Improve Forecast Accuracy by Managing Error

The Smart Forecaster

 Pursuing best practices in demand planning,

forecasting and inventory optimization

Improve Forecast Accuracy, Eliminate Excess Inventory, & Maximize Service Levels

In this video, Dr. Thomas Willemain, co-Founder and SVP Research, talks about improving Forecast Accuracy by Managing Error. This video is the first in our series on effective methods to Improve Forecast Accuracy.  We begin by looking at how forecast error causes pain and the consequential cost related to it. Then we will explain the three most common mistakes to avoid that can help us increase revenue and prevent excess inventory. Tom concludes by reviewing the methods to improve Forecast Accuracy, the importance of measuring forecast error, and the technological opportunities to improve it.

 

Forecast error can be consequential

Consider one item of many

  • Product X costs $100 to make and nets $50 profit per unit.
  • Sales of Product X will turn out to be 1,000/month over the next 12 months.
  • Consider one item of many

What is the cost of forecast error?

  • If the forecast is 10% high, end the year with $120,000 of excess inventory.
  • 100 extra/month x 12 months x $100/unit
  • If the forecast is 10% low, miss out on $60,000 of profit.
  • 100 too few/month x 12 months x $50/unit

 

Three mistakes to avoid

1. Ignoring error.

  • Unprofessional, dereliction of duty.
  • Wishing will not make it so.
  • Treat accuracy assessment as data science, not a blame game.

2. Tolerating more error than necessary.

  • Statistical forecasting methods can improve accuracy at scale.
  • Improving data inputs can help.
  • Collecting and analyzing forecast error metrics can identify weak spots.

3. Wasting time and money going too far trying to eliminate error.

  • Some product/market combinations are inherently more difficult to forecast. After a point, let them be (but be alert for new specialized forecasting methods).
  • Sometimes steps meant to reduce error can backfire (e.g., adjustment).
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Maximize Machine Uptime with Probabilistic Modeling

Maximize Machine Uptime with Probabilistic Modeling

If you both make and sell things, you own two inventory problems. Companies that sell things must focus relentlessly on having enough product inventory to meet customer demand. Manufacturers and asset intensive industries such as power generation, public transportation, mining, and refining, have an additional inventory concern: having enough spare parts to keep their machines running.
This technical brief reviews the basics of two probabilistic models of machine breakdown. It also relates machine uptime to the adequacy of spare parts inventory.

Want to Optimize Inventory? Follow These 4 Steps

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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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        Maximize Machine Uptime with Probabilistic Modeling

        The Smart Forecaster

         Pursuing best practices in demand planning,

        forecasting and inventory optimization

        Two Inventory Problems

        If you both make and sell things, you own two inventory problems. Companies that sell things must focus relentlessly on having enough product inventory to meet customer demand.  Manufacturers and asset intensive industries such as power generation, public transportation, mining, and refining, have an additional inventory concern:  having enough spare parts to keep their machines running. This technical brief reviews the basics of two probabilistic models of machine breakdown. It also relates machine uptime to the adequacy of spare parts inventory.

         

        Modeling the failure of a machine treated as a “black box”

        Just as product demand is inherently random, so is the timing of machine breakdowns. Likewise, just as probabilistic modeling is the right way to deal with random demand, it is also the right way to deal with random breakdowns.

        Models of machine breakdown have two components. The first deals with the random duration of uptime. The second deals with the random duration of downtime.

        The field of reliability theory offers several standard probability models describing the random time until failure of a machine without regard for the reason for the failure. The simplest model of uptime is the exponential distribution. This model says that the hazard rate, i.e., the chance of failing in the next instant of time, is constant no matter how long the system has been operating. The exponential model does a good job at modeling certain types of systems, especially electronics, but it is not universally applicable.

         

        Download the Whitepaper

         

        The next step up in model complexity is the Weibull model (pronounced “WHY-bull”). The Weibull distribution allows the risk of failure to change over time, either decreasing after a burn in period or, more often, increasing as wear and tear accumulate. The exponential distribution is a special case of the Weibull distribution in which the hazard rate is neither increasing nor decreasing.

