Skip to main content

Questions tagged [linear-programming]

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

158 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
9 votes
0 answers
200 views

Ill-conditioned LP in Benders decomposition

I have implemented a Benders decomposition for a constrained network flow but the LP solver (Gurobi) warns me of the ill-conditioning of the subproblem dual LP. As you can see below, the coefficients ...
Mauricio Zambon's user avatar
7 votes
0 answers
148 views

Is this a valid strong polynomial algorithm for deciding LP feasibility?

Let $$A \cdot X + B \preceq 0$$ be a system of linear inequalities with $X \in \mathbb{R}^n$ $A\in \mathbb{R}^{m\times n}$ and $B \in \mathbb{R}^m$ where $m \geq n$. According to Farkas lemma, exactly ...
C Marius's user avatar
  • 507
7 votes
0 answers
151 views

Modeling traffic in a city

I am trying to model traffic in a city, $(i,j)$ represents a road in a city. There are $H$ vehicles in a city they have some prescheduled set of destinations to visit, $A_{j,h}$ denotes arrival time ...
ooo's user avatar
  • 1,589
7 votes
0 answers
92 views

Building the Scheurman's Model II constraints for a multi period linear program

Scheurman's paper discusses Model I and model II Formulation to solve harvesting and scheduling problems. It is a specific implementation to solve multi period linear programs. Both models are also ...
dassouki's user avatar
  • 153
7 votes
0 answers
81 views

Modelling a simple ordering problem to have balanced delivery days

Assuming that I should buy 50 items from 25 different vendors with pre-known delivery duration between 2-7 day for each, which day of a week should I place each order so that the delivery days be even ...
Sean's user avatar
  • 159
6 votes
0 answers
84 views

Robust Linear Optimization for avoiding diminishing returns

My engineering problem can be formulated as an LP as shown below \begin{align} \max_{\mathbf{x}}~~&\mathbf{a}^T\mathbf{x} \\ \mbox{s.t.}~~~&\mathbf{b}^T\mathbf{x} \leq B~~,~~\mathbf{1}^T\...
dineshdileep's user avatar
6 votes
0 answers
108 views

Dual instability, degeneracy, tailing off effect - Which are the causes and which are the effects?

Dual instability, degeneracy, and the tailing off effect are often mentioned together in papers. However, I cannot seem to find a clear explanation on which of these cause the other and vice versa? ...
gmn's user avatar
  • 666
6 votes
0 answers
225 views

Airline revenue management re-solving problem

I am considering a bid prices (shadow price of the capacity constraint) problem (from Chen, L. and Homem-de Mello, T. (2009)., page 14) where the acceptable classes for booking requests for ...
SimonCello94's user avatar
6 votes
0 answers
100 views

Estimating multistop routing costs

In many OR problems, it is sometimes a good idea (or necessary) to relax routing constraints. An example of this occurs in the classical facility location problem, where a warehouse can send out a ...
Kuifje's user avatar
  • 13.4k
6 votes
0 answers
224 views

Provide basic solution to CLP

I'm using Pyomo to formulate an LP with approx 500,000 constraints and 200,000 decision variables. The LP is solved using CLP. Some instances fail to return even a feasible solution after many ...
Arjan Dijkstra's user avatar
6 votes
0 answers
95 views

Proof that the leaving variable cannot be selected as the entering one in the next round

Using the Dantzig's pivoting rule, can it be proven that the leaving variable of one round cannot be selected as the entering variable in the next round?
Clement Cloucharde's user avatar
6 votes
0 answers
182 views

Benefits of removing slack variables during presolve

I was reading Tobias Achterberg's thesis, and on page 138 he mentions the following presolving technique for linear equations (I'm slightly paraphrasing Example 10.2): Consider the equation $4x_1+...
Nikos Kazazakis's user avatar
5 votes
0 answers
115 views

Complexity of determining whether a LP or MIP is infeasible

What is the best complexity for the worst case scenario and the algorithm associated with it to determine if a linear programming (LP) is infeasible ? Further, what if we consider a mixed integer ...
G Oliveira's user avatar
5 votes
0 answers
42 views

In a binary logistic regression context, how to introduce a constraint to model the dependency between consecutive samples

Imagine we are running a logistic regression to identify opportunities for car sale promotion, using previous promotion campaign's result. Each $y$ is the increase of car sale after the promotion. ...
eight3's user avatar
  • 481
5 votes
0 answers
118 views

Construct a direction of recession of the dual that is from growth to dual function

Consider the primal problem $$\begin{array}{ll} \text{minimize} & c^\top x\\ \text{subject to} & Ax = b\\ & x \geq 0\end{array}$$ where $ A \in \mathbb {R}^{ m × n}$ has rank $m$. Suppose ...
justlearningmath's user avatar
4 votes
0 answers
92 views

Any recommendations for learning about polyhedra and integer programming?

