Blanket Orders

Customer as Teacher

Our customers are great teachers who have always helped us bridge the gap between textbook theory and practical application. A prime example happened over twenty years ago, when we were introduced to the phenomenon of intermittent demand, which is common among spare parts but rare among the finished goods managed by our original customers working in sales and marketing. This revelation soon led to our preeminent position as vendors of software for managing inventories of spare parts. Our latest bit of schooling concerns “blanket orders.”

Expanding the Inventory Theory Textbook

Textbook inventory theory focuses on the three most used replenishment policies: (1) Periodic review order-up-to policy, designated (T, S) in the books (2) Continuous review policy with fixed order quantity, designated (R, Q) and (3) Continuous review order-up-to policy, designated (s, S) but usually called “Min/Max.” Our customers have pointed out that their actual ordering process often includes frequent use of “blanket orders.” This blog focuses on how to adjust stocking targets when blanket orders are used.

Blanket Orders are Different

Blanket orders are contracts with suppliers for fixed replenishment quantities arriving at fixed intervals. For example, you might agree with your supplier to receive 20 units every 7 days via a blanket order rather than 60 to 90 units every 28 days under the Periodic Review policy. Blanket orders contrast even more with the Continuous Review policies, under which both order schedules and order quantities are random.

In general, it is efficient to build flexibility into the restocking process so that you order only what you need and only order when you need it. By that standard, Min/Max should make the most sense and blanket policies should make the least sense.

The Case for Blanket Policies

However, while efficiency is important, it is never the only consideration. One of our customers, let’s call them Company X, explained the appeal of blanket policies in their circumstances. Company X makes high-performance parts for motorcycles and ATV’s. They turn raw steel into cool things.

But they must deal with the steel. Steel is expensive. Steel is bulky and heavy. Steel is not something conjured overnight on a special-order basis. The inventory manager at Company X does not want to place large but random-sized orders at random times. He does not want to baby-sit a mountain of steel. His suppliers do not want to receive orders for random quantities at random times. And Company X prefers to spread out its payments. The result: Blanket orders.

The Fatal Flaw in Blanket Policies

For Company X, blanket orders are intended to even out replenishment buys and avoid unwieldy buildups of piles of steel before they are ready for use. But the logic behind continuous review inventory policies still applies. Surges in demand, otherwise welcome, will occur and can create stockouts. Likewise, pauses in demand can create excess demand. As time goes on, it becomes clear that a blanket policy has a fatal flaw: only if the blanket orders exactly match the average demand can they avoid runaway inventory in either direction, up or down. In practice, it will be impossible to exactly match average demand. Furthermore, average demand is a moving target and can drift up or down.

Hybrid Blanket Policies to the Rescue

A blanket policy does have advantages, but rigidity is its Achilles heel.  Planners will often improvise by adjusting future orders to handle changes in demand but this doesn’t scale across thousands of items.  To make the replenishment policy robust against randomness in demand, we suggest a hybrid policy that begins with blanket orders but retains flexibility to automatically (not manually) order additional supply on an as-need basis. Supplementing the blanket policy with a Min/Max backup provides for adjustments without manual intervention. This combination will capture some of the advantages of blanket orders while protecting customer service and avoiding runaway inventory.

Designing a hybrid policy requires choice of four control parameters. Two parameters are the fixed size and fixed timing of the blanket policy. Two more are the values of Min and Max. This leaves the inventory manager facing a four-dimensional optimization problem.  Advanced inventory optimization software will make it possible to evaluate choices for the values of the four parameters and to support negotiations with suppliers when crafting blanket orders.

 

 

Probabilistic Forecasting for Intermittent Demand

The Smart Forecaster

  Pursuing best practices in demand planning,

forecasting and inventory optimization

Intermittent, lumpy or uneven demand —particularly for low-demand items like service and spare parts — is especially difficult to predict with any accuracy. Smart Software’s proprietary probabilistic forecasting dramatically improves service level accuracy.  If any of these scenarios apply to your company then probabilistic forecasting will help improve your bottom line.

