As you build your supply chain model, you will notice slight differences in your simulation results 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.
Sensitive Dependence on Initial Conditions Creates the Butterfly Effect
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. 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)
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 or ships work best 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 known as “Attractor” solutions.
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. Despite these small differences, overall performance of these supply chains remains close to optimal for all of them (read more about this in “All Supply Chain Models are Approximations“).
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 situations change. Effective use of people, process and technology in supply chains enables them to learn and get closer and closer to optimal states (attractor states), and stay closer for longer and longer periods of time.
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. SCM Globe is a deterministic, nonlinear simulation.
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.
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!
You will see there is not a bug… But there is a butterfly.
More Insight into the Butterfly Effect and Nonlinear Dynamics
- Quick read and interesting article in Forbes “Chaos Theory, The Butterfly Effect, and the Computer Glitch that Started It All“
- Here is an example of the results produced by the simple Lorenz weather forecasting model.
- Engaging video by two professors at University of Nottingham, UK. They demonstrate the Butterfly Effect using examples from pool balls traveling across a pool table to the way weather systems evolve:
[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 the accuracy of certain calculations was improved. 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.]
Copyright © 2016 by SCM Globe Corp.