Little’s Law and Supply Chain Disruption

Sixty years ago, a young Professor at MIT, John Little, wrote a paper during his family vacation in Nantucket on a theorem which has become widely known as the Little’s Law. It was originally developed for queueing systems consisting of discrete objects, but has since become the Newton's Law in supply chain management to explain relationships among inventory, flow time, and turnover because of its theoretical and practical importance. With all the current global supply chain disruptions due to pandemic and geopolitical development, I thought it might be an interesting topic to discuss.

Mathematically, Little’s law is stunningly simple:?Lead Time = Work in Process(WIP) / Throughput Rate. For example, if a baseball ticket office receives about 240 customers per hour in average and it takes about 3 minutes (0.05hrs) to complete a transaction for purchasing a ticket, there would be about 240 times 0.05, or 12 people in the line in average. (Good luck if this example makes you think about attending the World Series Games between Houston Astros and Atlanta Braves!)

One of the powerful applications of Little’s Law is to bring clarity on bottlenecks for designing or operating complex operations. Little’s law has been widely used to optimize operations such as the FastPass queuing system at DisneyWorld. Each restaurant, especially fast food restaurants where speed is critical, has different ways in managing the waiting lines. McDonald tends to have multiple parallel lines serving several waiting queuing lines where you always feel your line is the slowest one. Panera Bread uses cashiers taking order from one line and then you pick up food at a separate line. Others have multiple cashiers serving one queuing line.?An analysis with Little’s law could often enhance both efficiency and customer experience. I shared an article about the relationship between tulip flowers and oil price which was also a relevant example of inventory bottleneck which caused oil future to fall to negative for the first time in history in 2020.

The operation of Long Beach and LA ports, similar to many others, have been hampered by the current supply chain disruptions with many container vessels waiting at sea for a berth at the Southern California ports because terminals are so full with Asian imports that there is little room for unloading. My son shared with me a fascinating story which occurred last week.

Mr Ryan Petersen, CEO of the freight forwarding startup Flexport, wanted to understand the situation at the ports of Long Beach and Los Angeles. So he rented a boat last week and personally observed the operations up close with real time insights to facilitate decision making. Based on his Twitter sharing on some fundamental insights about operations management while he was touring the ports, it is safe to assume that he understood Little’s law well.

Mr Peterson first determined that crane operation for unloading was not the bottleneck although it conceptually should be designed as the bottleneck due to the expensive equipment. Further investigation indicated that the bottleneck had shifted to the yard space at the container terminals. The terminals were simply overflowing with containers, which meant that they no longer had space to take in new containers either from ships or land. When you are designing an operation you must choose your bottleneck. Paraphrasing Mr Peterson, if the bottleneck appears somewhere that you didn't choose it due to disruption, the negative feedback loop can rapidly cycle out of control unless actions are taken to expand the capacity at the new bottleneck.

It turned out that one of the reasons for the logjam at the port was drivers could not take the containers off the chassis due to Long Beach zoning code which limits empty containers no more than two high in the truck yard to minimize the visual impact of industrial equipment in neighborhoods. He shared his observations via Twitter which apparently got the attentions of city and state officials. The city of Long Beach on last Friday issued an emergency order allowing businesses to temporarily increase how high they can stack ocean containers in their lots in an effort to reduce the massive gridlock gripping the ports of Los Angeles and Long Beach. The temporary change in Long Beach will not solve the global supply chain issues but Mr Peterson certainly made a difference for the Long Beach port through his leadership by converting his knowledge into action. Thanks!

Related Articles

What Oil Price has Anything to Do with Tulips??(05/17/2020)

Boston Tea Party and Trade with China (09/21/2020)

(Please join the 230,000 subscribers to my newsletter by clicking the?subscribe?button on the top of the article to be notified of new editions. Better yet, please join the conversation by sharing your comments. Thanks.)