of the $n$ indices such that the sum of the corresponding coefficients is higher than ...
61 views

### Theoretical aspect of using extended formulation

If I can show a polyhedron Y is an extended formulation of polyhedron X and every extreme point in Y is integral, does that automatically imply the projection of Y onto the variable space of X gives ...
79 views

### Linearity of an optimization problem which comprises the product of variables with constant values from a non-linear function

In a mathematical integer optimization problem, if the objective function is represented as $\sum x_k \cdot M_k$, where $M_k$ is a non-linear function whose value is known and just plugged in to the ...
95 views

### Constraint to handle the machine-configuration's change between initial position and its first occurrence in the process

I am working with a kind of a reconfigurable process planning, meaning that the same machine can have different configurations and perform multiple operations. Each machine has an initial ...
83 views

### constraint programming and scheduling issues

I have a constraint problem that i need to resolve, but i did not how know to model the problem: I have 11 employees, i will name them from a to k {a,b,c,d,e,f,g,h,i,j,k}. I have a small company that ...
299 views

### Divisibility constraint in Integer programming

I have a simple question regarding the divisibility in integer programming suppose the objective function is $\text{max}\quad x_1 + x_2$ where the constraint is that the sum of $x_1$ and $x_2$ are ...
48 views

### Priority Constraint

Suppose I have the following set of binary variables: $X_i$: $I$ ranges from {1,..,4} Highest priority among the three variables $X$ , $Y$ and $Z$ $Y_j$: $J$ ranges from {1,..,3} $Z_k$: $K$ ranges ...
77 views

### Inequality Constraint Linearization of a product of an integer and a binary variable

I have thought I had found the answer here: How to linearize the multiplication of an integer and a binary integer variable? But the answers to that questions didn't help me find a solution for my ...
71 views

### Minimizing a quadratic binary nonconvex function by CPLEX

I am using CPLEX 12.8 to minimize a quadratic binary nonconvex function, according to quadratic function by CPLEX. In particular, my function is the following:  \sum_{i=1}^{m-1} \sum_{f=1}^{F} \sum_{...
75 views

### confusing results of two models with different complexity

i have two models that address the same problem. the first one is : the second one is: for different instances for the same size (n=30) i found the following results ( the first column on the left ...
50 views

### Has the concept of TU other application than proving convex hull characterizations?

If a matrix is totally unimodular (TU), then we know that $\text{\{}x| Ax\leq b \text{\}}$ is integral for all integral $b$'s. This is often used for convex hull proofs, but does the concept of TU has ...
34 views

### Interger programming using gray encoding

Could anyone suggest me a tool or library which takes an integer programming problem written in DOCPLEX or CVXPY as input and outputs the equivalent problem using Gray binary encoding? I am happy to ...
143 views

### Operation hours optimization for circular schedule

Here is my problem. A store has X = 15 electical devices with the ability to work non-stop, fully charged, up to 8 hours. Their battery charge lasts 2 hours and the operating hours of the store differ ...
154 views

### Switching of decision variables to be larger than or equal to a decision variable according to an indicator variable value

I would like to seek some advice on modeling the following: I have two integer decisions variables, $x, x'$, that are either equal or greater than zero and either of them is greater than or equal to a ...
86 views

### How this problem can be defined as MultiObjective optimisation

I need to optimize the end-to-end latency of a multi-component application. Assuming that the application has 10 components, component 1-5 is hosted by device 1, and device 2 is hosting the other 5 ...
197 views

### How can I formulate this specific if-then constraint?

IF $\sum\limits_d X_{i,d}\ge6$ THEN $Y_i = 1$ (strictly) AND IF $\sum\limits_d X_{i,d}<6$ THEN $Y_i = 0$ (strictly) $X$ and $Y$ are binary variables. What I'm actually trying to do is to charge the ...
74 views

### Miller-Tucker-Zemlin subtour elimination constraints to obtain a minimum spanning tree

I need Miller-Tucker-Zemlin subtour elimination formulation for symmetric traveling salesman problem (STSP) to use to construct a minimum spanning tree. Ie, I need Miller-Tucker-Zemlin formulation ...