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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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 ...
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162 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 ...
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0answers
188 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\...
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2answers
114 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} \...
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1answer
112 views
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1answer
213 views

Comparing formulation for traveling salesman

I have a graph $G$ and have a set $S$ which are the points in the graph to visit in a TSP manner. Since the length of the TSP route can't be known as it can use any number of nodes to complete the ...
3
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1answer
131 views

How to express this logical constraint for an ILP?

I am trying to write an ILP for a problem but I have this logical constraint and I'm stuck. In my model I have: two binary variables: $x$ and $y$ One Integer variable: $z$ The logical constraint I am ...
3
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1answer
101 views

Find a particular optimal solution

After writing an integer linear program in AMPL, I solved it using CPLEX. Now, I have some variables that must necessarily be 1, others that must necessarily be 0 and finally it is possible that some ...
3
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1answer
123 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 $n$, $m$ ...
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1answer
239 views

Iterative calculus with Excel

I have this model: \begin{align}\max&\quad\small{(0.2(1.07)^{-1}+0.2(1.07)^{-2}+0.9(1.07)^{-3})x_A+0.4(1.07)^{-1}+0.5(1.07)^{-2}+0.3(1.07)^{-3})x_B}\\&\quad 0.2x_{A}+0.4x_{B}\geq300\,000 \\&...
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2answers
192 views

Find all Combinations of a Matrix

I have a $16\times11$ matrix and want to find all eligible* combinations of this matrix including always entities from all 11 columns. A simple example from a $2\times3$ matrix would be the following:...
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1answer
129 views

Gurobi C++: adding variables with vector

I am solving an LP by using GUROBI - C++ combo. Assume I have a variable $p \in \mathbb{R}^n$. I am adding this as a vector: ...
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1answer
103 views

Derive “true” shadow price for degenerated LPs using commercial solvers (e.g. Gurobi)

In linear programming for an optimal primal degenerate solution the values of the dual variables are in general not identical with the corresponding shadow prices. Several proposals on how to find the ...
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3answers
104 views

How to write distance specific constraint?

Suppose there are a few plants (p) and few customers (c). The supply (Sp), distance (Dpc), cost (COSTpc) and demand (DEMANDc) between them is given. I have a constraint that 90% of total demand of all ...
3
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1answer
114 views

Logical constraint in ILP

I want to write the following constraint: Let $z$ be an integer variable such that $0\le z\le M$, and $t$ be a binary variable where $M$ denotes big-M. The logical constraint is as follows: if $z \...
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1answer
123 views

Representing Date Variables in Pulp

I am working on an optimisation problem that involves minimising shipping demurrage. I am struggling to model how to represent the difference, (x-y) between dates where the ship is ready to be loaded ...
3
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1answer
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 ...
3
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1answer
57 views

Iterative calculus with Excel - N° 2

In continuation with the previous post, I propose you another problem. I have this model: \begin{align}\min&\quad F\\\text{s.t.}&\quad F-(1150x_{B_{1}}+1000x_{B_{2}}+1350x_{B_{3}}-S_{1})=430\...
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1answer
117 views

Linearizing constraint with continuous and boolean variables

I have two continuous variables $A$, $B$ and two binary variables $x$, $y$. Condition: if $A = B \wedge x = 1 \wedge y=1$ then $z = 1$ else $z = 0$ from In an integer program, how I can force a ...
3
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1answer
64 views

Maximum bipartite matching with breakpoints in edge weight function

I am looking for an analogy to the problem I am facing or better yet a paper or even code. I have: Nodes from set A and B. Edges are from a single A to many B. I am framing a max bipartite matching ...
3
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1answer
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 ...
3
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1answer
152 views

Pyomo add constraint error: Rule failed when generation expression for constraint

I am trying to solve a model with Pyomo and struggling with indexing. Below is a simple problem instance, where you can also see the error. The message is straightforward and self-explanatory but ...
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1answer
88 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 ...
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1answer
82 views

In Linear programming, how to determine if shadow price does not change linearly?

As the title says, in linear programming, is there a way to determine that the shadow price does not change linearly for a resource? I understand one way is to simulate but is there a way to tell ...
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1answer
92 views

Defining Solution Space in MILP / LP using If Then Statements

I have the following statements for an MILP: Variables: $c$ (can be $1$ or $0$); $\alpha_j$ (real numbers with $0\le\alpha_j\le1$). I have a linear inequality system for $\alpha_j$: $\sum_jv_j\...
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1answer
83 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 ...
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1answer
229 views

Linear programming sensitivity analysis using Matlab

I have a linear program in the MPS file format listing all the rows, columns, right-hand sides, etc. I can read that in Matlab and solve it using linprog. However, it seems there is no easy way to do ...
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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 ...
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0answers
47 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 ...
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0answers
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 ...
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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
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105 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 ...
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33 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 ...
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0answers
37 views

Extract binary value from continuous variable [duplicate]

I have a continuous variable $c$ which has value in between $[-R, +R]$. I want to create a boolean variable $x$ and, $x = 1$ when $c = 1.0$ otherwise $x = 0$ In more general form: $x = 1$ when $c \...
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4answers
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 ...
2
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1answer
125 views

Linearize sum of continuous and boolean variable

For maximizing the objective function $\sum_i{d_i y_i}+ A x - B \cdot \mathbb{I}_{x>0}$, how can I linearize $ A x - B \cdot \mathbb{I}_{x>0}$ term where $d_i, A$ and $B$ are positive constants ...
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1answer
109 views

How to formulate logical or constraint in cplex?

How to write the following constraint in cplex? the cost for full truck load is $700 and the cost of fractional truck load is \$800 *fraction up to $700
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1answer
40 views

How to properly define an edge set with an uncommon condition

I am trying to define an edge set as follows: $\mathcal{E}=\{(i,j)|i,j\in\mathcal{V}\land T_{ij}\leq R \land \text{$i$ and $j$ are not jointly in $\mathcal{K}$\}}$, where $\mathcal{V}$ is the set of ...
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1answer
145 views
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1answer
76 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 ...
2
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1answer
136 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 ...
2
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1answer
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 ...
2
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1answer
142 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 ...
2
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1answer
116 views

Is my formulation correct and how to formulate this IF-THEN constraint?

I have system with $N_U$ users and $N_T$ transmitters. Multiple transmitters can transmit to a single users and one transmitter can transmit to many users, i.e., two sets of transmitters serving two ...
2
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1answer
60 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: $min \left(\sum_{j=1}^{P} ...
2
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1answer
84 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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1answer
72 views

Can CPLEX output LP solution with primal variables only?

CPLEX writeSolution method outputs both primal and dual variable values of a LP. I know how to parse through the solution file to extract specific primal variable ...
2
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1answer
72 views

How can I formulate an objective function that minimises the number of items required to solve a problem

I am currently trying to solve a problem where I need to minimise transport cost through the choice of vehicle (and how many of each choice) subject to a given demand. The problem: There are currently ...
2
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1answer
45 views

Understanding MDP's Dual Linear Program

I'm trying to understand a proof in Puterman'05 (Markov Decision Processes: Discrete Stochastic Systems). My question is within Theorem 6.9.1 pertaining to the equivalence of solutions to the primal (...
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0answers
38 views

Solving transportation problem by the Network Simplex

I am trying to solve the following problem using Network Simplex method. But I have questions. My attempt: Basis Matrix$(B)$ Rows: 1, 2, 3, 4, 5 Column: (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) $$ \...