  • Do you have intermittent or lumpy demand with large, infrequent spikes that are many times the average demand?
  • Is it hard to obtain business information about when demand is likely to spike again?
  • Do you miss out on business opportunities because you can’t accurately forecast demand and estimate inventory requirements for certain unpredictable products?
  • Are you required to hold inventory on many items even if they are infrequently demanded in order to differentiate vs. the competition by providing high service levels?
  • Do you have to make unnecessarily large investments in inventory to cover unexpected orders and materials requirements?
  • Do you have to deliver to customers right away despite long supplier lead times?

If you’ve answered yes to some or all of the questions above, you aren’t alone. Intermittent demand —also known as irregular, sporadic, lumpy, or slow-moving demand — affects industries of all types and sizes: capital goods and equipment sectors, automotive, aviation, public transit, industrial tools, specialty chemicals, utilities and high tech, to name just a few. And it makes demand forecasting and planning extremely difficult. It can be much more than a headache; it can be a multi-million-dollar problem, especially for MRO businesses and others who manage and distribute spare and service parts.

Identifying intermittent demand data isn’t hard. It typically contains a large percentage of zero Save & Exit values, with non-zero values mixed in randomly. But few forecasting solutions have yielded satisfactory results even in this era of Big Data Analysis, Predictive Analytics, Machine Learning, and Artificial Intelligence.

 

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Traditional Approaches and their Reliance on an Assumed Demand Distribution

Traditional statistical forecasting methods, like exponential smoothing and moving averages, work well when product demand data is normal, or smooth, but it doesn’t give accurate results with intermittent data. Many automated forecasting tools fail because they work by identifying patterns in demand history data, such as trend and seasonality. But with intermittent demand data, patterns are especially difficult to recognize. These methods also tend to ignore the special role of zero values in analyzing and forecasting demand.Even so, some conventional statistical forecasting methods can produce credible forecasts of the average demand per period.  However, when demand is intermittent, a forecast of the average demand is not nearly sufficient for inventory planning.  Accurate estimates of the entire distribution (i.e., complete set) of all possible lead-time demand values is needed. Without this, these methods produce misleading inputs to inventory control models — with costly consequences.

Collague with gears ans statistical forecast modeling

 

To produce reorder points, order-up-to levels, and safety stocks for inventory planning, many forecasting approaches rely on assumptions about the demand and lead time distribution.  Some assume that the probability distribution of total demand for a particular product item over a lead time (lead-time demand) will resemble a normal, classic bell-shaped curve. Other approaches might rely on a Poisson distribution or some other textbook distribution.  With intermittent demand, a one-sized fits all approach is problematic because the actual distribution will often not match the assumed distribution.  When this occurs, estimates of the buffer stock will be wrong.  This is especially the case when managing spare parts (Table 1).

For each intermittently demanded item, the importance of having an accurate forecast of the entire distribution of all possible lead time demand values — not just one number representing the average or most likely demand per period — cannot be overstated. These forecasts are key inputs to the inventory control models that recommend correct procedures for the timing and size of replenishment orders (reorder points and order quantities). They are particularly essential in spare parts environments, where they are needed to accurately estimate customer service level inventory requirements (e.g., a 95 or 99 percent likelihood of not stocking out of an item) for satisfying total demand over a lead time.  Inventory planning departments must be confident that when they target a desired service level that they will achieve that target.  If the forecasting model consistently yields a different service level than targeted, inventory will be mismanaged and confidence in the system will erode.

Faced with this challenge, many organizations rely on applying rule of thumb based approaches to determine stocking levels or will apply judgmental adjustments to their statistical forecasts, which they hope will more accurately predict future activity based on past business experience. But there are several problems with these approaches, as well.

Rule of thumb approaches ignore variability in demand and lead time. They also do not update for changes in demand patterns and don’t provide critical trade-off information about the relationship between service levels and inventory costs.

Judgmental forecasting is not feasible when dealing with large numbers (thousands and tens of thousands) of items. Furthermore, most judgmental forecasts provide a single-number estimate instead of a forecast of the full distribution of lead-time demand values. Finally, it is easy to inadvertently but incorrectly predict a downward (or upward) trend in demand, based on expectations, resulting in understocking (or over-stocking) inventory.

 

How does Probabilistic Demand Forecasting Work in Practice?

Although the full architecture of this technology includes additional proprietary features, a simple example of the approach demonstrates the usefulness of the technique. See Table 1.

intermittently demanded product items spreedsheet

Table 1. Monthly demand values for a service part item.

