Inventory Planning Becomes More Interesting

The Smart Forecaster

 Pursuing best practices in demand planning,

forecasting and inventory optimization

Taiichi Ohno of Toyota is credited with inventing Just-In-Time (JIT) manufacturing in the 1950s. JIT ensures that a manufacturer produces only what is needed, only when required, and only in the necessary amount. That innovation has since had major impacts, some good, some less so.

A recent New York Times article “How the World Ran out of Everything” describes some of the “less so” impacts.  For example, JIT has kept inventory costs very low improving return on assets.  This in turn is rewarded by Wall Street, so many companies have spent the last few decades reducing their inventories dramatically. Focused as they were on financials, many companies ignored the risks inherent in reducing inventories to the point that “lean” began to border on “emaciated.” Combined with increased globalization and new risks of supply interruption, stock-outs have abounded.

Some industries have gone too far, leaving them exposed to disruption. In a competition to get to the lowest cost, companies have inadvertently concentrated their risk, been interrupted by shortages of raw materials or components, and sometimes forced to halt assembly lines. Wall Street does not look kindly on production halts.

We all know that random events have added to the problem. First among them has been the Covid pandemic. As the pandemic has hindered factory operations and spread disarray in global shipping, many economies worldwide have been tormented by shortages of an immense range of goods — from computer chips to lumber to clothing.

The damage is compounded when more unexpected things go wrong. The Suez Canal Blockage is a prime example, obstructing the main trade route between Europe and Asia. Recently, cyberattacks have added another layer of disruption.

The reaction creates its own problems, just as the cyberattack on the Colonial Pipeline created gas shortages through panic buying. Suppliers start filling orders more slowly than usual. Manufacturers and distributors reverse course and increase inventories and diversify their suppliers to avoid future stockouts. Simply expanding warehouses may not deliver the solution, and the need to determine how much inventory to keep is more urgent every day.Manager In Warehouse With Inventory Management Software

So how can you execute a real-world plan for JIT inventory amidst all this risk and uncertainty? The foundation of your response is your corporate data. Uncertainty has two sources: supply and demand. You need the facts for both.

On the supply side, exploit the data you have on recent supplier lead times, which reflect the current turbulence. Don’t use average values when you can use probability distributions that reflect the full range of contingencies. Consider this comparison. Supplier A is now reliably filling orders in exactly 10 days. Supplier B also averages 10 days but does with a 78%/22% mix of 7 and 21 days. Both A and B have an average replenishment delay of 10 days, but the operational results they provide will be very different. You can only recognize this if you use probability models of inventory performance.

On the demand side, similar considerations apply. First, recognize that there may have been a major shift in the character of item demand (statisticians call this a “regime change”), so purge from your analysis any data that represent the “good old days.” Then, again, stop thinking in terms of averages. While the average demand is important, it is not a sufficient descriptor of the problem you face. Equally important is the volatility of demand. Volatility is the reason you keep inventory in the first place. If demand were completely predictable, you would have neither stockouts nor excess inventory. Just as you need to estimate the full probability distribution of replenishment lead times, you need the full distribution of demand values.

Once you understand the range of variability in both supply and demand, probabilistic forecasting will allow you to account for disruptions and unusual events. Software will convert your data on demand and lead times into huge numbers of scenarios representing how your next planning period might play out. Given those scenarios, the software can determine how best to meet your goals for such metrics as inventory costs and stockout rates. Using solutions such as Smart Inventory Optimization , you will confidently plan based on your targeted stockout risk with minimal inventory carrying cost. You may also consider letting the solution prescribe optimal service level targets by assessing the costs of additional inventory vs. stockout cost.

In inventory planning, as in science, we cannot escape the reality of uncertainty and the impact of unusual events. We must plan accordingly: using inventory optimization software helps you identify the least-cost service level. This creates a coherent, company-wide effort that combines visibility into current operations with mathematically correct assessments of future risks and conditions.

Inventory planning has become more “interesting” and requires a greater degree of risk awareness and agility. The right software can help.

 

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    Probabilistic vs. Deterministic Order Planning

    The Smart Forecaster

    Man with a computer in a warehouse best practices in demand planning, forecasting and inventory optimization

    Consider the problem of replenishing inventory. To be specific, suppose the inventory item in question is a spare part. Both you and your supplier will want some sense of how much you will be ordering and when. And your ERP system may be insisting that you let it in on the secret too.

