# Linear programming

## Augmented epsilon constraint method: Multi-goal optimization with Pulp in Python In previous posts, we have discussed using PuLP in python for the implementation of multi-objective linear optimization methods such as maximizing for one objective, then adding it as a constraint, and solving for the other objective (or applying a scalar […]

## Scalarizing multi-objective optimization problems: Method comparison I already introduced various coding examples implementing multi-objective optimization. In these examples I implemented different strategies for searching a multi-objective optimum. One of these strategies was based on scalarizing multiple objectives into a single objective function using weights for each […]

## Prescriptive Analytics for Supply Chain Network Design One of the duties I frequently performed as an operations research analyst in consulting projects was optimizing companies’ supply chain network designs. A supply chain is a network that connects suppliers with customers to procure materials, transform them into final […]

## Linear integer programming with Google ortools in Python In a several other posts on Google’s ortools module in Python I have already solved the linear optimization problem stated below. The problem is a continuous problem as all optimization variables are from a continuous solution space. I could think […]

## Lean coding of simple linear optimization ortools models in Python In a previous post on Google’s ortools module in Python I solved the linear optimization problem stated below: The code written in my previous post can be reduced to fewer lines of code, resulting in lean code. In this post […]

## Simple linear programming with Google ortools in Python In other posts I have demonstrated how one can solve e.g. linear optimization problems using modules such as SciPy and PuLP in Python. In R I have also demonstrated e.g. the lpSolve package. In this post I want to demonstrate […]

## Multi-objective linear optimization with weighted sub-problems, using PuLP in Python In my most recent post on linear programming I applied PuLP for solving below linear optimization problem, using two approaches. Approach #1 was based on solving a sub-problem with one objective only first, then adding the optimal outcome of that […]

## Multi-objective linear optimization with PuLP in Python In some of my posts I used lpSolve or FuzzyLP in R for solving linear optimization problems. I have also used PuLP and SciPy.optimize in Python for solving such problems. In all those cases the problem had only one objective […]

## Continuous linear optimization in PuLP (Python) In a previous post I demonstrated how to solve a linear optimization problem in Python, using SciPy.optimize with the linprog function. In this post I want to provide a coding example in Python, using the PuLP module to solve below […]

## Solving linear problem with fuzzy constraints by sampling beta with FuzzyLP in R In a previous post I demonstrated how to use crispLP to solve a simple linear optimization problem with well-defined objective function and constraints. I have also demonstrated how to solve a fuzzy linear optimization problem with uncertain constraints, i.e. fuzzy constraint […]

## Linear optimization with fuzzy constraints conducted in R with FuzzyLP Using the FuzzyLP package in R I have demonstrated simple linear optimization of a well defined linear problem using the crispLP function in a previous post. In that example basic simplex algorithm was applied to solve the problem. In this […]

## Simple linear problem with FuzzyLP, using crispLP and basic simplex In previous posts I have demonstrated how to solve linear programs in R using lpSolve – or in Python using SciPy.optimize. In this coding example I want to show how to conduct simple linear optimization using the FuzzyLP package. FuzzyLP […]

## Linear optimization in Python: Using SciPy for linear programming In previous posts I showed how to conduct optimization in R (linear optimization with lpSolve, quadratic optimization with quadprog and non-linear gradient descent optimization with nloptr). In this post I show how to model and solve the linear optimization problem […]

## Cost minimal production scheduling – solving the assignment problem with lpSolve in R The assignment problem is a classic problem in linear program. If, for example, you have n jobs that need to be manufactured during the upcoming shift (in a manufacturing plant) and you have m machines to produce these tasks, then you want […]

## Solving linear transport problem with lp.transport in R, using lpSolve The transportation problem is one of the classical problems teached in linear programming classes. The problem, put simply, states that a given set of customers with a specified demand must be satisfied by another set of supplier with certain capacities […]