The Scourge of Skewness

The Smart Forecaster

 Pursuing best practices in demand planning,

forecasting and inventory optimization

Demand planners have to cope with multiple problems to get their job done. One is the Irritation of Intermittency. The “now you see it, now you don’t” character of intermittent demand, with its heavy mix of zero values, forces the use of advanced statistical methods, such as Smart Software’s patented Markov Bootstrap algorithm. But even within the dark realm of intermittent demand, there are degrees of difficulty: planners must further cope with the potentially costly Scourge of Skewness.

Skewness is a statistical term describing the degree to which a demand distribution is not symmetrical. The classic (and largely mythic) “bell-shaped” curve is symmetric, with equal chances of demand in any time period falling below or above the average. In contrast, a skewed distribution is lopsided, with most values falling either above or below the average. In most cases, demand data are positively skewed, with a long tail of values extending toward the higher end of the demand scale.

Bar graphs of two time series
Figure 1: Two intermittent demand series with different levels of skewness
Figure 1 shows two time series of 60 months of intermittent demand. Both are positively skewed, but the data in the bottom panel are more skewed. Both series have nearly the same average demand, but the one on top is a mix of 0’s, 1’s and 2’s, while the one on the bottom is a mix of 0’s, 1’s and 4’s.

What makes positive skewness a problem is that it reduces an item’s fill rate. Fill rate is an important inventory management performance metric. It measures the percentage of demand that is satisfied immediately from on-hand inventory. Any backorders or lost sales reduce the fill rate (besides squandering customer good will).

Fill rate is a companion to the other key performance metric: Service level. Service level measures the chance that an item will stock out during the replenishment lead time. Lead time is measured from the moment when inventory drops to or below an item’s reorder point, triggering a replenishment order, until the arrival of the replacement inventory.

Inventory management software, such as Smart Software’s SmartForecasts, can analyze demand patterns to calculate the reorder point required to achieve a specified service level target. To hit a 95% service level for the item in the top panel of Figure 1, assuming a lead time of 1 month, the required reorder point is 3; for the bottom item, the reorder point is 1. (The first reorder point is 3 to allow for the distinct possibility that future demand values will exceed the largest values, 2, observed so far. In fact, values as large as 8 are possible.) See Figure 2.

Histograms of two time series
Figure 2: Distributions of total demand during a replenishment lead time of 1 month
(Figure 2 plots the predicted distribution of demand over the lead time. The green bars represent the probability that any particular level of demand will materialize.)

Using the required reorder point of 3 units, the fill rate for the less skewed item is a healthy 93%. However, the fill rate for the more skewed item is a troubling 44%, even though this item too achieves a service level of 95%. This is the scourge of skewness.

The explanation for the difference in fill rates is the degree of skewness. The reorder point for the more skewed item is 1 unit. Having 1 unit on hand at the start of the lead time will be sufficient to handle 95% of the demands arriving during a 1 month lead time. However, the monthly demand could reach above 15 units, so when the more skewed unit stocks out, it will “stock out big time”, losing a much larger number of units.

Most demand planners would be proud to achieve a 95% service level and a 93% fill rate. Most would be troubled, and puzzled, by achieving the 95% service level but only a 44% fill rate. This partial failure would not be their fault: it can be traced directly to the nasty skewness in the distribution of monthly demand values.

There is no painless fix to this problem. The only way to boost the fill rate in this situation is to raise the service level target, which will in turn boost the reorder point, which finally will reduce both the frequency of stockouts and their size whenever they occur. In this example, raising the reorder point from 1 unit to 3 units will achieve a 99% service level and boost fill rate to a respectable, but not outstanding, 84%. This improvement would come at the cost of essentially tripling the dollars tied up in managing this more skewed item.

Thomas Willemain, PhD, co-founded Smart Software and currently serves as Senior Vice President for Research. Dr. Willemain also serves as Professor Emeritus of Industrial and Systems Engineering at Rensselear Polytechnic Institute and as a member of the research staff at the Center for Computing Sciences, Institute for Defense Analyses.

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      6 Essential Steps to Better Recovery Planning

      The Smart Forecaster

      Pursuing best practices in demand planning,

      forecasting and inventory optimization

      As we approach the midpoint in 2013, there is still a lot of economic uncertainty complicating your supply chain planning processes. Some look at this shaky economy and postpone needed investments that can position their organizations for a strong future.

      However, this is not the time to retreat from your supply chain improvement initiatives. Rather, it’s a time to double-down on your efforts to prepare for the inevitable business opportunities that lie ahead.

      Economic recovery is a time of sales opportunities. You want to make sure that you’re prepared to take advantage of them. Good demand and inventory planning can help.With the right software and planning processes, you can achieve a sound statistical basis for decision-making going forward while making informed adjustments as circumstances dictate. You can improve your ability to read demand signals, spot trends, model future events, and bring your inventory into balance with demand.