    Deterministic Model of Replenishment

    The simplest way to get a decent answer to this question is to assume the world is, well, simple. In this case, simple means “not random” or, in geek speak, “deterministic.” In particular, you pretend that the random size and timing of demand is really a continuous drip-drip-drip of a fixed size coming at a fixed interval, e.g., 2, 2, 2, 2, 2, 2… If this seems unrealistic, it is. Real demand might look more like this: 0, 1, 10, 0, 1, 0, 0, 0 with lots of zeros, occasional but random spikes.

    But simplicity has its virtues. If you pretend that the average demand occurs every day like clockwork, it is easy to work out when you will need to place your next order, and how many units you will need.  For instance, suppose your inventory policy is of the (Q,R) type, where Q is a fixed order quantity and R is a fixed reorder point. When stock drops to or below the reorder point R, you order Q units more. To round out the fantasy, assume that the replenishment lead time is also fixed: after L days, those Q new units will be on the shelf ready to satisfy demand.

    All you need now to answer your questions is the average demand per day D for the item. The logic goes like this:

    1. You start each replenishment cycle with Q units on hand.
    2. You deplete that stock by D units per day.
    3. So, you hit the reorder point R after (Q-R)/D days.
    4. So, you order every (Q-R)/D days.
    5. Each replenishment cycle lasts (Q-R)/D + L days, so you make a total of 365D/(Q-R+LD) orders per year.
    6. As long as lead time L < R/D, you will never stock out and your inventory will be as small as possible.

    Figure 1 shows the plot of on-hand inventory vs time for the deterministic model. Around Smart Software, we refer to this plot as the “Deterministic Sawtooth.” The stock starts at the level of the last order quantity Q. After steadily decreasing over the drop time (Q-R)/D, the level hits the reorder point R and triggers an order for another Q units. Over the lead time L, the stock drops to exactly zero, then the reorder magically arrives and the next cycle begins.

    Figure 1 Deterministic model of on-hand inventory

    Figure 1: Deterministic model of on-hand inventory

     

    This model has two things going for it. It requires no more than high school algebra, and it combines (almost) all the relevant factors to answer the two related questions: When will we have to place the next order? How many orders will we place in a year?

    Probabilistic Model of Replenishment

    Not surprisingly, if we strip away some of the fantasy from the deterministic model, we get more useful information. The probabilistic model incorporates all the messy randomness in the real-world problem: the uncertainty in both the timing and size of demand, the variation in replenishment lead time, and the consequences of those two factors: the chance of stock on hand undershooting the reorder point, the chance that there will be a stockout, the variability in the time until the next order, and the variable number of orders executed in a year.

    The probabilistic model works by simulating the consequences of uncertain demand and variable lead time. By analyzing the item’s historical demand patterns (and excluding any observations that were recorded during a time when demand may have been fundamentally different), advanced statistical methods create an unlimited number of realistic demand scenarios. Similar analysis is applied to records of supplier lead times. Combining these supply and demand scenarios with the operational rules of any given inventory control policy produces scenarios of the number of parts on hand. From these scenarios, we can extract summaries of the varying intervals between orders.

    Figure 2 shows an example of a probabilistic scenario; demand is random, and the item is managed using reorder point R = 10 and order quantity Q=20. Gone is the Deterministic Sawtooth; in its place is something more complex and realistic (the Probabilistic Staircase). During the 90 simulated days of operation, there were 9 orders placed, and the time between orders clearly varied.

    Using the probabilistic model, the answers to the two questions (how long between orders and how many in a year) get expressed as probability distributions reflecting the relative likelihoods of various scenarios. Figure 3 shows the distribution of the number of days between orders after ten years of simulated operation. While the average is about 8 days, the actual number varies widely, from 2 to 17.

    Instead of telling your supplier that you will place X orders next year, you can now project X ± Y orders, and your supplier knows better their upside and downside risks. Better yet, you could provide the entire distribution as the richest possible answer.

    Figure 2 A probabilistic scenario of on-hand inventory

    Figure 2 A probabilistic scenario of on-hand inventory

     

    Figure 3 Distribution of days between orders

    Figure 3: Distribution of days between orders

     

    Climbing the Random Staircase to Greater Efficiency

    Moving beyond the deterministic model of  inventory opens up new possibilities for optimizing operations. First, the probabilistic model allows realistic assessment of stockout risk. The simple model in Figure 1 implies there is never a stockout, whereas probabilistic scenarios allow for the possibility (though in Figure 2 there was only one close call around day 70). Once the risk is known, software can optimize by searching  the “design space” (i.e., all possible values of R and Q) to find a design that meets a target level of stockout risk at minimal cost. The value of the deterministic model in this more realistic analysis is that it provides a good starting point for the search through design space.

