Location-Allocation Problems
Abundant applications of Operations Research (OR) are found in logistics, the art of managing and controlling the flow of goods from the point where raw materials are collected to the point where finished products are delivered to the end consumers. In the case where a large number of customers reside in a large-scale region, it becomes inefficient to transfer finished products to all of them from a central warehouse. A better idea would be to build local distribution warehouses in the region to reduce transportation time and costs and improve customer service. However, costs associated with the construction, maintenance and operation of the warehouses increase as more warehouses are built. This is why determining the optimal number and locations of the warehouses in the region is important in ensuring that the overall result is a saving. This class of problems are known as location-allocation problems, which involve determining the optimal number and locations of facilities (such as warehouses, retail stores and gas stations) as well as the allocation of the customers to those facilities.
It is impossible to figure out simultaneously the optimal number and locations of the warehouses and the best way to allocate customers to each warehouse. A location-allocation problem must first be decomposed into three separate optimization problems:
- Determination of the optimum number of warehouses. This is usually done in an iterative manner. A process where new warehouses are added by dividing old ones is repeated until the point where saving gained from reduced transportation costs due to the addition of a new warehouse is equal to the expenses of further warehouse operation.
- Allocation of customers to the warehouses. In addition, distribution areas supplied from every warehouse are determined.
- Optimization of the locations of the distribution warehouses in the distribution areas determined in the previous step.
The results from the three problems are then combined to form the solution to the entire location-allocation problem. An example of a location-allocation problem would be where to set up 7 temporary clinics that provide free flu shots to children in a particular city where there are 25 hospitals in total. Each clinic will be located in one of the hospitals. The objective would be to select 7 hospital that minimize the total travel distance for all flu shot recipients.
GIS
The solutions of a location-allocation problem are usually presented in a geographical frame of reference. This is where Geographic Information System (GIS) becomes an important and handy tool for OR analysts. According to GIS.com:
GIS is a collection of computer hardware, software, and geographic data for capturing, managing, analyzing, and displaying all forms of geographically referenced information.
Basically, GIS enables you to visualize and analyze the relationship between certain attributes (e.g. the number of fire-accidents during a particular year) and location data (e.g. addresses) and then answer questions such as “How many fire departments should be placed in this region of the city?”. As shown in the figure, GIS can be thought of as a system that stacks layers of information over a map. However, a GIS is much more than just a simple mapping program. It is also a unique type of database of the world, a collection of intelligent maps, and a modeling tool that transforms existing datasets into new geographic datasets.
A great place to learn more details about GIS is GIS.com.
Visualizing Location-Allocation Problems Using GIS
The methods provided by GIS in visualizing the solutions to location-allocation problems include all types of eye candies such as pies, bars, icons, coloring and choropleth maps. The figure below, which is taken from the paper “Multicriteria Analysis and Visualization of Location-Allocation Problems“, shows an example of how one solution to a location-allocation problem is presented using GIS.
According to the paper, this figure shows us:
The amount of unassigned demand for sales after the optimization is presented in blue (the darker the color, the greater the value) and the regional number of different facilities is represented with pies whose diameter is proportional to the sum, the maximum being three (type 1= red, type 2 = green, type 3 = yellow).
There are many more advanced uses of GIS such as visualizing the differences of two solutions to the same location-allocation problem and customer movements over some regions. The paper just mentioned is great for learning all those methods.
References
“Planar Multifacility Location - the Location-Allocation Problem” by Vladimir Hanta, Conference on Scientific Computing, 2002
“Multicriteria Analysis and Visualization of Location-Allocation Problems” by Emilia Suomalainen, 2006
“What is GIS?” by ESRI, GIS.com
3 responses so far ↓
1 Hari // Feb 3, 2008 at 7:59 pm
Terrific work! I think your blog could well turn out to be the most prolific and comprehensive of all the OR blogs around currently. I wish I had the time to update my OR blog more frequently (I can’t seem to keep up primarily because a I also write a blog on literature, history and travel, which takes most of my time).
The layout and look and feel of your blog are great - very comprehensive. Look forward to more excellent posts. Hope also to meet you sometime at a conference maybe.
And one final point: When I started my OR blog, I’d wished ultimately that I could start at some point a magazine, not unlike the INFORMS OR/MS magazine, but something more complete - news and reporting about OR and MS from around the world, especially applied to key issues in the world such as global health, the latest science and business, explaining how OR helps in making the world work (even in remote places not just first world countries), and written in an accessible first person form. With someone like you taking the mantle, a magazine like that like that could well be a reality!
2 Suri // Feb 3, 2008 at 9:54 pm
Hello, Hari,
Welcome to ORMSblog and thanks for placing my link on your website.
Oh, boy. I can only wish that my blog will be one of the influential ones among all the websites relevant to OR. Writing articles about OR is more difficult than I thought, since my knowledge in this area is very limited. However, this website has been a great motivation for me to learn.
As you have mentioned, time is another factor that prevents us from writing more articles. I am also struggling everyday to find time for updating this blog. Maybe all of the OR bloggers like you and me should come together some day in the future and maintain a multi-author OR blog site.
A magazine is a great idea. We need more people to know what OR is and how their business could benefit from it. Yes, I agree that we need an OR magazine that is more accessible and different from the academic publications, since it would influence more young minds. I look forward to reading your magazine! When the magazine turns into reality, I would be glad to contribute if you need help.
Thanks again for your comments.
3 Howard // Feb 20, 2008 at 9:46 am
Thanks for this blog. We invite you to look at our blog at http://www.featherweightgold.com that is exploring warehouse optimization. We have coined “ExpressCube Featherweight Gold” - a new logistics and business related term that measures savings and efficiencies that companies can attain when they ship large volumes of boxes that contain light weight products. We invite you all to come, visit and if interested contribute to the conversations we helping to advance on best practices and benchmarks.
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