      Here are six areas of demand and inventory planning where changes you make now can lead to big payoffs when new opportunities arise:

      1. Optimize your inventories

      When the customer calls, you want to be able to ship. At the same time, you want to control your costs. The surest way to meet that goal is to find the inventory “sweet spot.” That’s where you have the minimum amount of inventory required to satisfy product demand over a specified lead time and at a desired service level.

      The ability to accurately set safety stock and inventory levels can set you apart from the competition, and make a difference in your bottom line. However, getting to that point requires a shift in your planning focus from just forecasting future demand to optimizing stocking levels to fill future orders.

      If you’d like to know more about achieving the “sweet spot,” you can find a good article published in APICS Magazine here.

      2. Implement intermittent demand forecasting solutions

      Companies in the service parts, auto aftermarket, and capital goods industries commonly experience intermittent, “slow moving” demand for a large percentage of their inventory items. Accurately forecasting demand and estimating safety stock levels for these types of items is probably the toughest challenge demand planners face. If you can accurately forecast your intermittently demanded parts and products, and have the correct amount of inventory and safety stock on the shelf, you’ve got most of the competition beat!

      The reason for this is that items that have intermittent demand do not have normal demand patterns or distributions, making them difficult to forecast using traditional forecasting methods (see the diagram below).

      Bar chart illustrating intermittent demand

      So, if you have an accurate means of forecasting intermittent demand and estimating safety stock requirements, you’ll be ahead of your competitors that don’t.

      If you’d like to know more about forecasting and planning items with intermittent demand, you can find an informative white paper here.

      3. Improve lead times

      The economic downturn has forced companies to rethink their sourcing strategies because of uncertain demand back home, long lead times to obtain their goods, rising labor costs abroad, and increasing transportation costs. Shortening replenishment lead times can reduce the time required to get the products you need and helps make your supply chain more efficient. It also makes it easier to react to changes in demand when recovery comes.

      4. Prioritize service levels

      Prioritizing service levels for your products can help insure that the items important to your sales are given the attention they need. For items that are highly demanded, consider setting service levels higher than for those with less demand. Also try doing a revenue-based ABC analysis of your company’s stock-keeping units (SKUs) and set service levels accordingly in your software planning solution.

      For example, you might set the service levels for your “bread and butter” items at 95-99% or higher, while setting service levels much lower (at 70-80% or even less) for other items. In this way, you may find that you need much less stock for some of your SKUs and more stock for others to effectively achieve your overall service level goals.

      5. Use more recent demand history in creating your forecasts

      Because the economy has been changing so fast, it may be time to shorten the demand history used in generating your forecasts so more emphasis is placed on recent trends and demand patterns—reflecting the “new normal”—rather than those contained in outdated history from 3 or 4 years ago. This, of course, should be done in consultation with your management team and preferably as part of an organized S&OP process that thoroughly evaluates both the risks and benefits of adopting this strategy.

      6. Invest in technologies and resources that help you capitalize on opportunities

      Investing in the right tools and processes increases your competitive advantage. If you aren’t doing so already, here are some valuable things to consider:

      • Start an S&OP process, or fine tune your current process, to include key stakeholders in the supply chain and also ensure that demand forecasting and inventory planning provide key inputs in that planning process.

      • If your forecasting software is not good at picking up trends, or cannot handle the portion of your inventory with intermittent demand, find software that’s up to the task.

      • Find software that will take your forecast results and generate accurate inventory stocking levels to satisfy demand for your products, components or raw materials over specified lead times and at service levels you desire.

      • Look for software solutions that are scalable, yet have a relatively low total cost of ownership, fast payback and high ROI.

      • Finally, don’t scrimp on training; get all the training and consulting you need to get the “biggest bang” from your software investments.

      Do you have anything to add? What are you doing to prepare for the economic recovery? Please leave a comment.

      Charles Smart is the founding President of Smart Software. He currently serves as Vice Chairman, on Smart Software’s Board of Directors, as a company spokesman and in development of strategic business relationships. Prior to founding Smart Software, he was a management consultant at the Stanford Research Institute (SRI International) and Policy Analysis, Inc., and served as a Lieutenant in the U.S. Navy.

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          A CFO’s Perspective on Demand Planning – “More Strategic Than You Think”

          The Smart Forecaster

          Pursuing best practices in demand planning,

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          Bud Schultz, CPA, Vice President of Finance for NKK Switches, presented his company’s experience with demand planning during a recent webinar. The following is a brief summary of Bud’s key points; view the complete webinar by clicking here.

          Q: Tell us about NKK’s business and demand planning challenges.

