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Questions tagged [linear-programming]

An optimization technique for minimizing or maximizing a function of several variables in the presence of constraints where all relationships are linear.

Linear Programming is a mathematical optimization technique for minimizing or maximizing a linear function of several variables (called the objective function) subject to several linear constraints. The objective function and the set of constraints are collectively called the Linear Program.

The dual Simplex Method is a commonly used solution technique in Linear Programming. There are several commercial and open-source software packages for solving linear programs.

Brief history:
1939. Production, planning. [Kantorovich]
1947. Simplex algorithm. [Dantzig]
1947. Duality. [von Neumann, Dantzig, Gale-Kuhn-Tucker]
1947. Equilibrium theory. [Koopmans]
1948. Berlin airlift. [Dantzig]
1975. Nobel Prize in Economics. [Kantorovich and Koopmans]
1979. Ellipsoid algorithm. [Khachiyan]
1984. Projective-scaling algorithm. [Karmarkar]
1990. Interior-point methods. [Nesterov-Nemirovskii, Mehorta, ...]

External links:

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Building an objective function involving counting in pyomo for assignment problem

My Pyomo model is trying to solve a task assignment problem where 4 workers needs to be assigned to 8 tasks, so that's 2 tasks per worker. One of the objective function model.obj2 tries to minimize the sum of the types of materials used by each…
Athena Wisdom
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Lost on how to append numpy vectors/matrices/arrays

I'm currently trying to build a practice linear parameter estimation python program using numpy but I've never written in python before and I'm very loose with numpy. I have a series of x,y data points that I want to loop over and build a new vector…
Eliot Shedlock
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Minimise set size in task assignation problem

I have to create a solution for assigning tasks to users according to some rules and I wanted to give linear programming a try. I have a list of tasks that require a certain skill and belong to a specific team, and I have a list of available users,…
Goodyear
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Optimal transport for large source and destination nodes Scipy linear program

I want to solve an optimal transport for source and destination nodes of sizes 42000 and 18000 respectively. I know that Scipy Linear Programming Module now includes HIGHS so it should be pretty efficient to use. However, I have been running the…
indispinablenorm
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Python - Error using linprog ("Invalid input for linprog: provide a 3 x 2 array for bounds, not a 2 x 3 array")

I am trying to use the linprog in python to solve this problem: # Minimize = (0.035*x1) + (0.015*x2) + (0.025*x3) # x1+x2+x3=1.2 # 0<=x1<=0.7 # 0<=x2<=0.3 # 0<=x3<=0.5 c = [0.035, 0.015, 0.025] #objective function A_eq = [[1, 1, 1]] b = [1.2] lb =…
teratoulis
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How to extract variable values that equal a certain value (pyomo)?

I am building a routing optimization model using pyomo on python. I have solved my model but I am trying to extract the decision variable information for my model. My model is binary, and the values I am looking for are values of my model.z decision…
Berbatov
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Scheduling problem and nonlinear simulations

My problem appears to be a scheduling problem, but there’s a few twists I don’t know how to handle - I’m not even sure what terms to Google. I have a set of “resources”, which may or may not have a lower bound on their first availability date (or…
Infinity77
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Define sets and parameters from csv file to be used in pyomo optimization max quantity waste collected problem

First time Pyomo user here. I am trying to build an optimization model that will maximize the quantity of waste collected in a waste recycling network consisting of customers i and recycling centres j. (i.e. maximize quantity waste Qij flowing from…
give the ball to bobby
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Linear Programing of 16GB of data on 8GB of RAM

I'm doing some linear optimization on a matrix that takes up 16GB of memory using the spicy.optimize.linprog method. However, my computer only has 8GB of RAM. I already consider the option of simply getting more RAM but besides that what other thing…
Minh Pham
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Python PulP linear optimisation for off-grid PV and battery system

I'm trying to use linear optimisation to minimise the size of solar PV and battery for an off-grid property. I have solar irradiance data and household energy consumption data - I have created a year's worth (8760 data points) of the data below. I…
jmcq2
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Why the reduced cost for the nonbasic variable can be negative?

I am working the column generation with the IP solver CPLEX. When the master problem was solved to optimal, I output the basis information, and I found that there is a nonbasic varible takes value 1.0, and its reduced cost is negative, although the…
E. Su
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How to include a function in CPLEX objective function?

I am trying to formulate and solve an optimization problem using IBM CPLEX framework using python API. My objective function is as follows: where and are my integer variables. I define the variables as follows in my code: function f is as…
Shahrooz Pooryousef
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Is there a way for extreme points of a convex set to get as close to each other as possible?

This question relates to linear programming problems.
user18434171
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Need to Write a CIP file for SCIP

I'm starting to use SCIP for a research problem that used integer programming with disjunctions. My early work will be a program that writes a CIP file and then using SCIP from the command line, in Linux. My plan is to use my existing work to…
engineer
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National competition in programming math problem

I encountered this problem practicing for an upcoming national competition. The problem goes as follows: You need to create a mixture of two ingredients being in relation to 1:1. You are given N different mixtures, each having its own weight Wi, and…
Ivan Zanov
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