        Weibull Reliability Plot

        Figure 1: Three different Weibull survival curves

        Figure 1 illustrates the Weibull model’s probability that a machine is still running as a function of how long it has been running. There are three curves corresponding to constant, decreasing and increasing hazard rates. For obvious reasons, these are called survival curves because they plot the probability of surviving for various amounts of time (but they are also called reliability curves). The black curve that starts high and sinks fast (β=3) depicts a machine that wears out with age. The lightest curve in the middle fast (β=1) shows the exponential distribution. The medium-dark curve (β=0.5)  is one that has a high early hazard rate but gets better with age.

        Of course, there is another phenomenon that needs to be included in the analysis: downtime. Modeling downtime is where inventory theory enters the picture. Downtime is modeled by a mixture of two different distributions. If a spare part is available to replace the failed part, then the downtime can be very brief, say one day. But if there is no spare in stock, then the downtime can be quite long. Even if the spare can be obtained on an expedited basis, it may be several days or a week before the machine can be repaired. If the spare must be fabricated by a far-away supplier and shipped by sea then by rail then trucked to your plant, the downtime could be weeks or months. This all means that keeping a proper inventory of spares is very important to keeping production humming along.

        In this aggregated type of analysis, the machine is treated as a black box that is either working or not. Though ignoring the details of which part failed and when, such a model is useful for sizing the pool of machines needed to maintain some minimum level of production capacity with high probability.

        The binomial distribution is the probability model relevant to this problem. The binomial is the same model that describes, for example, the distribution of the number of “heads” resulting from twenty tosses of a coin. In the machine reliability problem, the machines correspond to coins, and an outcome of heads corresponds to having a working machine.

        As an example, if

        • the chance that any given machine is running on any particular day is 90%
        • machine failures are independent (e.g., no flood or tornado to wipe them all out at once)
        • you require at least a 95% chance that at least 5 machines are running on any given day

        then the binomial model prescribes seven machines to achieve your goal.

         

        Modeling machine failures based on component failures

        Maximize Machine Uptime with Probabilistic Modeling

        The Weibull model can also be used to describe the failure of a single part. However, any realistically complex production machine will have multiple parts and therefore have multiple failure modes. This means that calculating the time until the machine fails requires analysis of a “race to failure”, with each part vying for the “honor” of being the first to fail.

        If we make the reasonable assumption that parts fail independently, standard probability theory points the way to combining the models of individual part failure into an overall model of machine failure. The time until the first of many parts fails has a poly-Weibull distribution. At this point, though, the analysis can get quite complicated, and the best move may be to switch from analysis-by-equation to analysis-by-simulation.

         

        Simulating machine failure from the details of part failures

        Simulation analysis got its modern start as a spinoff of the Manhattan Project to build the first atomic bomb. The method is also commonly called Monte Carlo simulation after the biggest gambling center on earth back in the day (today it would be “Macau simulation”).

        A simulation model converts the logic of the sequence of random events into corresponding computer code. Then it uses computer-generated (pseudo-)random numbers as fuel to drive the simulation model. For example, each component’s failure time is created by drawing from its particular Weibull failure time distribution. Then the soonest of those failure times begins the next episode of machine downtime.

        simulation of machine uptime over one year of operation

        Figure 2: A simulation of machine uptime over one year of operation

        Figure 2 shows the results of a simulation of the uptime of a single machine. Machines cycle through alternating periods of uptime and downtime. In this simulation, uptime is assumed to have an exponential distribution with an average duration (MTBF = Mean Time Before Failure) of 30 days. Downtime has a 50:50 split between 1 day if a spare is available and 30 days if not. In the simulation shown in Figure 2, the machine is working during 85% of the days in one year of operation.

         

        An approximate formula for machine uptime

        Although Monte Carlo simulation can provide more exact results, a simpler algebraic model does well as an approximation and makes it easier to see how the key variables relate.

        Define the following key variables:

        • MTBF = Mean Time Before Failure (days)
        • Pa = Probability that there is a spare part available when needed
        • MDTshort = Mean Down Time if there is a spare available when needed
        • MDTlong = Mean Down Time if there is no spare available when needed
        • Uptime = Percentage of days in which the machine is up and running.