My knowledge on convex polyhedra and systems of linear inequalities (facets, edges, Farkas Lemma, projections, duality, etc.) is very scattered, and I'l like to go through a book to solidify it. I'm ...
user56202's user avatar
  • 233
4 votes
0 answers
100 views

How to linearize or convexify a constraint with a square root of sum of two variables?

Here is the constraint: $$\text{Pa} + \text{Pb}=a + b \sqrt{\text{Ir}^2 +\text{Ii}^2} + c (\text{Ir}^2 +\text{Ii}^2)$$ Here $\text{Pa}, \text{Pb}, \text{Ir},$ and $\text{Ii}$ are variables. $a, b, c$ ...
Ghulam Mohy-ud-din's user avatar
4 votes
0 answers
67 views

bilinear problem proof for NP-completeness of degeneracy check

In the paper "Some NP-complete problems in linear programming" (https://doi.org/10.1016/0167-6377(82)90006-2), there are several proofs given to show that testing for degeneracy in LPs is NP-...
Brannon's user avatar
  • 900
4 votes
0 answers
121 views

Modeling question on continuous variable that dependens on binary variables

Given a model with a binary variable $b_s$ that describes whether taking an item $s$ from a set $S$ or not. Consider that some other constraint in the model depends upon whether all items of the set ...
Andreas's user avatar
  • 313
4 votes
0 answers
244 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 ...
Qurious Cube's user avatar
4 votes
0 answers
262 views

Does anyone have the criss cross algorithm programming code to solve linear programming problems?

I have a project that requires programming code for the simplex algorithm and criss-cross algorithm. The purpose of this project is to compare the two methods. I've tried to find it, but the ...
newbie's user avatar
  • 81
4 votes
0 answers
71 views

Continue on "Is there a known MILP to schedule routes after routes are made"

I have made some progress on my previous question (Is there a known MILP to schedule routes after routes are made). I have derived the sets of the problem, which are: 1) Itineraries of vehicle: $i \in ...
dimboukosis's user avatar
4 votes
0 answers
171 views

Publishing paper that uses LP solver to solve equation

I was reading this paper by Cerna et al. (2018)1. In the paper there are only CPLEX-solvable equations given by the authors and the results. How valuable is this paper, and what is its quality? Can ...
ooo's user avatar
  • 1,589
4 votes
0 answers
242 views

How can I formulate this multi-objective optimization problem?

Now, for each system $X$ $(X=A,B,C,E)$, my objective is $$\max\min\frac{s_{x_u}}{d_{x_u}}$$ here, $x=a$ for system A, $x=b$ for system B and follows... and for the whole system, my objective is $$\max\...
KGM's user avatar
  • 2,285
4 votes
1 answer
92 views

Nurse Rostering constraints - LP

I am fairly new to linear programming since I came across this topic at university this semester. We mainly focus on nurse rostering. In the lecture, we created a very basic rostering model with an ...
nflgreaternba's user avatar
3 votes
0 answers
64 views

Block Simplex Algorithm, i.e., Block Active Set for Linear Programming

What investigation has there been of Block Simplex Algorithms, i.e., block active set for Linear Programming, i.e., block pivoting? This is a follow-up to Why do active set methods or the simplex ...
Mark L. Stone's user avatar
3 votes
0 answers
137 views

Linearize objective function with non-linear terms

I have a problem with linear constraints but in the objective function I want to have some linear terms along with a $x^2$ term. So it is like the following: $$\min \sum \limits _i \sum \limits _j (a[...
christouandr7's user avatar
3 votes
0 answers
107 views

Projected Gradient Ascent for linear programming

I need to find a reasonable maximum for a linear programming problem, for which standard solvers for linear programming are just too slow. I was thinking of using projected gradient ascent, but do not ...
Carol Eisen's user avatar
3 votes
0 answers
114 views

Does a linear program always attains its (finite) infimum?

Consider the following (Lp). \begin{align}\min&\quad\mathbf{c} \cdot \mathbf{x}\\ \text{s.t. }&\quad A\mathbf{x} \geq \mathbf{b} \\ &\quad\mathbf{x} \geq \mathbf{0}\end{align} If $S$ is ...
Farhad Rouhbakhsh's user avatar
3 votes
0 answers
66 views

Dual of the alternative solutions

Suppose we have two alternative solutions for a linear program. Are their corresponding dual solutions the same? (in terms of the values for each dual variable)
Junior MIP's user avatar
3 votes
0 answers
89 views

Function approximation of a complex objective function

I would like to approximate the following objective function using a simpler function that can use be defined in gurobi. \begin{equation} \min_{I_{i,v}} \ \sum^{N_v}_{v}\sum^{TT_v}_{i} \ C_{loss,...
Jose_Peeterson's user avatar
3 votes
0 answers
136 views

Are there hybrid metaheuristic-solvers to solve combinatorial optimization problems?

