Using column generation to minimize production waste

Minimizing production waste can result in significant cost savings. However, calculating just the right production configuration can be a tedious task.

Let’s take the example of a firm which delivers sheet metal. The sheets it delivers are all of the same width but can differ in length. The raw material used by the company are metal sheets of 3 meters wide by 20 meters long. Clients can order any length metal sheets (as long as it doesn’t exceed 20 meters).

Let’s say there is demand for the following lengths of sheet metal (all are 3 meters wide). The number of demands are denoted in the next line. E.g. for 40 items of length 6 have to be produced, 5 items of length 9 have to be produced and so on.

items_demands
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December 11, 2012Permalink Leave a comment

Linear programming in R: an lpSolveAPI example

First of all, a shout out to R-bloggers for adding my feed to their website!

Linear programming is a valuable instrument when it comes to decision making. This post shows how R in conjunction with the lpSolveAPI package, can be used to build a linear programming model and to analyse its results.

The lpSolveAPI package provides a complete implementation of the lp_solve API.

The example case;

A trading company is looking for a way to maximize profit per transportation of their goods. The company has a train available with 3 wagons. When stocking the wagons they can choose between 4 types of cargo, each with its own specifications. How much of each cargo type should be loaded on which wagon in order to maximize profit?

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July 14, 2012Permalink 11 Comments