The Butterfly Effect

As you create your supply chain model, there will be slight variations in the results produced by your simulations and the simulation results produced by similar – but not exactly identical – models created by others. Slight differences in where you place facilities and how you create 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 model as compared to results from a similar model. Or amounts of on-hand inventory and operating costs may differ somewhat. The longer you run your simulation, and the more changes you make, the more different your results will become from the results of others. Yet despite these differences, the best models (those performing with the lowest operating costs and lowest inventory levels) will all converge on one or two similar designs.

The simulations will show which supply chain designs work best in any given situation. They will show whether trucks or railroads or airplanes work better in that situation. They will show the best locations for different facilities, and they will show how inventory flows through those facilities. They will also identify facilities in a supply chain where problems are most likely to occur, and provide good answers for how to best 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.

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 – http://en.wikipedia.org/wiki/Attractor)

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, overall performance remains close to optimal for all of them.

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” – http://en.wikipedia.org/wiki/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 about “Day 0” calculations in question 3 of the FAQs section). 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.

 

[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 accuracy of some calculations. In this current version (Ver 2.7, in production since October 2013) there have been no bugs reported in the 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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