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.

 

 

 

Safety Stock to Bridge the Forecast-Accuracy Gap

(From David McPhetrige, founder of TopDown Lean Systems, LLC, providing correct, comprehensive, multi-attribute safety-stock analysis, http://topdownleansystems.com.)

Surveys indicate that even world-class companies have average forecast accuracy in only the high 70%’s, especially at the SKU or component level that makes or breaks service levels and financial performance. Contributors to forecast inaccuracy include factors that can be addressed through best practices, and factors that will always be unpredictable:

  • Chronic bias, which can be minimized with effective Sales/Inventory/Operations Planning, or SIOP. (It’s a safe bet that world-class businesses are already doing this, and they are still achieving only high 70%’s.)
  • Unforeseen and unforeseeable special causes, such as natural disasters.

The reality is that forecasting can be only so accurate, in part because it predicts the timing and magnitude of only three types of variation:

  1. Trend
  2. Seasonality
  3. Certain foreseeable special causes, such as promotions

A forecast can predict the timing and magnitude of these variations only so well. Realistically, then, many businesses – and even world-class companies – are left with a significant forecast-accuracy gap that, if not bridged, compromises target fill rates, inventory performance and financial goals.

So first, how do you bridge this gap today? Obviously, you strive continuously to improve your forecasting accuracy, and you always will. That said, though, here are some bridging “techniques” that I’ve observed and even been part of, and likely you can think of some that I’ve missed:

  • Mind-set: Complain about, but begrudgingly resign yourself to, suboptimal inventory and fill-rate performance, and related costs and risks
  • P&L: Increase the budget for airfreight, expediters or other expediting costs and expenses
  • Balance Sheet: Increase safety-stock levels
  • Obsolete/Slow-moving: Increase efforts to return excess materials to suppliers

Some of these techniques can and do help achieve service-level targets. But at a minimum, they rarely help, and may in fact hurt, financial performance. Fortunately, a financially-beneficial service-level bridge from forecast to reality is right there in your data! How so?

Well, there is still variation that’s left over after bias, unforeseeable special causes and the three variations with predictable timing: Common-cause random variation in demand (or usage, for components) and replenishment lead time.

The good news is that it is possible to quantify the magnitude of random variation by analyzing historical demand and/or lead-time data. Of course, the timing of random variation is unpredictable (that’s what makes it random), and this means that common-cause random variation must be addressed with properly-determined safety stock.

At this point, you may be saying, “I’m already doing that. I use a statistical technique to determine my safety stock levels.” Forgive the blunt and clichéd reply, but – how’s that working for you? Honestly, is your technique consistently achieving your fill-rate targets on an item-by-item basis? Or does it often seem to put too much inventory in place? And in many cases, does it put too little inventory in place, and you have to subjectively override or increase the calculated safety-stock level?

The fact that your safety-stock calculation is unreliable does not mean that there is no statistical solution. What it does mean, however, is that you must

  1. Properly identify and isolate the common-cause random variation from all the other variations, and
  2. Use a correct, comprehensive statistical safety-stock approach that includes not just common-cause random variations in demand and lead time, but all six factors that affect safety stock, service levels, inventory performance and expediting.

We aren’t talking about a spreadsheet, or perhaps an unused ERP feature. We’re talking about outside expertise in safety-stock analysis.

A recent CSCO Insights executive brief (from Supply Chain Digest and Cognizant) entitled “Five Strategies for Improving Inventory Management Across Complex Supply Chain Networks” recommends this as the first of five strategies: “Get Much More Granular with Safety Stock Management.” (http://www.scdigest.com/assets/reps/exec_brief_network_inventories.pdf.)

This brief advises using “many more attributes associated with each SKU.” The result of this expanded effort is compelling: “The greater the [safety-stock] precision a company will have.” The CSCO Insights authors advise that to do this “obviously requires a lot more work,” and that this increased analysis offers “rich dividends.” The brief concludes that pursuing the strategy of a “higher level of safety stock management” may require a “relatively uncommon skill set” that may best be provided by outside expertise.

Total Flow Management

 

Euclides A. Coimbra and his associates at the Kaizen Institute have created a wonderful and detailed work on the application of continuous improvement to supply chains.  Here is a full exploration and application of lean from end to end of the extended value stream.  Two thumbs up!