    Summary

    Modern software provides answers to operational questions with various degrees of detail. Using the example of the time between replenishment orders, we’ve shown that the answer can be calculated approximately but quickly by a simple deterministic model. But it can also be provided in much richer detail with all the variability exposed by a probabilistic model. We think of these alternatives as complementary. The deterministic model bundles all the key variables into an easy-to-understand form. The probabilistic model provides additional realism that professionals expect and supports effective search for optimal choices of reorder point and order quantity.

     

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    Goldilocks Inventory Levels

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    You may remember the story of Goldilocks from your long-ago youth. Sometimes the porridge was too hot, sometimes it was too cold, but just once it was just right. Now that we are adults, we can translate that fairy tale into a professional principle for inventory planning: There can be too little or too much inventory, and there is some Goldilocks level that is “just right.” This blog is about finding that sweet spot.

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    Managing the inventory across multiple facilities arrayed in multiple echelons can be a huge challenge for any company. The complexity arises from the interactions among the echelons, with demands at the lower levels bubbling up and any shortages at the higher levels cascading down.

    Redefine Exceptions and Fine Tune Planning to Address Uncertainty

    The Smart Forecaster

     Pursuing best practices in demand planning,

    forecasting and inventory optimization

    Inventory Planning from the Perspective of a Physicist

    In a perfect world, Just in Time (JIT) would be the appropriate solution for inventory management. If you can exactly predict what you need and where you need it and your suppliers can get what you need without delay, then you do not need to maintain much inventory locally.  But as the saying goes from famous pugilist Mike Tyson, “everyone has a plan until they get punched in the mouth.” And the latest punch in the mouth for the global supply chain was last week’s Suez Canal Blockage that held up $9.6B in trade costing an estimated $6.7M per minute[1].  Disruptions from these and similar events should be modeled and accounted for in your planning.

    The assumption that you can exactly predict the future was apparent in Isaac Newton’s laws. Since the 1920’s with the introduction of quantum physics, uncertainty became fundamental to our understanding of nature. Uncertainty is built into fundamental reality.  So too should it be built into Supply and Demand Planning processes.  Yet too often, black swan events such as the Suez Canal blockage are often thought of as anomalies and as a result, discounted when planning. It is not enough to look back in hindsight and proclaim that it should have been expected. Something needs to be done about addressing the occurrence of other such events in the future and planning stocking levels accordingly.

    We must move beyond the “thin tailed distribution” thinking where extreme outcomes are discounted and plan for “fat tails.”  So how do we execute a real-world JIT plan when it comes to planning inventory? To do this, the first step is to estimate the realistic lead time to obtain an item. However, estimation is difficult due to lead time uncertainty.  Using actual supplier lead times in your company database and external data, you can develop a distribution of possible future lead times and demands within those lead times. Probabilistic forecasting will allow you to account for disruptions and unusual events by not limiting your estimates to what has been observed solely on your own short-term demand and lead time data.  You’ll be able to generate possible outcomes with associated probabilities for each occurrence.

    Once you have an estimate of the lead time and demand distribution, you can then specify the service level you need to have for that part. Using solutions such as Smart Inventory Optimization (SIO), you will be able confidently stock based on the targeted stock-out risk with minimal inventory carrying cost. You may also consider letting the solution prescribe optimal service level targets by assessing the costs of additional inventory vs. cost of stockout.

    Finally, as I have already noted, we need to accept that we can never eliminate all uncertainty. As a physicist, I have always been intrigued by the fact that, even at the most basic levels of reality as we understand it today, there is still uncertainty. Albert Einstein believed in certainty (determinism) in physical law.  If he were an inventory manager, he might have argued for JIT because he believed physical laws should allow perfect predictability. He famously said, “God does not play with dice.”  Or could it be possible that the universe we exist in was a “black swan” event in a prior “multi-verse” that produced a particular kind of universe that allowed us to exist.

    In inventory planning, as in science, we cannot escape the reality of uncertainty and the impact of unusual events.  We must plan accordingly.

     

    [1] https://www.bbc.com/news/business-56559073#:~:text=Looking%20at%20the%20bigger%20picture,0.2%20to%200.4%20percentage%20points.

