Top 3 Reasons You Should Understand the Math Behind Network Design

Commercial network design tools (like IBM’s ILOG LogicNet Plus XE) hide the math formulations behind an easy-to-use interface and take care of the sophisticated solve automatically.

This is how it should be.  You don’t want to think about the math when doing a project like this.  You want to successfully complete the project.

However, in the book, we cover some of the math behind these problems.  Why do we do this?

  1. To Help You Build Better Models.  You don’t need to write the math on your own or go into the details of how the solver works.  But if you understand the math, you will be better able to set up models to do what what you want them to do.
  2. To Help You Understand What Might Be Hard vs Easy.  If you understand the math, you will understand what may make your model hard to solve.
  3. To Help You Validate the Results.  Generating a solution to a network design problem requires an understanding of Mixed Integer Programming.  But, with commercial software, you are presented results.  By understanding the math, you will be able to validate the results and make sure the solution is valid.  This allows you to better manage projects and ensure good results.


Multi-Objective Optimization in Network Design

One of the big improvements in commercial network design technology is the additional of multi-objective optimization.  As supply chain managers know, designing the right supply chain means balancing different objectives.  By being able to understand how different objectives relate to each other, you can make better decisions.

We recorded a short interview with Supply Chain Television Channel and CSCMP on multi-objective optimization (it starts at about the 7:00 minute mark).

The book has a chapter devoted to multi-objective optimization as well as information throughout the book.  For example, in Chapter 4 where we talk about different service levels we provide some insight on how to think about different objectives.

Material for a Discussion on Oil Prices and Transportation Costs

Supply chain managers watch the price of oil carefully.  The price of oil is closely related to the price of diesel fuel and that is closely correlated to total transportation spend.  An IBM blog post provides additional information on how this impacts the supply chain and a link to a nice article in The Wall Street Journal on the same topic.

In the book, we provide a mini-case study showing how oil prices impact diesel costs.   The following scatterplot shows the raw data– the weekly price of oil vs the weekly price of  diesel for 300+ observations.

This case study as well as the links above provide a nice introduction to the impact of oil prices on the supply chain.

Classic and Simple Network Design Case

On IBM’s blog, there is a simple case of a firm that was producing product in Mexico and Virginia and distributing from the two plants.  They wanted to simply analyze the territories of the distribution points and have more product shipped between the sites.  The maps below show the before and after for this design.  This firm spent quite a lot in transportation and this move alone saved them $5 million.



MSC Industrial’s New DC in Columbus

MSC Industrial recently announced that they are building a $55 million distribution center in Columbus, OH.  This will be their fifth distribution center (or Customer Fulfillment Center- CFC).  They are building it “to support its growth strategy and maintain its signature service model as the Company grows.”

Here is a key quote from the press release:

 “Our current success and growth plan requires us to add a new CFC to support our world-class service model as we continue to grow.  After conducting a thorough review, Columbus provided the most compelling opportunity to expand our distribution network in the most cost-effective manner, in a region that fits well with our existing network and provides easy access to key markets and resources, as well as a rich pool of local talent. Over the long-term, our investment in this facility will yield high returns as we more efficiently manage and expand our service volume.”

Although this article does not mention network design directly (although they do mention “conducting a thorough review”), $55 million decisions like this usually don’t happen without some type of network design and optimization.  When firms are spending this much money on a facility, they do not want to put it in the wrong place.

Also, it is interesting to note that the new center was added to support growth and service, not reduce costs.


Toshiba Uses Network Design to Evaluate Options

Toshiba recently presented at the Manufacturing Leadership Summit.  They gave a talk on “Using SCM to Create Competitive Advantage.”  (SCM = Supply Chain Management).

In the talk, they mentioned that they used network design technology to evaluate different options.  We often see this in a project.  A company many have many different ideas for changing their supply chain.  It is important to test those ideas and determine what impacts they will have on the overall supply chain. For example, if a firm can add more facilities to better serve customers, it is important to know if the transportation costs will go up by $500,000 or $5,000,000.  The importance of service may change as a result of this.

In the talk, they mentioned that their new strategies helped in the following ways:

  • The cost per shipment decreased by more than 12%
  • Obsolescence reduced by more than 40%
  • Missed service calls reduced by more than 16%


Südzucker uses Network Design to Adjust to Changes in European Regulations

IBM released a case study showing how Südzucker, Europe’s leading supplier of sugar products with an annual revenue of approximately €7 billion, used network design to adjust to changing regulations in Europe.

Here is a key quote from the case.  The link to the IBM case has more details:

When the European Union adopted a new market regulation for the sugar industry in 2006, Südzucker was forced to re-evaluate their entire supply chain network. On the one hand the company’s ability to export sugar to world markets became very limited, on the other hand major sugar deficit areas within the European Union were created. This led to a much greater focus on sales and distribution. Südzucker also knew this ruling would give them the ability to enter new sugar markets like Greece, Italy, Spain and the United Kingdom. Their challenge was to merge their national supply chain networks to create one integrated and powerful European supply chain network. The company had to determine how to modify their supply chain network by adding new facilities to ensure excellent service but also minimize transportation costs.”


Network Design in a Closed-Loop Supply Chain at Johnson Controls

IBM recently published a case study with the battery division of Johnson Controls.  The supply chain for a battery is complicated because it is a closed loop.  New batteries are shipped to the retailers.  The retailers collect the used batteries and send them back back to the recycling center.  The recycled batteries, along with new raw material, are then send back to the plants to make new batteries.

Although this closed-loop supply chain is complex, Johnson Controls still has to answer many typical network design questions such as:

  • Which suppliers and facilities should be used to optimize transportation costs?
  • How much capacity should be contracted with each supplier and facility?
  • Which battery plant and distribution center should serve which customers?