# All Supply Chain Models are Approximations

All supply chain models must be approximations because making absolutely precise measurements of supply chain entities in the real world is not possible. One can make very precise measurements (fractions of millimeters and seconds) at the level of a machine tool making an engine part. One can still be precise at the level of a whole factory (fractions of meters and minutes). But what level of precision is realistic when measuring operations across an entire supply chain?

Is it possible to measure the precise weight of every product in a supply chain down to the last fraction of a kilogram? What if the products being measured are shipping containers loaded with a similar mix of items, but not precisely the same mix of items in every shipping container? Is it possible to measure the precise length of a delivery route? When people talk about the distance between two facilities do they mean the distance from one facility’s loading dock to the other facility’s loading dock, or the distance from the front entrance of one facility to the other? When measuring time is it realistic to attempt to measure seconds and minutes or better to go with hours and days?

Levels of Precision in Supply Chain Models

Google Maps measures route distances based on how closely its route line actually follows the real road. The screenshot below shows how the blue Google Map route lines follow actual roads closely — but not exactly. Even two actual vehicles traveling on these roads will record slightly different distances due to things such as swerving within their lanes or the turning radius of the turns they make. Potential distance errors from close, but not exact, route lines can add up to several kilometers on a short route and much more on a longer route, especially if there are lots of twists and turns on a route. So route distances are always approximations.

Truck speeds are also approximations. When a truck departs, will it always travel at exactly 90 kilometers per hour? What if there is a traffic jam or the truck has engine problems? What about the time it takes to drop off or pick up products at facilities on the route? Specifying exact speeds down to the last kilometer per hour is not possible in the real world. So within a supply chain simulation truck speeds represent an average speed over the route that includes the factors above.

Supply chain models can only be defined at levels of detail that correspond to what is possible in the real world. What does it mean for a truck to leave a factory at precisely 20.05 hours after it returned from its last delivery? Is that realistic? Will there be a manager with a stopwatch on the loading dock dispatching trucks at precisely the right moment?

Margins of Error in the Simulations

Small differences in measurements one way or another are not significant because they are within the margin of error of the supply chain model. Opinion polls and research surveys operate with acceptable margins of error defined as 4 – 8 percent with a 95 percent confidence interval. The same is true of supply chain models and simulations. Results shown by simulations are not absolutely precise. Depending on small differences in data values used to define the four entities, results can vary 4 – 8 percent (and occasionally more). In simulations this is known as the “Butterfly Effect”.

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

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. Small differences between the models do not make a significant impact on their overall performance. Small differences in operating costs and inventory levels shown in the simulations are not significant if they fall within the margin of error for the simulation.

Supply chain models that produce simulation results within the margin of error of a simulation are equally good. For instance, suppose a simulation based on model A creates a total on-hand inventory level of 350,356, and a simulation based on model B creates a total on-hand level of 350,489. These simulation results are within the margin of error, and both supply chain models are equally qood.

Realistic Levels of Supply Chain Optimization

Because measurements of activities related to individual machine tool operations and individual factory operations can be done at greater levels of precision, optimizations for machine tools and factories can also be quite precise. But measurements of supply chain operations must necessarily be less precise than for machine tools and factories. So optimization solutions for supply chains are also less precise.

Optimizing supply chain operations by using levels of detail that exceed what a supply chain model can realistically support may be mathematically possible, but it produces supply chain designs that cannot be implemented in the real world. This is because the level of precision required of the supply chain to produce the calculated optimal performance is unattainable.

For instance, suppose there is a truck in your supply chain that runs on a route from Cincinnati and drops off products at stores in Indianapolis and Chicago. After some experimentation you find the best result comes from a delay between departures for the truck of precisely 13.36 hours, as shown in the screenshot below.

This best result also assumes the truck can run its route to Indianapolis, Chicago and back (calculated at 957.84 km) and then wait precisely 13 hours and 21.6 minutes before departing again. It also assumes the truck will maintain a speed of exactly 90 km/hr over the length of the route. Calculations can be done assuming all these variables will be just as specified. But that does not mean the resulting precision of the calculations is realistic because the assumptions that made them possible are unrealistic.

Small changes to these precise but unrealistic numbers can deliver results that are almost as good. And small changes can create realistic designs that could be implemented in actual supply chains. Having a delay between departure of 12 hours instead of exactly 13.36 hours, and making minor adjustments to the product delivery quantities at the two stores gives results that are somewhat different but are still within the margin of error for the simulation. So they are just as good, and much more realistic.

Strive for Good Supply Chains not Perfect Supply Chains

Avoid the illusion of precision that comes from using two decimal points of accuracy in the creation of your supply chain model. Even if you do use two decimal points of accuracy and create a supply chain model that produces optimal results over a 30 or 60 day period, it is still just an abstraction, and not something that could be built or operated in the real world.

Use measurements for your supply chain entities that are realistic. Be conservative in the numbers you use. Assume products are a bit heavier and bigger, make vehicles travel a bit slower, set rent costs a little higher, and have demand levels somewhat greater than expected, etc. When you find a supply chain model that works well with those assumptions, then you know it will work even better if the actual numbers turn out to be more advantageous than those you used.

In a complex world where changes are hard to predict and hard to control, supply chains should be built with an appropriate degree of resiliency. The degree of resiliency is reflected in the conservative nature of the measurements and assumptions you use to build your model. The best supply chains are those that deliver good results even under conditions that are more demanding than what was expected.

Perfect performance in a predictable world is an illusion. Value lies in designing supply chains that deliver good performance in a difficult world.

As you build more realistic and complex supply chain models be sure to use the modeling techniques presented in “Tips and Techniques for Building Supply Chain Models