# 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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### Linear optimization problem with user-defined cost function

I have a linear optimization problem for which I am looking for a suitable optimization solution that can fulfill my requirements. Here is an explanation of the optimization problem: There are a ...
63 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?
61 views

### Linear programming: extending problems yields non linearity

I had a linear programming problem with the following objective function $$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{j}x_jq_jC_{ij} \right) c_i$$ Where $q, p, C, c$ are known. Let the term ...
328 views

### Pulp: slack variable to identify & measure extent infeasible in supply problem

I am currently modelling a supply problem that attempts to optimise a rail schedule which moves products from a production plant, to a warehouse to satisfy sales. The model is working fine (thanks in ...
115 views

### Physical Interpretation of a dual of an LP

I was recently asked to physically interpret a dual of an LP for an audience who does not know mathematics/OR (without LP, dual, bounds, etc.). Though I attempted it and was very close to what the ...
136 views

### Estimation of the number of optimum vertices

Consider any linear programming model of $n$ variables and $m$ constraints which has multiple optimum solutions. If it is possible, I'd like to know the lower and upper limits (in terms of $n$, $m$ ...
695 views

### Linear programming convexity

Is it possible for a linear programming model to be non-convex ? If it is, please, provide a simple 2 variables example and explain why it is non-convex. EDIT 1: I have been wondering, maybe the ...
59 views

### Weapon Target Assignment Problem + Time Windows

So I am very familiar with the WTAP it the static case. What I am wondering, is there a formulation that has "time windows" as well? Let's say you have some weapons and some targets, you know the ...
40 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. Erling
64 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 ...
115 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 ...
56 views

### Linear programming with correction term based on decision vector

I had a linear programming problem where I am optimizing some function $$f(x) = \sum_{j}x_jq_jp_j - \sum_{i}\left(\sum_{j}x_jq_jC_{ij} \right) c_i$$ Where $q, p, C, c$ are known. I now want to ...
225 views

### Suggest me good books to learn heuristics to solve Operations Research problems using python

Suggest me some good books with implementation of heuristics using python to solve operations research problems
89 views

### On dual-formulation of a given primal for a set-covering problem

I need to solve an LP-relaxation of an airline crew pairing optimization problem (CPOP). The problem formulation is a modified SCP and is as follows: Primal of the CPOP: \begin{align}\min&\quad\...
86 views

### Specific usecase of two-phase simplex algorithm

The problem below aims to find to most optimal way to transport the fuel : A company Er must transport a type of fuel from its two refineries Ra and Rb to its two points of sale PV1 and PV2. The ...
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### Dantzig decomposition and Column Generation for equality constraints

I was trying to apply Dantzig Decomposition followed by Column Generation. The following is how I was taught. \begin{array}{l} \text { Minimize }-10 x_1-2 x_{2}-4 x_{3} \\ \text { subject to: } x_{1}+...
174 views

### How to write quantity discount constraint?

In a simple transportation problem like below image, how to model a constraint for shipment discount e.g. if quantity transported from any origin to any destination is more than 100 unit then the ...
127 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 ...
39 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 ...
340 views

### How to set these constraints in a linear optimization problem (PuLP)?

I am trying to implement an employee (nurse) scheduling problem and seek some advice on how to implement a specific constraint.The problem is as follows: There is a set of employees and days (both ...
387 views

### LP dependent on the ordering of the data

This is a rather simple question. Can a solution to a linear programming problem be dependent on the order in which the data is read/presented/stored? I know, that the time it takes to solve the ...
106 views

### Same values constraint and grouping of variables

In a linear program, I would like some variables to: 1. Take the same values 2. Group some variables i.e. some variables should take same values or lie within certain percentage. 3. All different ...
244 views

### How to enforce this specific constraint in PuLP?

I am trying to implement an employee (nurse) scheduling problem and seek some advice on how to implement a specific constraint.The problem is as follows: There is a set of employees and days (both ...
94 views

### Is the optimal objective of a linear program continuous in its right-hand-side?

Consider a linear program $$f(b)=\min_{x}\{c^\top x: A x = b, x\geq 0\}$$ (assume it is feasible and bounded for all $b$). My understanding is that $f(b)$ is a convex piecewise linear function of $b$ ...
125 views

### Manually indicate initial basis for coin-or lp solver CLP

I have a set partitioning formulation with each constraint being an equality constraint to meet the given demand (right-hand side of the constraint). For each constraint, I have a slack and a surplus ...
110 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 ...
288 views

### PuLP Transport Problem - How to add outcomes of decision variables together

I am working on a rail scheduling problem that moves product from a production plant to a storage facility to satisfy demand. I am new to PuLP so finding this difficult to understand why this isn't ...
86 views

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### How to write a LP/MIP to mark the items in a time-series list after a fixed delta?

I have a time series list like this. ...
103 views

### how to penalize a shortfall of a sum of absolute values

I have a model where there is a constraint on the sum of absolute values, and I would like to add a penalty on the shortfall from the constraint. More specifically: \begin{align*} \text{maximize}\ &...
95 views

### Linear programming explanation in Algorithms by Sanjoy Dasgupta

I am reading about simplex algorithms in a textbook titled Algorithms by Dasgupta-Papadimitriou-Vairani. On each iteration, simplex has two tasks: Check whether the current vertex is optimal (and if ...
301 views

### Transforming a Quadratic constraint to SOCP

I have a problem similar to Markowitz portfolio optimization that I would like to transform into second-order cone programming. I have a linear objective function with a quadratic constraint (assuming ...
115 views

### Minimizing a variable over the intersection of simplex and linear constraints

I am solving: \begin{align} \begin{array}{rll} y^* = \min & y & \\ \mathrm{s.t.} & a_i^\top x \leq y, & i=1,\ldots,m \\ & x \succeq 0,\ \mathbf{1}^\top x = 1. & \end{array} \...
154 views

### Propagate value through a graph

Here is my question where I am propagating distance through the graph, I was wondering if it is possible to do when the graph has cycles, i.e., traveling the same node multiple time then is it ...
193 views

### Controlling the constraint execution sequence in docplex

I have tried to implement my question asked here with the help of Github code link. Below is the linearized version of the MTZ like constraint as per the answer given here. Constraints below assign ...
180 views

### TSP subtour elimination with multiple formulations

Referring to the question here. Given a set $S$, which we need to travel following TSP rules. I was wondering if this sub tour elimination method is good enough or not? Let $b_{i,j}$ denote edge ...
972 views

### Is there a way to view added constraints in Gurobi (Python)?

I should note that I am very new to Gurobi so apologies if this is obvious. I am working on a project for a class to maximize profit on a theoretical flight network by deciding which routes to fly at ...