The Butterfly Effect

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As you build your supply chain model, you will notice slight differences in the simulation results produced by your model and the simulation results produced by others who create similar – but not exactly identical – supply chain models. Small differences in the placement of facilities, the definition of vehicles, and creation of routes add up during the thousands of calculations done by the SCM Globe simulation engine. A facility may run out of products a day earlier or later in your simulations as compared to results from simulations of others working on the same case study. Amounts of on-hand inventory and operating costs may differ somewhat.

Yet regardless of these differences, simulations still show which supply chain designs work best in any given situation. They show whether trucks or railroads or airplanes work better in that situation. They show the best locations for different facilities, and they show how inventory flows through those facilities. They also identify facilities in a supply chain where problems are most likely to occur, and provide useful data for deciding how to respond to those problems.

Although each individual simulation follows its own unique trajectory, if you use the simulation results to keep adjusting your supply chain model so as to minimize cost and inventory while always meeting product demand, then your supply chain model, and all other models in a given situation, will converge on one or two best solutions (read more about this in “All Supply Chain Models are Approximations“).

  Best Solutions are Known as “Attractors”

In the mathematical field of system dynamics, an attractor is a set of numerical values toward which a system tends to evolve from a wide variety of initial starting conditions. When combinations of system values (such as the four entities – products, facilities, vehicles, and routes) get close enough to an attractor (an optimal state), the system will remain stable near the attractor, even if small changes are made to individual system values. (Wikipedia: The Free Encyclopedia –

In supply chain terms, this means that despite initial differences between beginning supply chain models, all supply chains operating in a particular situation will achieve optimal performance in a similar manner. They will all converge on one or two optimal or attractor solutions. An attractor solution is a combination of values for products, facilities, vehicles and routes that optimizes total supply chain performance in that particular situation. Once different supply chains get close enough to an attractor solution, small changes or differences in their values for products, facilities, vehicles and routes do not have a significant impact. Despite small differences, overall performance of these supply chains remains close to optimal for all of them.

In the real world supply chains can neither attain nor maintain perfect optimization because there are too many unpredictable and uncontrollable variables at work. Real supply chains can approach optimal solutions, but random variances will always force supply chain operations to be less than optimal. Supply chains must continuously adjust their operations as conditions change to approach optimal performance (attractor states). Effective use of people, process and technology in supply chains enables them to learn and get closer and closer to optimal states, and stay closer for longer and longer periods of time.

Sensitive Dependence on Initial Conditions

As you make changes to the four entities (products, facilities, vehicles, routes), your changes ripple through the model and change the way the model behaves. SCM Globe is a deterministic, non-linear simulation. There are endless changes you can make. And each time you make a change, your simulation takes a trajectory determined by the cumulative effect of all the changes you have made so far. Each person’s simulation results can become increasingly different as they work with their individual supply chain models. Here is why:

In chaos theory, the butterfly effect is the sensitive dependence on initial conditions in which a small change in one state of a deterministic, non-linear system can result in large differences in a later state. The name of the effect, coined by Edward Lorenz, is derived from the metaphorical example of the details of a hurricane (exact time of formation, and exact path taken) being influenced by minor perturbations such as the flapping of the wings of a distant butterfly several weeks earlier. Lorenz discovered the effect when he observed that runs of his weather model with initial condition data that was rounded in a seemingly inconsequential manner would fail to reproduce the results of runs with the unrounded initial condition data. A very small change in initial conditions had created a significantly different outcome. (Wikipedia: The Free Encyclopedia – “Butterfly effect” –

SCM Globe is Not a Simple Linear System

We are used to working with relatively simple linear models where cause and effect is clear, and where only certain types of changes can be made. SCM Globe is different. It is a virtual sandbox where you can make an unlimited number of changes in any combination you want, and then run simulations to see what happens.

Small changes in one part of an SCM Globe model can produce unexpected or counter-intuitive results in other parts of the model (this happens in the real world too). It can be puzzling, even alarming. And at times it will cause more than a little frustration as you try to figure out how to respond to these results. You may come to believe there is a bug somewhere in the simulation.

There is not a bug. But there is a butterfly.

Sc 3 - Onhand Panela1(images courtesy of Creative Commons)

When in doubt, download the simulation data into a spreadsheet and check the math (be sure to read the answer to question 3 in FAQs). Pick a facility or a product and track it day by day through the simulation. What do you see? The numbers add up… but the result can be unexpected!

For More Insight on the Butterfly Effect…


[Disclaimer: Developers and users of SCM Globe have run thousands of different simulations and analyzed the results thousands of times since release of version 1.0 of the simulation engine in the fall of 2011. In that original version and succeeding versions, bugs were found and fixed, and we improved the accuracy of certain calculations. In this current version (Ver 2.7, in production since October 2013) there are known bugs in editing and displaying supply chain data and they are listed in the FAQs. But no bugs have been found in the actual supply chain simulations, even as usage has increased significantly. If you do find a bug please contact us immediately, and send the simulation data that reflects this bug. Be sure to read the FAQs section to see why deliveries are sometimes missed, and understand the “Day 0” calculations used to start all simulations.]


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