Some of the graphics look to once have been powerpoint and when reproduced are to small and grainy to be able to read.  There isn’t an index so finding topics is limited to the table of contents.  The book is hard bound, and printed on good paper.

Some of the vocabulary is odd; “border of line” might be better said as” interface” or “borderline”.

Economic Order Quantity, or as referred to in this book, Wilson’s Formula, is treated in a refreshing way.

We can say that Wilson’s formula still applies today.  The only problem is when people assume that changeover time (or, generally speaking, ordering cost) is rigid and cannot be reduced.  Many people don’t think to do Wilson’s calculations because they are still misled by two strong paradigms: flow at any cost and efficiency at any cost.

The ‘flow at any cost’ paradigm is a rising paradigm that is currently gaining in popularity.  People hear about the wonderful Toyota Production System (TPS) and start to increase the flow by reducing the batch sizes blindly, without looking at Wilson’s formula.  What happens is that the CAPEX requirements explode, because the small batch sizes together with big changeover times decrease efficiency.  The result is that flow is indeed achieved – but at the expense of capital expenditure, not by internally reducing the changeover time and increasing equipment flexibility.  You can see this effect in many rich companies that are implementing Lean manufacturing and the TPS.

For a more in depth review check out Jon Miller’s posting on Gemba Panta Rei,
Review of Total Flow Management by Euclides Coimbra.

Demand Segmentation and Building a Lean Fulfillment Stream

 

 

 

Hot off the press from the Lean Enterprise Institute

Page 12 & 13 have a brief description of Coefficient of Variation and a SKU Scatter Diagram (weekly volume vs. SKU stability).  10 weeks usually isn’t sufficient for meaningful or statistically significant calculation of standard deviation.

The guidelines given need to be tempered with the granularity of the data.  While a coefficient of variation of less than 1.0 can be considered stable for weekly data, it would be considered very noisy when using monthly data and quite stable when using daily demand.

This small quibble aside the authors Martichenko and von Grabe do a wonderful job describing lean principles for the supply chain, or as they prefer, the fulfillment stream.

 
 

 

Replenishment Strategies

Determining an appropriate production model starts with Demand Profile and Demand Segmentation.  High volume low variability items, and low volume high variability items behave very differently.  How to decide if a particular product is a candidate for a one piece flow cell or a craftsmen job bench?  Look to the coefficient of variation for a clue.

Demand Segmentation - Volume vs Variability

 

Type 1 – Rate-base or Just-in-time

  • forecasting of the flow rate or takt time
  • RCCP – rough  cut capacity planning to monitor impact of mix and volume on pace maker operation
  • produce to rate (or TAKT) vs discrete order or customer pull
  • demand flow vs time-phased requirements planning
  • maintain flow priority and timing
  • no detailed Capacity Requirements Planning required
  • no or minimal shop order launch or inventory transactions
  • highly visual and standardized shop floor control
  • “one-piece” flow, zero inventory, standard WIP – work-in-process
  • seamless flow/pull of material
  • Dynamic cycle time (Little’s Law)

Type 2 – Pull

  • combination of discrete forecasting and/or demand rate-based forecasting
  • MRP planning — pull Kanban, Heijunka visual shop floor control
  • RCCP, but no detailed CRP
  • flat Bills Of Materials
  • more cellular manufacturing
  • point-of-use vs. central stores
  • inventory is strategic: standard inventory, time-based replenishment, pull based on consumption vs. push based on demand
  • based on statistically balanced rate, build to level-loaded demand with calculated standard inventory buffers

Type 3 – Push or Job Shop Discrete

  • discrete requirements planning (firm orders and long range forecast)
  • Rough Cut Capacity Plan
  • time phasing of requirements
  • application of order policies: lead time, safety stock & time
  • Capacity Requirements Planning
  • MRP shop order launch & order maintenance (message filters and “noise management”)
  • ability to aggregate disparate requirements across multiple products by work center, supplier, product
  • central stores of inventory
  • multi-level inventory: stores, pick, kit, move, queue
  • batch processing
  • demand leveling difficult and uneconomical