          NKK Switches, based in Scottsdale, Arizona, is a leading manufacturer and supplier of electromechanical switches. The business involves many different switch types—toggles, push-button, rotary, even some programmable switch types. We are known for our high quality, and for our ability to meet an exceptionally broad range of customer requirements on a turnkey (custom configuration) basis. NKK Switches produces customized solutions from component parts sourced exclusively from manufacturing facilities in Japan and China.

          There are literally millions of possible switch configurations, and we never know what configured solutions our customers will order. This makes our demand highly intermittent and exceptionally difficult to forecast. In fact, until fairly recently we considered our demand unforecastable. We operated on a build-to-order basis, which meant that customer orders could not be fulfilled until their component parts were produced and then fashioned into finished goods by NKK. This resulted in long lead-times, painful for our customers and a competitive challenge for our sales organization.

          Q: What did you expect to get from improved product demand forecasting?

          When we began to investigate the value of demand forecasting software (SmartForecasts from Smart Software), we tried to view the decision from a Return on Investment (ROI) point of view. We did some capital budgeting, making assumptions about potential reductions in inventory levels, reduced inventory carrying costs and other potential savings. Although the capital budgets returned positive returns on investment, we nevertheless were unable to move forward based on that information. We lacked confidence in our assumptions, and we were worried that we wouldn’t be able to justify the safety stock and inventory levels that the software would suggest.

          What we didn’t expect was a challenge from our parent company. In light of the capabilities of a newly implemented ERP system, they would consider a new approach. If we could produce demonstrably reliable demand forecasts, they would consider procuring raw materials and producing switch components on a build-to-forecast rather than build-to-order basis. This opened the door to a much more profound impact. We tracked actuals against forecasts over a twelve-month period and found that our forecasts, particularly in aggregate, were exceptionally accurate: actual demand was within 3% of forecast. Once we were able to prove the validity of our forecasts, we were able to move forward with the parent company’s plan to manufacture product based on those forecasts.

          Q: How did accurate forecasts of product lines with intermittent demand data transform NKK’s operations?

          From the many different combinations we manufacture to order, individual switch parts can show very intermittent demand (long periods with zero orders and then seemingly random spikes), but we can identify more consistent patterns across switch series. All of the part numbers in a given series have common components and raw materials, such as plastic housing, brackets and other hardware, gold, silver and LEDs.

          Providing our manufacturing facilities with reliable forecasts ended up allowing us to make dramatic changes. Our manufacturing plants could start procuring raw materials that in the aggregate would eventually be used in production of different part numbers within that series, even if the specific part numbers to be produced were unknown at the time the forecasts were made. And in many instances, despite the irregular demand history data, it was even possible for the suppliers to manufacture specific part numbers based on the forecast.

          Once the program is fully implemented, we anticipate our leads times will be reduced to half the time or even less. Shorter lead times will result in lower reorder points, resulting in higher service levels while reducing our inventory requirements.

          Bud Schultz leads all finance and accounting functions at NKK. His background as a Certified Public Accountant, attorney, engineer and pilot for the US Air Force provide unique perspective on finances for engineering and manufacturing operations.

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              Discussing Intermittent Demand with Supply Chain Brain’s Bowman

              The Smart Forecaster

              Pursuing best practices in demand planning,

              forecasting and inventory optimization

              The unique challenges of inventory planning for spare parts, large capital goods and other infrequently or irregularly moving items drives the importance of finding smarter methods to forecast this kind of intermittent demand. Robert Bowman, Editor of Supply Chain Brain Magazine, and I discussed this topic at the October APICS conference in Denver, and video of our conversation is available at Supply Chain Brain‘s website.

              Why plan for intermittent demand? Well, why plan for any demand? If you can understand what the likely range of demand will be until you can get more, you will know how much stock to keep in reserve, so you have just enough. This is the heart of demand forecasting and inventory optimization. Intermittent demand is exceptionally difficult to forecast, but this same principle holds true.

              Unlike other demand patterns, where historical data suggests regular trends, ebbs and flows, seasonality or other discernible patterns, intermittent demand appears to be random. There are many periods of zero demand interspersed with irregular, non-zero demand. This occurs frequently with service parts, where parts are replaced when they break, and you just don’t know when that will occur. Most service parts inventories (70% or more!) can experience intermittent demand. Demand for specialized or configured products is also likely to be intermittent.

              Supply Chain Brain has made the more in-depth discussion of this topic Bowman and I shared available here. For new visitors to Supply Chain Brain, a quick account sign-up is required to access the video.

              Jeff Scott serves as Vice President, Marketing & Alliances for Smart Software.

