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Is a Center-of-Gravity Analysis Right For Your Network?

Due to relatively low desktop computing power and the lack of available supply chain-focused modeling software, early 1990s logisticians were forced to use spreadsheets to optimize distribution networks. Beyond Lotus 1-2-3, the next level of sophistication in determining where to locate DCs was a “center-of-gravity” (CoG) analysis. Derived from applied mathematics, the concept of CoG was most likely demonstrated in any introductory high school physics course: If you wanted to balance a baseball bat on your index finger so that the bat remains horizontal, common sense would suggest choosing a point equidistant from the ends. However, this does not achieve balance. Instead, you want to choose the point where the amount of weight is equally distributed to the left and right of your finger, which is much closer to the end of the barrel of the bat. This balancing point is the baseball bat’s “center of gravity,” which can be calculated using algebraic formulas.  Applying this concept to logistics, the center of gravity for demand can be calculated using the same applied mathematics, based on the amount of flow (e.g., cases) over a specific distance (e.g., miles).  Certainly an improvement over spreadsheet calculations, but does center-of-gravity analysis still hold weight in determining your network design?  The answer is a cliché:  It depends.

 

Situations where a center-of-gravity analysis adds value:

  1. Direct Store Delivery (DSD) Networks with multi-stop deliveries with a high density of customers in the same zip code. For DSD demand, delivery expense is the largest component of the supply chain and minimizing the weighted average miles for delivery is almost always aligned with to the calculated center of gravity.
  2. Determining “candidate” DC locations as an “input” to a national network study (not, however, as an answer or output). In other words, when determining the center points for pockets of demand, you want a best-of-breed distribution network model to consider as an option.
  3. Single DC networks that do not justify a six-figure software investment nor have a skilled professional to run that type of software.
  4. To help validate, or build an inference to, results of a complex network model requiring complex, PhD-level mathematics. In other words, does my answer pass the “sniff” test if the CoG analysis indicates Pittsburgh, PA, and my sophisticated modeling software is telling me El Paso, TX, is correct?

 

The downside of a center-of-gravity (only) solution:

  1. Only delivery miles and demand flow are typically considered in most CoG algorithms. This means that inbound and interplant costs are ignored. Our experience finds these “in-flow” costs influence the location of the DCs more than delivery costs, due mainly to concentrated sourcing points. Do not be fooled, though, sub-optimizing outbound flows via a CoG analysis does NOT necessarily achieve the least total delivered cost solution.
  2. The distance considered by CoG calculations are “as-the-crow-flies,” and ignore over-the-road miles or other geographic obstacles, such as bodies of water or mountains.
  3. Transportation rates for common carriers are not the same per mile for each origin/destination pair due to equipment imbalances by region. For example, freight rates into New England are much different per mile than freight rates into Southern Florida. Another related downside is that minimum charges from carriers are not considered in CoG calculations.
  4. Real world logistics constraints are ignored in CoG calculations.Typically, these constraints can be integral to finding the correct solution.  For example, storage space constraints, production capacities, storage-condition eligibility (ambient versus frozen), delivery time maximums, etc. all need to be simultaneously considered by the analysis.
  • Mode of transport is ignored by CoG calculations, thus for clients with a mix of parcel, LTL, and FTL deliveries in their customer delivery profiles, more than just weighted-distance variables are needed. Shipping costs per mile or per pound are very different for a mixed-modal delivery network and need to be considered by the analysis.

 
 
In conclusion, CoG analysis has a much narrower window of applicability than most leaders in supply chain management think, due to its age and past utilization. In fact, our experience over the last 25 years indicates that in the vast majority of supply chains, CoG analysis alone will lead to the WRONG conclusions. It can also lead to a significant missed opportunity to lower your overall supply chain costs.  This is further complicated by the fact that a large percentage of supply chain leaders think that a CoG analysis is “essentially” what MILP software is doing.  As you can see from the points made above, a CoG approach is very different than MILP, and inferior in most respects.
 
—Craig Vorse, St. Onge Company
 
 

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