Using R to visualize geo optimization algorithms

May 26, 2013

(This article was first published on progRamming for the fun of it , and kindly contributed to R-bloggers)

Site optimization is the process of finding an optimal location for a plant or a warehouse to minimize transportation costs and duration. A simple model only consists of one good and no restrictions regarding transportation capacities or delivery time. The optimizing algorithms are often hard to understand. Fortunately, R is a great tool to make them more comprehensible.

The basic math
A basic contineous optimization problem is to deliver goods to $n$ customers. Every customer has a individual demand $a_j$ and is approached directly from our warehouse. The single routes have a length of $d_j$. The objective function to be minimized is:

$$min(\sum^{n}_{j=1} a_j \cdot d_j)$$ 
How can on calculate distances? Typical distance measures for flat surfaces most of you are probably familiar with are Taxicab distance and Euclidean distanceWe will calculate spherical distances to get a better solution for large routes: $$\\d_{a,b} = arccos[sin(y_a)\cdot sin(y_b)+cos(y_a)\cdot cos(y_b)\cdot cos(x_a-x_b)] \cdot R\\$$ R denotes the Earth radius: ~ 6,370 km. Keep in mind:
  • …To use geographical coordinates in the form of decimal degrees
  • … To transform them to radian units (by multiplying pi/180).

How to optimize
We will use an iterative way for optimizing:
  1. set an initial warehouse location: $x_{start}$ and $y_{start}$ 
  2. for every iteration the current warehouse location $(x_w, y_w)$ is calculated by: $$x_w=\frac{\sum_{j=1}^{n}{a_j \cdot \overline{x}/d_j}}{\sum_{j=1}^{n}{a_j/d_j}}  \quad \quad y_w=\frac{\sum_{j=1}^{n}{a_j \cdot \overline{y}/d_j}}{\sum_{j=1}^{n}{a_j/d_j}}$$

Red circles are customer locations. Their surface area represents the individual demands. The single iterations start with dark blue circles and end with the final warehouse location, colored in green.

Click here to download the data file. Below the code:

To leave a comment for the author, please follow the link and comment on their blog: progRamming for the fun of it . offers daily e-mail updates about R news and tutorials on topics such as: Data science, Big Data, R jobs, visualization (ggplot2, Boxplots, maps, animation), programming (RStudio, Sweave, LaTeX, SQL, Eclipse, git, hadoop, Web Scraping) statistics (regression, PCA, time series, trading) and more...

If you got this far, why not subscribe for updates from the site? Choose your flavor: e-mail, twitter, RSS, or facebook...

Comments are closed.


Mango solutions

RStudio homepage

Zero Inflated Models and Generalized Linear Mixed Models with R

Dommino data lab

Quantide: statistical consulting and training



CRC R books series

Six Sigma Online Training

Contact us if you wish to help support R-bloggers, and place your banner here.

Never miss an update!
Subscribe to R-bloggers to receive
e-mails with the latest R posts.
(You will not see this message again.)

Click here to close (This popup will not appear again)