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      Coping with Surging Demand During the Rebound

      The Smart Forecaster

       Pursuing best practices in demand planning,

      forecasting and inventory optimization

      Many of our customers that saw demand dry up during the pandemic are now seeing demand return.  Some are seeing a significant demand surge. Other customers in critical industries like plastics, biotech, semiconductors and electronics saw demand surges starting as far back as last April. For suggestions about how to cope with these situations, please read on.

      Surging demand usually creates two problems: inability to fill orders and inability to get replenishment due to supplier overload. This situation requires changes in the way you use your advanced planning software. Here are three tips to help you cope.

       

      Tip #1: Narrow your temporal focus

       

      In normal times (remember those?), more data implied better results. Nowadays, old data poison your calculations, since they represent conditions that no longer apply. You should base forecasts and other calculations on data from the current situation. Where to cut off past data may be obvious from a plot of the data, or you may decide to set a “reasonable” cutoff date based on a consensus of colleagues.  Smart Software has developed machine learning algorithms that automatically identify how much historical data should be optimally fed to the forecast model. Be on the lookout for these enhancements to the software that will be rolling out soon. In the meantime, conduct accuracy tests using held-out actuals using different historical start dates.  Smart’s forecast vs. actual feature will support this automatically.

      Smart Demand Planner forecasts vs. actual report

       

      Tip #2: Increase your planning tempo

       

      When operations are stable, you can set your inventory policies and trust them to be appropriate for a long time. When times are turbulent, it is important to increase the frequency of your planning cycles to keep old policy settings from drifting too far away from optimality.  More frequent recalibration of your stocking policies and forecasts means that you’ll be quicker to catch trends that will surprise your competition and always keep you steps ahead.  With software capable of automatically selecting optimal values, all that work can be done in one shot by the software. You should review those changes and possibly tweak them, but it makes sense to let the software do the bulk of the work.

       

      Tip #3: Do more What-If planning

       

      In turbulent times, you might expect even more turbulence in the future. Using your software for what-if planning helps you prepare for changes that may be coming. For example, suppose you’ve been in touch with a key supplier who hints that they may be raising prices or may have to slip their delivery schedules. By feeding the software different inputs, you can do contingency planning. If prices go up, you can see how responding by changing order quantities would impact your inventory operating costs and inventory investment. If lead times go up, you can see what the impact would be on item availability. This foreknowledge helps you figure out what your counter-moves would be before the crisis hits.

      If there ever was a time when we could cruise on automatic pilot, it’s in the rear-view mirror. Your organization, coping with explosive growth, has many challenges. Old answers are obsolete; new answers have to come from somewhere, fast. Advanced software that leverages probabilistic forecasting can help, along with changes in planning processes.

       

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        A Primer on Probabilistic Forecasting

        The Smart Forecaster

         Pursuing best practices in demand planning,

        forecasting and inventory optimization

        If you keep up with the news about supply chain analytics, you are more frequently encountering the phrase “probabilistic forecasting.” If this phrase is puzzling, read on.

        You probably already know what “forecasting” means. And you probably also know that there seem to be lots of different ways to do it. And you’ve probably heard pungent little phrases like “every forecast is wrong.” So you know that some kind of mathemagic might calculate that “the forecast is you will sell 100 units next month”, and then you might sell 110 units, in which case you have a 10% forecast error.

        You may not know that what I just described is a particular kind of forecast called a “point forecast.” A point forecast is so named because it consists of just a single number (i.e., one point on the number line, if you recall the number line from your youth).

        Point forecasts have one virtue: They are simple. They also have a flaw: They give rise to snarky statements like “every forecast is wrong.” That is, in most realistic cases, it is unlikely that the actual value will exactly equal the forecast. (Which isn’t such a big deal if the forecast is close enough.)

        This gets us to “probabilistic forecasting.” This approach is a step up, because instead of producing a single-number (point) forecast, it yields a probability distribution for the forecast. And unlike traditional extrapolative models that rely purely on the historical data, probabilistic forecasts have the ability to simulate future values that aren’t anchored to the past.

        “Probability distribution” is a forbidding phrase, evoking some arcane math that you may have heard of but never studied. Luckily, most adults have enough life experience to have an intuitive grasp of the concept.  When broken down, it’s quite straightforward to understand.

        Imagine the simple act of flipping two coins. You might call this harmless fun, but I call it a “probabilistic experiment.” The total number of heads that turn up on the two coins will be either zero, one or two. Flipping two coins is a “random experiment.” The resulting number of heads is a “random variable.” It has a “probability distribution”, which is nothing more than a table of how likely it is that the random variable will turn out to have any of its possible values. The probability of getting two heads when the coins are fair works out to be ¼, as is the probability of no heads. The chance of one head is ½.