The 24 monthly demand values for a service part itemare typical of intermittent demand. Let’s say you need forecasts of total demand for this item over the next three months because your parts supplier needs three months to fill an order to replenish inventory. The probabilistic approach is to sample from the 24 monthly values, with replacement, three times, creating a scenario of total demand over the three-month lead time.

How does the new method of forecasting intermittent demand work

Figure 1. The results of 25,000 scenarios.

 

You might randomly select months 6, 12 and 4, which gives you demand values of 0, 6 and 3, respectively, for a total lead-time demand (in units) of 0 + 6 + 3 = 9. You then repeat this process, perhaps randomly selecting months 19, 8 and 14, which gives a lead-time demand of 0 + 32 + 0 = 32 units. Continuing this process, you can build a statistically rigorous picture of the entire distribution of possible lead-time demand values for this item. Figure 1 shows the results of 25,000 such scenarios, indicating (in this example) that the most likely value for lead-time demand is zero but that lead-time demand could be as great as 70 or more units. It also reflects the real-life possibility that nonzero demand values for the part item occurring in the future could differ from those that have occurred in the past.

With the high-speed computational resources available in the cloud today, probabilistic forecasting methods can provide fast and realistic forecasts of total lead-time demand for thousands or tens of thousands of intermittently demanded product items. These forecasts can then be entered directly into inventory control models to insure that enough inventory is available to satisfy customer demand. This also ensures that no more inventory than necessary is maintained, minimizing costs.

 

A Field Proven Method That Works

Customers that have implemented the technology have found that it increases customer service level accuracy and significantly reduces inventory costs.

Warehouse or storage getting inventory optimization

A nationwide hardware retailer’s warehousing operation forecasted inventory requirements for 12,000 intermittently demanded SKUs at 95 and 99 percent service levels. The forecast results were almost 100 percent accurate. At the 95 percent service level, 95.23 percent of the items did not stock out (95 percent would have been perfect). At the 99 percent service level, 98.66 percent of the items did not stock out (99 percent would have been perfect).

The aircraft maintenance operation of a global company got similar service level forecasting results with 6,000 SKUs. Potential annual savings in inventory carrying costs were estimated at $3 million. The aftermarket business unit of an automotive industry supplier, two-thirds of whose 7,000 SKUs demonstrate highly intermittent demand, also projected $3 million in annual cost savings.

That the challenge of forecasting intermittent product demand has indeed been met is good news for manufacturers, distributors, and spare parts/MRO businesses.  With cloud computing, Smart Software’s field-proven probabilistic method is now accessible to the non-statistician and can be applied at scale to tens of thousands of parts.  Demand data that was once un-forecastable no longer poses an obstacle to achieving the highest customer service levels with the lowest possible investment in inventory.

 

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    • Blanket Orders Smart Software Demand and Inventory Planning HDBlanket Orders
      Our customers are great teachers who have always helped us bridge the gap between textbook theory and practical application. A prime example happened over twenty years ago, when we were introduced to the phenomenon of intermittent demand, which is common among spare parts but rare among the finished goods managed by our original customers working in sales and marketing. This revelation soon led to our preeminent position as vendors of software for managing inventories of spare parts. Our latest bit of schooling concerns “blanket orders.” […]
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      The New Forecasting Technology derives from Probabilistic Forecasting, a statistical method that accurately forecasts both average product demand per period and customer service level inventory requirements. […]
    • Engineering to Order at Kratos Space – Making Parts Availability a Strategic Advantage
      The Kratos Space group within National Security technology innovator Kratos Defense & Security Solutions, Inc., produces COTS s software and component products for space communications - Making Parts Availability a Strategic Advantage […]
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        Engineering to Order at Kratos Space – Making Parts Availability a Strategic Advantage

        Introduction

        The Kratos Space group within National Security technology innovator Kratos Defense & Security Solutions, Inc., produces COTS software and component products for space communications, tailored products for individual customers, as well as complete satellite and terrestrial ground segment solutions.  Theirs is a highly demanding market often requiring engineered-to-order systems with exceptional performance and rapid delivery cycles.  Kirk Smith, Vice President of Business Systems Innovation, sat down with us to explain how parts management and planning has become central to their operational excellence, supporting numerous custom projects per year.