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              The top 3 reasons why your spreadsheet won’t work for optimizing reorder points on spare parts

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              We often encounter Excel-based reorder point planning methods. In this post, we’ve detailed an approach that a customer used prior to proceeding with Smart. We describe how their spreadsheet worked, the statistical approaches it relied on, the steps planners went through each planning cycle, and their stated motivations for using (and really liking) this internally developed spreadsheet.

              Spare Parts Planning Isn’t as Hard as You Think

              Spare Parts Planning Isn’t as Hard as You Think

              When managing service parts, you don’t know what will break and when because part failures are random and sudden. As a result, demand patterns are most often extremely intermittent and lack significant trend or seasonal structure. The number of part-by-location combinations is often in the hundreds of thousands, so it’s not feasible to manually review demand for individual parts. Nevertheless, it is much more straightforward to implement a planning and forecasting system to support spare parts planning than you might think.

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              • 7 Key Demand Planning Trends Shaping the Future7 Key Demand Planning Trends Shaping the Future
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                  Lessons From Superstorm Sandy

                  The Smart Forecaster

                  Pursuing best practices in demand planning,

                  forecasting and inventory optimization

                  The destructive impact of Hurricane Sandy has been both staggering and instructive. Our thoughts and best wishes for rapid recovery go out to all who have suffered personal or economic loss or damage. Now, in Sandy’s aftermath, we find ourselves thinking about accelerating recovery and planning for the next unforeseen event.

                  Our work with clients in the heavily hit mass transit sector presented a sobering view of damaged infrastructure, heavy equipment, and losses of essential inventory. Those most affected have seen a crush of work as inventory managers take stock of what they have, what they need and procure a mountain of replacement parts and products. This uniquely massive replenishment cycle presents all sorts of opportunities and considerations. For those who are still in this phase, and to help our collective preparation for the Next Big Event, here are a few thoughts:

                  Opportunity to immediately “right size” inventory

                  You may be in a position to receive a large, one-time infusion of funding for replacement inventory. It could be insurance money, federal relief or rainy day funds from your own treasury. Use the funding to establish the best possible inventory mix. Do not order to previously established Min/Max levels. Doing so may simply repeat excesses and shortfalls of the past.

                  A major event like Sandy presents a rare opportunity to transform your inventory. Start with an accurate demand forecast over the replenishment period, and generate safety stocks and reorder points that would address your critical needs. This can be accomplished in a matter of hours or days. Ordinarily, implementing optimal inventory levels may occur over several years, as excess inventory is gradually depleted. Now, however, you have a one-time opportunity to jump to the right answer. This shift can substantially reduce replenishment spending, freeing hundreds of thousands of dollars for other, more critical recovery uses.

                  Prioritize classes to be replenished

                  Be clear on what you need for crucial operations, and prioritize your replenishment. Which parts have long lead-times, and which are readily available? Obviously short lead-time items can be acquired in stages—getting just enough now, making funds available for the longer lead-time items.

                  Determine how much is “just enough”

                  This is where an accurate demand forecast, safety stocks and reorder point calculations come into play. Consider the service level you require—the likelihood that products will be on the shelves when you need them—which is really your tolerance for risk. Do this for each item, or class of items. This will tell you how much safety stock, in addition to your expected lead time forecast, you should have on hand. Iterating on service level-driven requirements will enable you to maximize the value of the replenishment budget at hand.

                  Statistical forecasting for intermittent demand vs. ‘rule of thumb’ methods

                  Now is the time to shift from ‘the way we’ve done it’ to the most accurate demand forecasting and inventory optimization process available to you. Greater forecast accuracy requires less safety stock—again, making inventory dollars available for other users. The greatest single category for improvement is intermittent demand. Most organizations do not apply solid statistical methods to this, instead resorting to the “heavy hammer rule”—have lots on hand because no one knows. Here is an area where SmartForecasts is especially adept, with a patented solution for forecasting intermittent demand. The resulting safety stock recommendations hit the service level goal nearly 100% of the time. Getting this right will save lots of spending now, and help minimize the potential for excess, obsolete inventory in the future.

                  Nelson Hartunian, PhD, co-founded Smart Software, formerly served as President, and currently oversees it as Chairman of the Board. He has, at various times, headed software development, sales and customer service.

                  Leave a Comment

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                  Smart Software Announces Next-Generation Patent

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                  Prepare your spare parts planning for unexpected shocks

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                  In today’s unpredictable business climate, we do have to worry about supply chain disruptions, long lead times, rising interest rates, and volatile demand. With all these challenges, it’s never been more vital for organizations to accurately forecast parts usage, stocking levels, and to optimize replenishment policies such as reorder points, safety stocks, and order quantities. In this blog, we’ll explore how companies can leverage innovative solutions like inventory optimization and parts forecasting software that utilize machine learning algorithms, probabilistic forecasting, and analytics to stay ahead of the curve and protect their supply chains from unexpected shocks.

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