        The same approach can describe a more interesting random variable, like the daily demand for a spare part.  Figure 2 shows such a probability distribution. It was computed by compiling three years of daily demand data on a certain part used in a scientific instrument sold to hospitals.

         

        Probabilistic demand forecast 1

        Figure 1: The probability distribution of daily demand for a certain spare part

         

        The distribution in Figure 1 can be thought of as a probabilistic forecast of demand in a single day. For this particular part, we see that the forecast is very likely to be zero (97% chance), but sometimes will be for a handful of units, and once in three years will be twenty units. Even though the most likely forecast is zero, you would want to keep a few on hand if this part were critical (“…for want of a nail…”)

        Now let’s use this information to make a more complicated probabilistic forecast. Suppose you have three units on hand. How many days will it take for you to have none? There are many possible answers, ranging from a single day (if you immediately get a demand for three or more) up to a very large number (since 97% of days see no demand).  The analysis of this question is a bit complicated because of all the many ways this situation can play out, but the final answer that is most informative will be a probability distribution. It turns out that the number of days until there are no units left in stock has the distribution shown in Figure 2.

        Probabilistic demand forecast 2

        Figure 2: Distribution of the number of days until all three units are gone

         

        The average number of days is 74, which would be a point forecast, but there is a lot of variation around the average. From the perspective of inventory management, it is notable that there is a 25% chance that all the units will be gone after 32 days. So if you decided to order more when you were down to only three on the shelf, it would be good to have the supplier get them to you before a month has passed. If they couldn’t, you’d have a 75% chance of stocking out – not good for a critical part.

        The analysis behind Figure 2 involved making some assumptions that were convenient but not necessary if they were not true. The results came from a method called “Monte Carlo simulation”, in which we start with three units, pick a random demand from the distribution in Figure 1, subtract it from the current stock, and continue until the stock is gone, recording how many days went by before you ran out. Repeating this process 100,000 times produced Figure 2.

        Applications of Monte Carlo simulation extend to problems of even larger scope than the “when do we run out” example above. Especially important are Monte Carlo forecasts of future demand. While the usual forecasting result is a set of point forecasts (e.g., expected unit demand over the next twelve months), we know that there are any number of ways that the actual demand could play out. Simulation could be used to produce, say, one thousand possible sets of 365 daily demand demands.

        This set of demand scenarios would more fully expose the range of possible situations with which an inventory system would have to cope. This use of simulation is called “stress testing”, because it exposes a system to a range of varied but realistic scenarios, including some nasty ones. Those scenarios are then input to mathematical models of the system to see how well it will cope, as reflected in key performance indicators (KPI’s). For instance, in those thousand simulated years of operation, how many stockouts are there in the worst year? the average year? the best year? In fact, what is the full probability distribution of the number of stockouts in a year, and what is the distribution of their size?

        Figures 3 and 4 illustrate probabilistic modeling of an inventory control system that converts stockouts to backorders. The system simulated uses a Min/Max control policy with Min = 10 units and Max = 20 units.

        Figure 3 shows one simulated year of daily operations in four plots. The first plot shows a particular pattern of random daily demand in which average demand increases steadily from Monday to Friday but disappears on weekends. The second plot shows the number of units on hand each day. Note that there are a dozen times during this simulated year when inventory goes negative, indicating stockouts. The third plot shows the size and timing of replenishment orders. The fourth plot shows the size and timing of backorders.  The information in these plots can be translated into estimates of inventory investment, average units on hand, holding costs, ordering costs and shortage costs.

        Probabilistic demand forecast 3

        Figure 3: One simulated year of inventory system operation

         

        Figure 3 shows one of one thousand simulated years. Each year will have different daily demands, resulting in different values of metrics like units on hand and the various components of operating cost. Figure 4 plots the distribution of 1,000 simulated values of four KPI’s. Simulating 1,000 years of imagined operation exposes the range of possible results so that planners can account not just for average results but also see best-case and worst-case values.

        Probabilistic demand forecast 4

        Figure 4: Distributions of four KPI’s based on 1,000 simulations

         

        Monte Carlo simulation is a low-math/high-results approach to probabilistic forecasting: very practical and easy to explain. Advanced probabilistic forecasting methods employed by Smart Software expand upon standard Monte Carlo simulation, yielding extremely accurate estimates of required inventory levels.

         

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