        The Challenge:  

        Engineering-to-order in Kratos’ world means that traditional finished goods forecasting won’t help you plan for the future.  In the tailored marketplace, the past does not provide a usable forecast for the future, even within the Space group’s focused technology areas. You just don’t know ahead of time everything your next tailored system customer is going to request.  This is problematic for the company’s contract manufacturers (CMs) that produce key lower level assemblies – they can’t know what to expect, and without some advice will have no ability to pre-order and stock requisite component parts.  Short forecast horizons and long component lead times makes competitive bidding for new projects difficult, where time to delivery is crucial.  

        Leveraging a competitive advantage

        “With tailored and custom solutions, the Number 1 reason we win is that we solve very challenging problems for our customers,” says Smith.  But a close second is a strategic advantage – the ability to deliver those tailored systems quickly.  Kratos has an array of previously designed and engineered building blocks (chassis and board level assemblies) that can be applied to newly designed solutions.  This speeds design, but because these building blocks are tailored for each customer, stocking them for future sales is problematic – there are many variants.  If Kratos could find a way to effectively forecast their board and component level requirements, they would be able to reduce end-to-end production time, minimize part shortages that delay delivery, and prevent excesses that create obsolete inventory.  

        The Solution: 

        Kratos pursued a hybrid planning approach, combining sales planning by its business development team with statistical forecasting from Smart Software.  Smith explained the process: Part 1 – Annual forecast at the CM built assembly level:
        • Use Smart to produce a rolling 12-month assembly level forecast for the CM.
        • Compare this with the Business Development Opportunity Forecast
        • Merge the insights from Smart with the Opportunity Forecast
        • Provide resulting adjusted assembly forecast to the CM for revenue and capacity planning.
        Part 2 – Provide component level forecasts to Contract Manufacturers:
        • Feed assembly level forecast into the ERP Bill of Material function, exploding component level demand for all parts.
        • Aggregating demand by part number, generate component level forecasts.
        • Provide forecasts to CM procurement to enable them to determine when to buy ahead or increase orders to capture volume price breaks. When they see an opportunity, they contact Kratos, get permission, and increase buys – with the effect of driving down material cost and lead times.
        • Also, providing annual forecasts reduces buy-back pressure from the CMs – Kratos is obligated to buy back unused components, but now the CMs can see opportunity at the component level and the value of retaining stocks.
         

        Results: 

        Over the past three years this approach has allowed Kratos to reduce material cost. Moreover, Kratos is able to work with its Contract Manufacturers to reduce stockout risk and achieve shorter delivery commitments.  While dealing with components with up to six month lead times, they are able to confidently propose and achieve customer delivery dates. Jon Good, General Manager at contract manufacturer NeoTech, shared their experience.  “We use the Smart forecast provided by Kratos’ Space group to assist in taking advantage of price breaks on material at higher quantities that wouldn’t otherwise be visible in our current business model.  This enables us to reduce material cost which translates into reduced pricing to Kratos in the long run.” Good added that another use is to predict probable material consumption over a longer period of time than would be visible only on open orders.  “This enables us to more realistically understand our inventory on hand position in terms of excess.  These two benefits allow NEOTech to make smarter decisions related to purchasing and inventory management while at the same time saving days and weeks in the front end of the process and delivering the end product to Kratos as rapidly as possible.” Looking forward, Smith sees even greater opportunity to team with Kratos Space CMs to streamline their supply chain and associated costs.  “The bottom line,” says Smith, “is that we are now able to more effectively communicate with our CM partners, despite the lack of forecastability in our business, and simultaneously reduce material cost and shorten lead times.”      
        Managing the Inventory of Promoted Items

        The Smart Forecaster

         Pursuing best practices in demand planning,

        forecasting and inventory optimization

        In a previous post, I discussed one of the thornier problems demand planners sometimes face: working with product demand data characterized by what statisticians call skewness — a situation that can necessitate costly inventory investments. This sort of problematic data is found in several different scenarios. In at least one, the combination of intermittent demand and very effective sales promotions, the problem lends itself to an effective solution.