        Then there is a simple approximation for the Uptime:

        Uptime ≈ 100 x MTBF/(MTBF + MDTshort x Pa + MDTlong x (1-Pa)).    (Equation 1)

        Equation 1 tells us that the uptime depends on the availability of a spare. If there is always a spare (Pa=1), then uptime achieves a peak value of about 100 x MTBF/(MTBF + MDTshort). If there is never a spare available (Pa=0), then uptime achieve its lowest value of about 100 x MTBF/(MTBF + MDTlong). When the repair time is about as long as the typical time between failures, uptime sinks to an unacceptable level near 50%. If a spare is always available, uptime can approach 100%.

        Relating machine downtime to spare parts inventory

        Minimizing downtime requires a multi-pronged initiative involving intensive operator training, use of quality raw materials, effective preventive maintenance – and adequate spare parts. The first three set the conditions for good results. The last deals with contingencies.

        Inventory Planning for Manufacturers MRO SAAS

        Once a machine is down, money is flying out the door and there is a premium on getting it back up pronto. This scene could play out in two ways. The good one has a spare part ready to go, so the downtime can be kept to a minimum. The bad one has no available spare, so there is a scramble to expedite delivery of the needed part. In this case, the manufacturer must bear both the cost of lost production and the cost of expedited shipping, if that is even an option.

        If the inventory system is properly designed, spare parts availability will not be a major impediment to machine uptime. By the design of an inventory system, I mean the results of several choices: whether the shortage policy is a backorder policy or a loss policy, whether the inventory review cycle is periodic or continuous, and what reorder points and order quantities are established.

        When inventory policies for products are designed, they are evaluated using several criteria. Service Level is the percentage of replenishment periods that pass without a stockout. Fill Rate is the percentage of units ordered that is supplied immediately from stock. Average Inventory Level is the typical number of units on hand.

        None of these is exactly the metric needed for spare parts stocking, though they all are related. The needed metric is Item Availability, which is the percentage of days in which there is at least one spare ready for use. Higher Service Levels, Fill Rates, and Inventory Levels all imply high Item Availability, and there are ways to convert from one to the other. (When dealing with multiple machines sharing the same stock of spares, Inventory Availability gets replaced by the probability distribution of the number of spares on any given day. We leave that more complex problem for another day.)

        Clearly, keeping a good supply of spares reduces the costs of machine downtime. Of course, keeping a good supply of spares creates its own inventory holding and ordering costs. This is the manufacturer’s second inventory problem. As with any decision involving inventory, the key is to strike the right balance between these two competing cost centers. See this article on probabilistic forecasting for intermittent demand for guidance on striking that balance.

         

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          Want to Optimize Inventory? Follow These 4 Steps

          The Smart Forecaster

           Pursuing best practices in demand planning,

          forecasting and inventory optimization

          Service Level Driven Planning (SLDP) is an approach to inventory planning. It prescribes optimal service level targets continually identifies and communicates trade-offs between service and cost that are at the root of all wise inventory decisions. When an organization understands this relationship, they can communicate where they are at risk, where they are not, and effectively wield their inventory assets.  SLDP helps expose inventory imbalances and enables informed decisions on how best to correct them.  To implement SLDP, you’ll need to look beyond traditional planning approaches such as arbitrary service level targeting (all of my A items should get 99% service level, B items 95%, C items 80%, etc.) and demand forecasting that unrealistically attempts to predict exactly what will happen and when. SLDP unfolds in 4 steps: Benchmark, Collaborate, Plan, and Track.