I have a problem which is formulating a linear program. To solve large instances I implement a metaheuristic to solve my problem. In my problem, I have two objective functions. With my linear program, ...
MAJID majid's user avatar
3 votes
0 answers
108 views

Polynomial Time Solution For a Mixed-Integer Linear Programming Specific Case

Consider the following mixed-integer linear programming (MILP): \begin{equation*} \begin{array}{ll@{}ll} \text{maximize} & 1 & \\ \text{subject to}& x_{i} \geq 0, &i=1 ,\dots, m\\ ...
Samuel Bismuth's user avatar
3 votes
0 answers
139 views

Harvest planning problem

I need to model the following problem: For a planning horizon of $P$ equal periods, one has $N$ harvesting locations and $K$ contractors who can harvest at those locations ($K < N$). Each ...
Víctor Fing's user avatar
3 votes
0 answers
145 views

How is the dual revised simplex method equivalent to running the RSM on the dual problem?

I've seen the claim (in the title) several places, but can't quite understand why it's true. From what I understand so far, the revised simplex method solves an LP in standard computational form, $$\...
LinearDysfunctional's user avatar
3 votes
0 answers
184 views

How to linearize a max min objective function?

Let us suppose that I have a $\max \min$ objective function that only depends on one set of variables: $\underset{x}\max \underset{y}\min dy$ Associated with the linear set of constraints and right ...
JKHA's user avatar
  • 679
3 votes
0 answers
269 views

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 ...
user.mokho's user avatar
3 votes
0 answers
87 views

PuLP Python: How to linearize an inequality involving an integer variable

I am working on a Copper payables problem where the objective function is to maximise the sum of copper payable over a time period, T. The total amount of payable tonnes i.e. what the customer will ...
cmp's user avatar
  • 327
3 votes
0 answers
83 views

Where I can study some job shop scheduling by course (video )?

I am seeking the help to know where I can study the job shop scheduling Heuristics or using solver by some course/video as I see some of books and papers hard to understand . It is hoped that the ...
Yue Chao's user avatar
3 votes
0 answers
832 views

How can I see the engine log when solving a LP using pulp (python)?

I wonder which command should I use to see how the steps the pulp solver is doing when solving a linear program.
Pep's user avatar
  • 39
3 votes
0 answers
150 views

Simplex method on graphs: How do I find a basic solution using the Ford-Fulkerson algorithm?

I'm tasked with solving a minimal cost flow problem. I'm asked to first use the Ford-Fulkerson algorithm on my graph to find a basic solution that will then be used to do the simplex method on that ...
WindBreeze's user avatar
3 votes
0 answers
50 views

High-mix manufacturing capacity

I'm not an expert in OR but I would like to determine what is the maximum manufacturing capacity of a plant (or how much a plant can produce of mix products). Each person in the plant has a known set ...
Otmane Zizi's user avatar
3 votes
0 answers
77 views

Public available MPS files with semi-continuous variables

Is there some MPS files with semi-continuous variables public available anywhere? To me it seems MIPLIB does not contain any.
ErlingMOSEK's user avatar
  • 3,166
3 votes
0 answers
422 views

On solving the Restricted Master Problem in Column Generation technique

I am working on developing a column generation (CG) based optimization framework for a large-scale airline crew pairing problem (a set-covering problem). First, I generate an initial feasible solution ...
Divyam Aggarwal's user avatar
3 votes
0 answers
101 views

Constraint equivalence in PuLP

I'm working on an optimization problem in PuLP and I have to enforce a daily minimum of shifts and a daily maximum of assigned shifts. I have the following constraints to ensure each day has a minimum ...
Joep's user avatar
  • 101
3 votes
1 answer
148 views

Big LP program to be submitted to NEOS Server (union-closed sets conjecture)

I have a big LP program with around $91,000$ variables and $2,900,000$ constraints. They are all binary variables, but I want to try also relaxing the problem putting $0 \le x \le 1$ bounds. I am not ...
Fabius Wiesner's user avatar
2 votes
0 answers
86 views

Re-formulating an LP where a subset of constraints can be loosened?

I have an LP of the structure below (omitting some constraints that are not directly applicable for this question). $$\text{min } c'x$$ $$Ax + By \geq d$$ for a given $A \in R^{m \times a}_{>0}, B \...
Mason's user avatar
  • 515
2 votes
0 answers
51 views

Implement a rolling horizon approach into a schedulig problem

I have just come across the topic of 'Rolling Horizon' in my literature research and would now like to apply it myself, but unfortunately I don't know where to start. This is my model, which is ...
lukdooxb1's user avatar
2 votes
0 answers
36 views

Addressing Variable Multiplication in Constrained Infinity-Norm Maximization with Hypercube & Polyhedron Constraints

I am reaching out to this knowledgeable community for assistance with a complex optimization problem that I have been investigating. Here is the formulation of the problem I'm addressing: $$\tag{1} \...
Diego Fonseca's user avatar
2 votes
0 answers
95 views

Understanding the condition of the bounded variable algorithm in the linear programming

Following is the section 7.3 of Operation Research An Introduction by Hamdy A. Taha, Define the upper-bounded LP model as, $$\max z=\{CX|(A,I)X=b,0\leq X\leq U\}$$ The bounded algorithm uses only the ...
N00BMaster's user avatar