        Reviewing terms, recall that “service level” is the probability of not stocking out while waiting for a replenishment order to arrive, while “fill rate” is the percentage of demand that is satisfied immediately from stock. In my previous post, “The Scourge of Skewness”, I pointed out that a certain type of demand distribution, having a “long right tail”, will lead to fill rates that can be much lower than service levels. I also pointed out that sometimes the only way to improve the fill rate is to increase the target service level to an unusually high level, which can be expensive.

        In this post, I’ll look at solving the problem in one special case: skewness resulting from effective sales promotions mixed with “intermittent demand”. Intermittent demand has a large proportion of zero values, with nonzero values mixed in at random. Successful sales promotions, obviously positive, have a downside: they can confuse the “demand signal” with spikes in your demand history, and can undermine forecasts and bias safety stock calculations. When intermittent demand and effective sales promotions are the source of your data’s skewness, methods exist to work around the problem to achieve both higher fill rates and more accurate demand forecasts.

        How Promotions Increase Skewness

        Successful promotions abruptly increase item demand. This creates anomalies, or “outliers”, which contribute to forming a skewed distribution. Knowing when promotions occurred in the past, we can adjust an item’s record of past demand. We produce an alternate demand history as if there had been no promotions, by replacing the outliers with values more representative of the “natural” level of demand. These adjustments reduce demand skewness. Reduced skewness can lead to significant reductions in both expected forecasts and safety stocks, which add together to form reorder points.

        Successful promotions are likely to be repeated. When that happens, the promotion effects can be added in to demand forecasts to increase their accuracy. The effect of future promotions on inventory management will be to increase the risk of stockouts, so a sensible response is to work at the operational level to build up temporary supply, in a quantity keyed to the estimated impact of prior promotions on the effected items.

         

        Using Event Modeling to Improve Demand Forecasting

        It’s possible to model the impact of like events, and apply this to planned events in the future. Doing so can improve your forecast in two big ways: by projecting the demand jolt you expect from a planned event; and rationalizing the spikes in the past that were caused by events, making your baseline activity more visible and more accurately forecastable. We do a lot of this in SmartForecasts, so allow me to use our experience there to show you what I mean.

        Event Modeling entails the following steps:
        • Automatically estimating the impact of previous promotions (which is a useful result in itself).
        • Adjusting historical demand to statistically remove the effect of promotions.
        • Creating promotion-free forecasts.
        • Revising the forecasts for any future time periods in which promotions are planned.

        We call this this type of analysis “Promo forecasting”. We use the word “promotions” to describe what you do yourself to improve your results. We use “events” to describe what the world does to you, usually to your detriment; examples include strikes, power outages, warehouse fires and other unlucky happenings.

        To understand how Event Modeling can help you cope with skewness when doing demand forecasting for high-volume items, consider Figures 1-3.

        Figure 1 shows that this item’s demand pattern is clearly seasonal, and the forecast is both seasonal and “tight”, meaning that the forecast uncertainty interval (“margin of error”, shown in cyan lines) is very narrow.

        Figure 2 shows an alternative history in which a promotion in June 2014 reversed the usual seasonal low associated with June sales. This demand pattern was forecasted using the Automatic forecasting tournament in SmartForecasts, as in Figure 1. This time, the promotion scrambled the seasonal pattern enough to create an inappropriate non-seasonal forecast, and one that has a much larger margin of error.

        Finally, Figure 3 shows how Promo forecasting handles the same promoted scenario, retaining a seasonal forecast and building into the forecast an estimate of the effect of a planned repeat promotion in 2015.

        The Case of Intermittent Demand

        In Figure 1, the item was a high-volume finished good and the task was demand forecasting. Promo modeling is also useful when dealing with the task of setting safety stocks and reorder points for items with intermittent demand, whether the items are finished goods, components or spare parts. Intermittent demand very often has a skewed distribution that makes it difficult to achieve high item availability with a small investment in inventory.

        Figure 4 illustrates the problem that a successful promotion can accidentally create for inventory management. If such a spike arises from the natural, un-promoted demand, then the only way to maintain high fill rates is to provide safety stocks large enough to cope with these random surges. In this case, the big spike in demand of 500 units in February 2013 was the result of a one-time promotion.