           

          Step 1. Benchmark Performance

           

          All participants in the inventory planning and investment process must hold a common understanding of how current policy is performing across an agreed upon set of inventory metrics. Metrics should include historically achieved service levels and fill rates, delivery time to customers, supplier lead time performance, inventory turns, and inventory investment. Once these metrics have been benchmarked and can be reported on daily, the organization will have the information it needs to begin prioritize planning efforts. For example, if inventory has increased but service levels have not, this would indicate that the inventory is not being properly allocated across SKUs.  Reports should be generated within mouse-clicks enabling planners to focus on analysis instead of time intensive report generation.   Past performance isn’t a guarantee of future performance since demand variability, costs, priorities, and lead times are always changing. So SLDP enables predictive benchmarking that estimates what performance is likely to be in the future. Inventory optimization software utilizing probability forecasting can be used to estimate a realistic range of potential demands and replenishment cycles stress testing your planning parameters helping uncover how often and which items to expect stockouts and excess.

           

          Step 2. “What if” Planning & Collaboration

           

          “What if” inventory modeling and collaboration is at the heart of SLDP. The historical and predictive benchmarks should first be shared with all relevant stakeholders including sales, finance, and operations. Efforts should be placed on answering the following questions:

          – Are both the current performance and investment acceptable?
          – If not, how should they be improved?
          – Which SKUs are likely to be demanded next and in what quantities?
          – Where are we willing to take more stock out risk?
          – Where must stock-out risk be minimized?
          – What are the specific stock out costs?
          – What business rules and constraints must we adhere to (customer service level agreements, inventory thresholds, etc.)

          Once the above questions are answered, new inventory planning policies can be developed.  Inventory Optimization software can reconcile all costs associated with managing inventory including stockout costs to generate the right set of planning parameters (min/max, safety stock, reorder points, etc.) and prescribed service levels.  The optimal policy can be compared to the current policy and modified based on constraints and business rules. For example, certain items might be targeted at a target service level in order to conform to a customer service level agreement.   Various “what if” inventory planning scenarios can be developed and shared with key stakeholders. For example, you might model how shorter lead times impacts inventory costs. Once consensus has been achieved and the risks and costs are clearly communicated,  the modified policies can be uploaded to the ERP system to drive inventory replenishment.

           

          Step 3. Continually Plan and Manage by Exception

          SLDP continually reforecasts optimized planning parameters based on changing demands, lead times, costs, and other factors. This means that service levels and inventory value have the potential to change.  For example, the prescribed service level target of 95% might increase to 99% the next planning period if the stock-out costs on that item increased suddenly. This is also true if opting to arbitrarily target a given service level or fix planning parameters to a specific unit quantity. For example, a target service level of 95% might require $1,000 in inventory today but $2,000 next month if lead times spiked.  Similarly, a reorder point of 10 units might get 95% service today and only 85% service next month in response to increased demand variability. Inventory Optimization software will identify which items are forecasted to have significant changes in service level and/or inventory value and which items aren’t being ordered according to the consensus plan. Exception lists are automatically produced making it easy for you to review these items and decide how to manage them moving forward. Prescriptive Analytics can help identify whether the root cause of the change is a demand anomaly, change in overall demand variability, change in lead time, or change in cost helping you fine tune the policy accordingly.

           

          Step 4. Track Ongoing Performance

           

          SLDP processes regularly measure historical and current operational performance.   Results must be monitored to ensure that service levels are improving and inventory levels are decreasing when compared to the historical benchmarks determined in Step 1.  Track metrics such as turns, aggregate and item specific service levels, fill rates, out-of-stocks, and supplier lead time performance.  Share results across the organization and identify root causes to operational inefficiencies.  SLDP processes makes performance tracking easy by providing tools that automatically generate the necessary reports rather than placing this burden on planners to manage in Excel. Doing so enables the organization to uncover operational issues impacting performance and provide feedback on what is working and what should be improved.

          Conclusion

          The SLDP framework is a way to rationalize the inventory planning process and generate a significant economic return. Its organizing principle is that customer service levels and inventory costs associated with the chosen policy should be understood, tracked, and continually refined. Utilizing inventory optimization software helps ensure that you are able to identify the least-cost service level.  This creates a coherent, company-wide effort that combines visibility into current operations with scientific assessments of future risks and conditions. It is realized by a combination of executive vision, staff subject matter expertise, and the power of modern inventory planning and optimization software.

          See how Smart Inventory Optimization Supports Service Level Driven Planning and download the product sheet here: https://smartcorp.com/inventory-optimization/

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