# Questions tagged [linear-programming]

For questions related to problems that optimize (i.e., minimize or maximize) a linear objective subject to linear constraints.

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### Benders decompositions: Number of iteration does not remain same

I am solving an LP(i.e 118-bus system economic dispatch for 130% loading) using benders decomposition. The problem takes 26 iterations to converge. This means that the process adds 25 cuts to the ...
66 views

### Optimisation Multiple Constraints

I am trying to solve a linear algebra problem: an optimisation problem and I am using CVXOPT. I've split the problem into 3 components In its simplest form, The general formulation for CVXOPT is \...
172 views

### Are decomposition methods applicable on large linear programs?

Working on a very large Linear Program, we tried out some primitive implementations of decomposition techniques such as Lagrangian relaxation and column generation. However, none of these were able to ...
81 views

### Linearly independent rows in simplex

I'm having some trouble understanding about the independent rows in a basic solution. In the book Introduction to linear optimization by B&T, the authors give the definition of a basic solution as ...
151 views

### Are there small LPs out there?

A fair share of academic research and software development focuses on solving ever-larger problems, particularly when it comes to LPs. I am however curious to know in what contexts and to what extent ...
93 views

### Upper and lower bounds of a variable equal

I'm working on a MILP (Mixed-Integer Linear Programming) problem with the Java API of Cplex. In order to easily exclude some variables from my problem I thought about setting both their lower and ...
65 views

### Examples of LP problems in irrigate engineering

I need examples of linear programming problems applied to irrigation system. My idea is to give students many examples of LP applications in the irrigation engineering.
74 views

### Minimax problem with a large high dimensional feasible region

How to solve minimax mixed integer problem with a large high dimensional feasible region? \begin{aligned} \max_{\vec{x}}\min_{\vec{y}} \quad & \vec{r} \cdot \vec{x} + \vec{s} \cdot \vec{y}\\ \...
191 views

### Simplified risk game: writing a pratical Minimax objective for mixed integer programming

Problem To ensure fairness of the game, I am writing a bot that plays against itself. I have trouble rewriting a minimax objective to a practical maximization in mixed integer programming. The amount ...
87 views

### KKT conditions analysis for binary constraints

I am wondering if boolean constraints in a linear program can be solved (after linear relaxation from $x\in\{0,1\}$ to both $x\ge0$ and $x\le1$) using KKT analysis. Most of the algorithms that I have ...
114 views

### Linear Relaxation of Boolean Constraint for Solving Integer Linear Program Using KKT

I am trying to convert a boolean LP to LP using LP relaxation by converting $x \in {0,1}$ to both $x \ge 0$ and $x \le 1$. Then to use it in my problem analysis, I am trying to build the KKT ...
276 views

### Model “if and only if” indicator constraints in Linear programming

Apologies if this question has been asked, but I haven't been able to find it. I'm modelling something with Gurobi and want to do the following: \begin{align}\text{cond} < \dfrac{1}{3} &\iff x =...
114 views

### Best way to add dummy to transportation problem? Zero cost will be always chosen first?

I know that an unbalanced transportation problem could be made a balanced transportation problem by adding a dummy node which equals the difference between demand and supply. In literature, dummy ...
228 views

### CPLEX log always the same after hours (“Gap” and “Best Integer” always blanks)

I'm using the Java API of CPLEX 12.6.1 (with license) to solve a MILP (Mixed-Integer Linear Programming) maximization problem. The point is that, after 21 hours, CPLEX has consumed 32 GB of RAM and ...
73 views

### Need help with an appointment scheduling problem

I am currently stuck on writing a linear programming model to describe the process of appointment scheduling for an Oncological Center. I wanted to share it with you guys and see if anyone here could ...
48 views

### Employee allocation based on ranking: Mathematical Model

Suppose I have three employees and I have to assign three employees based on their ranks. If an employee has rank 1 that means he is best. Say, I have the following table ...
71 views

### MODM to create balanced groups of students to maximise diversity

I am very new to LP, Goal Seek, Decision Models etc and I have a multiple-objective decision making problem that may or may not require a mix of techniques although I am trying to solve it purely ...
76 views

### An efficient Integer programming model for the minimum spanning tree problem?

Let $T=(V, E')$ be a spanning tree of a graph $G=(V, E)$. Rather than verifying for any subset of vertices $S\subseteq V$ that $|E'(S)|=|S|-1$, is there an efficient way to satisfy the spanning tree ...
3k views

### Is there a Linear Programming Library that natively supports fractions instead of floating point arithmetic?

If one recalls how the Simplex method is taught by hand in most LP classes it takes place entirely in $\mathbb{Q}$. All operations yield exact fractions. For this reason I'm looking for linear ...
240 views

### What is a good way to penalise LP relaxation?

I have a binary integer program. It is of a large size and the solver is taking longer time. I am thinking of relaxing the binary integer variable and making it a continuous variable. How can I ...
178 views

### Obtaining the system of irredundant inequalities from a set of inequalities using CPLEX

Given a linear system of inequalities $Ax \geq b$, I would ideally like to compute the irredundant set for those set of inequalities. I know how to do so mathematically, but I was wondering if there ...
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### How to deal with a decision variable in the objective function that depends on if-else conditions involving other decision variables?

I'm modeling an optimization problem in which a decision variable $x_1$ in the objective function depends on if-else conditions involving decision variables $x_2$ and $x_3$, as the following equation, ...
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### Name for subclass of ILP without any inequality constraints (including constraints on x)

In "Myths and Counterexamples of Mathematical Programming" myth "IP Myth 21" says: The problem of finding $x\in \mathbb{Z}$ such that $Ax=b$, where $A\in\mathbb{Z}^{m\times n}$ ...
206 views

### Faster implementation of “or” constraints in ILP

I have implemented a set of "or" constraints in my ILP using binary decision variables (as in this method). It works fine for smaller problems, but when I try to increase the number of ...
90 views

### Mixed Integer Programming - How to model the dependency of two variables in an objective function

I have two variables $a$ and $b$, in which $a$ is the amount of goods and $b$ is the amount of boxes of the given sizes. So $b$ (box size + number) is dependent on a (goods quantity). If $a$ is ...
64 views

### LP instead of IP formulation of assignment problem

In the example files of GLPK, the assignment problem is written as a linear program. I don't understand why this isn't an integer programming problem. The problem formulation: ...
108 views

### warmstarting simplex algorithm- how much can problems differ from each other?

I'm working on an implementation of the simplex algorithm. I want to solve problems in real time every 30 minutes. They could be interpreted as a classic transportation problem. I couldn't really say ...
308 views

### If-then constraint with continuous variables

I was usually using if-then constraints with integer variables but ended up using continuous variables and got confused. I have variables $x_{ij}\in\mathbb{R}_{\geq 0}$, and would like to force the ...
137 views

### How to linearize the product of a binary and a continuous variable? [duplicate]

Suppose we have a binary variable $b \in \{0, 1\}$ and a continuous (possibly negative) variable $y \in \mathbb{R}$. How can we linearize the product $b \cdot y$?
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### Two binding constraints - Linear Programming

I'm having some troubles to continue solving my system, I'm used to solve such systems but with "one" binding constraint, if someone could give me some helpful hints so I can solve it I will ...
I want to solve a job shop scheduling problem. I got $n$ Jobs that have to be scheduled on $k$ Machines. A Job $i$ has 2 or 3 Tasks $j$, and there is a known sequence of the Tasks of a Job. One ...