        Taking Account of Promotions to Improve Inventory Management

        Unwittingly treating the spike in the example above as part of the natural demand variability results in a poor fill rate. To achieve a target service level of, say, 95% with a lead time of one month would require a reorder point of 38 units, computed as the sum of an expected forecast over the one month replenishment lead time of 21 units supplemented by a safety stock of 17 units. This investment would result in a disappointing fill rate of only 36%.

        However, recognizing that the spike is a one-time promotion and replacing the 500 units with 0 obviously would make a big difference. The reorder point would drop from 38 units to 31 (the sum of an expected demand of 7 units and a safety stock of 24 units) and the fill rate would increase to 94%.

        Of course, it is not ok to just throw out inconvenient demand spikes whenever they make life uncomfortable; there has to be a valid “business story” behind the adjustment of historical demand. If the spike is the result of a data processing error, then by all means, fix it. If the spike coincides with a promotion, then replacing the spike with, say, the median demand (often zero, as in this example) will result in a much more sustainable inventory investment that still meets aggressive performance targets. Future promotions of the same type on the same item will require some extra effort to prepare for the temporary surge in demand, but the recommended reorder point will be correct in the long run.

        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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              The Advantages of Probability Forecasting
              }

              The Smart Forecaster

               Pursuing best practices in demand planning,

              forecasting and inventory optimization

              Most demand forecasts are partial or incomplete: They provide only one single number: the most likely value of future demand. This is called a point forecast. Usually, the point forecast estimates the average value of future demand.

              Much more useful is a forecast of full probability distribution of demand at any future time. This is more commonly referred to as probability forecasting and is much more useful.

              The Average is Not the Answer

               

              The one advantage of a point forecast is its simplicity. If your ERP system is also simple, the point forecast fills in the one number needed by the ERP system to do workforce scheduling or raw material purchases.

              The disadvantage of a point forecast is that it is too simple. It ignores additional information in an item’s demand history that can give you a more complete picture of how demand might unfold: a probability forecast.

              Going Beyond the Average: Probability Forecasting

               

              While the point forecast provides limited information, e.g., “The most likely demand next month is 15 units”, the probability forecast adds crucial information, e.g., “There is a 20% chance that demand will exceed 28 units and a 10% chance that it will be less than 5 units”.

              This information lets you do risk assessment and contingency planning. Contingency planning is necessary because the point forecast usually has only a small chance of actually being correct. A probability forecast may also say “The chance of demand being 15 units is only 10%, even though it is the single most likely value.” In other words, there is a 90% chance that the point forecast is wrong. This kind of error is not a mistake in the forecasting calculations: it is the reality of dealing with demand volatility. It might better be called an “uncertainty” than an “error”.

              An operations manager can use the extra information in a probability forecast in both informal and formal ways. Informally, even if an ERP system requires a single-number forecast as input, a wise manager will want to have some clue about the risks associated with that point forecast, i.e., its margin of error. So a forecast of 15 ± 1 unit is a lot safer than a forecast of 15 ± 10. The ± part is a compression of a probabilistic forecast. Figure 1 below shows an item’s demand history (red line), point forecasts for the next 12 months (green line) and their margins of error (cyan lines). The lowest forecast of about 3,300 units occurs in June, but the actual demand might be as much as 800 units higher or lower.

              Bonus: Application to Inventory Management

               

              Inventory management requires that you balance item availability against the inventory cost. It turns out that knowing the full probability distribution of demand over a replenishment lead time is essential for setting reorder points (also called mins) on a rational, scientific basis. Figure 2 shows a probability forecast of total demand during the 33 week replenishment lead time for a certain spare part. While the average lead time demand is 3 units, the most likely demand is zero, and a reorder point of 14 is needed to insure that the chance of stocking out is only 1%. Once again, the average is not the answer.

              Knowing more is always better than knowing less and the probability forecast provides that extra bit of crucial information. Software has been able to supply a point forecast for over 40 years, but modern software can do better and provide the whole picture.

               

               

              Figure 1: The red line shows the demand history of a finished good. The green line shows the point forecasts for the next 12 months. The blue lines indicate the margins of error in the 12 point forecasts.

               

               

              Figure 2: A probabilistic forecast of demand for a spare part over a 33 week replenishment lead time. The most likely demand is zero, the average demand is 3, but a reorder point of 14 units is required to have only a 1% chance of stock out.

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                    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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