Logistics | Lean Sigma Supply Chain

Square Root Law – inventory in multiple locations

Got asked what would happen to inventory when the number of stocking locations change. I thought for a minute and remembered a quick estimate. The Square Root Law states that total safety stock can be approximated by multiplying the total inventory by the square root of the number of future warehouse locations divided by the current number.

X2 = (X1) * √ (n2/n1)

n1 = number of existing facilities

n2 = number of future facilities

X1 = existing inventory

X2 = future inventory

Here’s an example:

Current inventory is 4000 units, 2 facilities grow to 8. Using the square root law the future inventory = (4000) * √ (8/2) = 8000 units.

Table top simulation – dock operations

Simulation is the act of imitating or mimicking the behavior of some situation or some process by means of something suitably analogous. The imitation of a process can be used for debugging, and validating process design changes or use to communicate or train associates.

Simulations can be used for:

process design
testing new ideas
debugging designs
testing understanding
gaining commitment
testing alternatives
communicating and training

Sometimes the simulation is role playing theater, other times the ‘game’ has logic and is reproducible, with known inputs and expected outputs. The photo here is of a recent workshop where we studied how the warehouse dock floor would look after changing the pick waving rules and packaging. Here outbound goods will be switching from trailer loose stack to returnable shipping containers.

Would we need more floor space? Do we have enough pickers and loaders? How do we pick and load multiple deliveries nose-to-tail?

While computer modeling is certainly a consideration the use of table-top simulation has many benefits:

Many problems are difficult or expensive to test in real life
Many people process information visually
A number of alternatives can be quickly tested as the team uncovers issues and finds solutions
Simulation costs are very low; you don’t need expensive software or extensive training

Here’s the process we used to build our ‘war game’:

Decide what we wanted to test; i.e. the output – in this case floor loading and labor resources
Gather the input – shipping orders for a typical busy day, number of pickers by zone, number of packing loaders, shift schedules, picking and loading rates, floor space and equipment dimensions (carts, containers, trailers, etc)
Determine the constraints, rules; e.g. number of loaders per trailer, length of breaks
Document assumptions; e.g any trailer can be at any dock door, break and lunches can be staggered, etc.
Be creative and design the game pieces (entities) and determine their quantities; in this exercise carts, containers, bins, trailers
Scale physically (1inch=5feet), scale time (1 day of 10 hours took an hour of game time)
Collect metrics, such as; line per hour, wave start and end time, trailer load duration, number of floor spaces occupied, number of time floor space turned over, number of workers needed

Once the model ‘behaved’ like the current process the team began introducing rule changes which uncovered obstacles. One of the first changes was reducing the wave batch size from 90 minutes to 30. Next came changes to packaging and trailer loading. By the end of the workshop new procedures were debugged and ready for full scale dry runs leading to a live implementation next month. Stay tuned …

Tips for sizing your warehouse

Don’t get fooled by “averages”
Consider using statistical tools, such as standard deviation, to analyze operational data – both in and out bound
Understand which system components can expand by adding labor, and which can’t
Design expansion capability in from the start; SKU count almost always goes up, not down over time
Get executives to sign off on future sales projections that will serve as the basis of the design; if they won’t or can’t, then round up
Be very leery of unrealized plans to increase inventory turns; easier said then done
Consider ability to add overtime and additional shifts to expand initial system capacity
Recognize more companies regret having less capacity than those that think systems were over-specified
You can usually add labor to increase throughput in pick modules, but if a sorter is maxed out, there is not much you can usually do

Safety Stock Optimization

Many of you are looking for a correct, comprehensive safety-stock calculation. My company’s approach is based on more than 15 years of development and testing. As we have learned through extensive experience, optimized safety stock requires more than a formula. We use complex demand–data modeling and calculations. We provide a service, not a spreadsheet. You send us your data. We send you the results.

Our safety-stock model is correct and comprehensive, providing optimal safety stock levels for your service-level and financial-performance targets. We include all the factors that affect safety stock and service level, and apply the proper statistical techniques to them. We do not utilize the usual stockout-event-based metric, but the same quantity-based fill-rate criterion that most companies use to measure actual service-level performance during a month, quarter or year. Our calculations represent the right-skewed and sporadic patterns typical of real demand data. Our model also includes past-due demand and its disruptions, probability of past-due-demand cancellation, lead time, reorder quantity (MOQ, EOQ, etc.), package size and reorder-review frequency. Finally, our results provide a high degree of confidence, typically 95%, of consistently achieving your target service levels without costly expediting.

For more details, see our white papers at www.topdownleansystems.com/white.htm. Page 16 of the “Common Safety Stock Calculations” white paper has examples of our safety-stock analysis. Also, see how you do on our Safety Stock Quiz, at www.topdownleansystems.com/quiz.htm.

To demonstrate the power of our approach, we would be happy to calculate and analyze safety-stock levels for a sample of your inventory items at no charge. Send me data on up to 30 of your items, and we will send you results – safety stock quantity and safety stock days for each item. Our analysis also includes each item’s range of expected actual performance for fill rate; average reorder and on-order quantities; average quantity on-hand, days on-hand and inventory turnover; average daily demand and demand activity percentage.

We require this data for each item: Item identifier, target fill rate, reorder quantity (MOQ, EOQ, batch size, lot size, etc.) or reorder frequency, package size (order multiple), lead time, probability of past-due-demand cancellation, days in actual service-level measurement cycle, and as much historical daily time-series demand as possible (three years is best, two is better, one is good). We perform extensive pre-screening on your input data to identify potential issues and to avoid “garbage in, garbage out.”

Send me your contact information via www.topdownleansystems.com/contact.php. I’ll provide you with a file containing input-data examples. Of course, I’ll be happy to explain our model in more detail and to answer your questions, at your request.

David McPhetrige, TopDown Lean Systems