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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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Gurobi and java and empty solution

I'm using Gurobi with java to solve a ILP problem. I set all and I start the program. But Gurobi doesn't even try to solve my problem and gives my an empty solution all variable set to 0. During the relaxed step Gurobi shows that the minimum value…
Milo
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Breakdown an integer value to an array of integer maintaining the sum

I am working on a project where I need to breakdown an integer value according to an array of percentage values. My end array must contain integer value and the sum of the array must be equal to the initial integer. Below is a fake example. We have…
Michael
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Solving Assignment Problem with conditional minimum group sizes using CVXPY

I'm using cvxpy within python to solve a particular type of assignment problem. I'd like to assign M people to N groups in a way that minimizes cost, with the following constraints on groups: Groups cannot have more than J members If a group is…
profj
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Speeding up integer linear optimisation with Pulp

I am trying to solve a massive linear integer optimisation problem (MILP) having more than 45.000 binary variables and ~350.000 constraints. I am using Pulp for solving the problem, but I cannot find the solution in a reasonable amount of time.…
aprospero
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Solving rational number Linear Programming problem in Python

I have an LP with integer constraints that I want to solve in exact arithmetic, using Python. In fact, I only need a feasible point. Edit: "Exact arithmetic" here means rational numbers, of unbounded enumerator and denominator. Previous…
Hennich
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Java Library? - Simplex / Linear Programming / Optimization

I'm looking for an optimization library. My two requirements are that it does not use JNI and that it does not have license restrictions preventing it from being used on multiple computers commercially. The only one I've found that meets these…
Ben McCann
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How would I efficiently find the min and max values of the variables in this constraint system?

I have a system where I need to calculate the possible range of values for each variable (I don't need to find a solution to the system). Here is an illustration of an example system: Each blue line is a node (named by the label above it), and the…
lifeformed
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Scheduling optimization to minimize the number of timeslots (with constraints)

I'm working on a scheduling optimization problem where we have a set of tasks that need to be completed within a certain timeframe. Each task has a schedule that specifies a list of time slots when it can be performed. The schedule for each task can…
ldwii
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Optimization problem in Python

I need to solve a problem. I have 5 devices. They all have 4 kind of I/O types. And there is a target input/output combination. At first step, I want to find all combinations among the devices so that the total I/O number of selected devices are all…
Sansal
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What is the run time complexity of integer linear programming (ILP)?

What is the run time complexity of integer linear programming (ILP) problem when, there are N number of variables and R number of constraints? For coding purpose I am using Matlab's intlinprog function. Any reference would be helpful.
Saikat
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Minimize the max value in Gurobi optimaztion

I am developing a model to solve a MIP problem using gurobi and python. The problem involves travel times over a set of predefined routes. One of the objective functions I am trying to realize is to minimize the maximum travel time for the selected…
David Oliver
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Gurobi Python API: model.addVars() too slow

I'm currently working on using Gurobi Python API to solve a large-scale LP. I found that the process of adding variables takes too much time, in some cases even more than the optimizing time. My code is roughly like this (I deleted the read data…
user12345
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PuLP - How to specify the solver's accuracy

I will try to keep my question short and simple. If you need any further information, please let me know. I have an MIP, implemented in Python with the package PuLP. (Roughly 100 variables and constraints) The mathematical formulation of the problem…
Axel
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Linear program question

I'm trying to prepare for my midterm and I was going over some problems out of my algorithm book but can't seem to figure out the following problem: Find necessary and sufficient conditions on the reals a and b under which the linear program max:…
sap
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Find the Discrete Pair of {x,y} that Satisfy Inequality Constriants

I have a few inequalities regarding {x,y}, that satisfies the following equations: x>=0 y>=0 f(x,y)=x^2+y^2>=100 g(x,y)=x^2+y^2<=200 Note that x and y must be integer. Graphically it can be represented as follows, the blue region is the region that…
Graviton
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