Rethinking forecast accuracy: A shift from accuracy to error metrics

Measuring the accuracy of forecasts is an undeniably important part of the demand planning process. This forecasting scorecard could be built based on one of two contrasting viewpoints for computing metrics. The error viewpoint asks, “how far was the forecast from the actual?” The accuracy viewpoint asks, “how close was the forecast to the actual?” Both are valid, but error metrics provide more information.

Accuracy is represented as a percentage between zero and 100, while error percentages start at zero but have no upper limit. Reports of MAPE (mean absolute percent error) or other error metrics can be titled “forecast accuracy” reports, which blurs the distinction.  So, you may want to know how to convert from the error viewpoint to the accuracy viewpoint that your company espouses.  This blog describes how with some examples.

Accuracy metrics are computed such that when the actual equals the forecast then the accuracy is 100% and when the forecast is either double or half of the actual, then accuracy is 0%. Reports that compare the forecast to the actual often include the following:

  • The Actual
  • The Forecast
  • Unit Error = Forecast – Actual
  • Absolute Error = Absolute Value of Unit Error
  • Absolute % Error = Abs Error / Actual, as a %
  • Accuracy % = 100% – Absolute % Error

Look at a couple examples that illustrate the difference in the approaches. Say the Actual = 8 and the forecast is 10.

Unit Error is 10 – 8 = 2

Absolute % Error = 2 / 8, as a % = 0.25 * 100 = 25%

Accuracy = 100% – 25% = 75%.

Now let’s say the actual is 8 and the forecast is 24.

Unit Error is 24– 8 = 16

Absolute % Error = 16 / 8 as a % = 2 * 100 = 200%

Accuracy = 100% – 200% = negative is set to 0%.

In the first example, accuracy measurements provide the same information as error measurements since the forecast and actual are already relatively close. But when the error is more than double the actual, accuracy measurements bottom out at zero. It does correctly indicate the forecast was not at all accurate. But the second example is more accurate than a third, where the actual is 8 and the forecast is 200. That’s a distinction a 0 to 100% range of accuracy doesn’t register. In this final example:

Unit Error is 200 – 8 = 192

Absolute % Error = 192 / 8, as a % = 24 * 100 = 2,400%

Accuracy = 100% – 2,400% = negative is set to 0%.

Error metrics continue to provide information on how far the forecast is from the actual and arguably better represent forecast accuracy.

We encourage adopting the error viewpoint. You simply hope for a small error percentage to indicate the forecast was not far from the actual, instead of hoping for a large accuracy percentage to indicate the forecast was close to the actual.  This shift in mindset offers the same insights while eliminating distortions.

 

 

 

 

Service-Level-Driven Planning for Service Parts Businesses

Service-Level-Driven Service Parts Planning is a four-step process that extends beyond simplified forecasting and rule-of-thumb safety stocks. It provides service parts planners with data-driven, risk-adjusted decision support.

Step 1. Ensure that all stakeholders agree on the metrics that matter. All participants in the service parts inventory planning process must agree on the definitions and what metrics matter most to the organization. Service Levels detail the percentage of time you can completely satisfy required usage without stocking out. Fill Rates detail the percentage of the requested usage that is immediately filled from stock. (To learn more about the differences between service levels and fill rate, watch this 4-minute lesson here.) Availability details the percentage of active spare parts that have an on-hand inventory of at least one unit. Holding costs are the annualized costs of holding stock accounting for obsolescence, taxes, interest, warehousing, and other expenses. Shortage costs are the cost of running out of stock including vehicle/equipment down time, expedites, lost sales, and more. Ordering costs are the costs associated with placing and receiving replenishment orders.

Step 2. Benchmark historical and predicted current service level performance. All participants in the service parts inventory planning process must hold a common understanding of predicted future service levels, fill rates and costs and their implications for your service parts operations. It is critical to measure both historical Key Performance Indicators (KPIs) and their predictive equivalents, Key Performance Predictions (KPPs). Leveraging modern software, you can benchmark past performance and leverage probabilistic forecasting methods to simulate future performance. By stress testing your current inventory stocking policies against all plausible scenarios of future demand, you will know ahead of time how current and proposed stocking policies are likely to perform.

Step 3. Agree on targeted service levels for each spare part and take proactive corrective action when targets are predicted to miss. Parts planners, supply chain leadership, and the mechanical/maintenance teams should agree on the desired service level targets with a full understanding of the tradeoffs between stockout risk and inventory cost. By leveraging what-if scenarios in modern parts planning software, it is possible to compare alternative stocking policies and identify those that best meets business objectives. Agree on what degree of stockout risk is acceptable for each part or class of parts. Likewise, determine inventory budgets and other cost constraints. Once these limits are agreed, take immediate action to avoid stockouts and excess inventory before they occur. Use your software to automatically upload modified reorder points, safety stock levels, and/or Min/Max parameters to your Enterprise Resource Planning (ERP) or Enterprise Asset Management (EAM) system to adjust daily parts purchasing.

Step 4. Make it so and keep it so. Empower the planning team with the knowledge and tools it needs to ensure that you strike agreed-upon balance between service levels and costs by driving your ordering process using optimized inputs (forecasts, reorder points, order quantities, safety stocks). Track your KPI’s and use your software to identify and address exceptions. Don’t let reorder points grow stale and outdated.  Recalibrate the stocking policies each planning cycle (at least once monthly) using up-to-date usage history, supplier lead times, and costs. Remember: Recalibration of your service parts inventory policy is preventive maintenance against both stockouts and excess stock.

Riding the Tradeoff Curve

The Smart Forecaster

 Pursuing best practices in demand planning,

forecasting and inventory optimization

What We’re Up Against

As a third-generation Boston Red Sox fan, I’m disinclined to take advice from any New York Yankee ballplayer, even a great one but have to agree that sometimes, you just need to make a decision.   However, wouldn’t it be better if we knew the tradeoffs associated with each decision. Perhaps one road is more scenic but takes longer while the other is more direct but boring. Then you wouldn’t have to simply “take it” but could make an informed decision based on the advantages/disadvantages of each approach.

In the supply chain planning world, the most fundamental decision is how to balance item availability against the cost of maintaining that availability (service levels and fill rates). At one extreme, you can grossly overstock and never run out until you go broke and have to close up shop from sinking all your cash into inventory that doesn’t sell.  At the other extreme, you can grossly understock and save a bundle on inventory holding costs but go broke and have to close up shop because all your customers took their business elsewhere.

There is no escaping this fundamental tension. They way to survive and thrive is to find a productive and sustainable balance. To do that requires fact-based tradeoffs based on the numbers. To get the numbers requires software.

The general drift of things is obvious. If you decide to keep more inventory, you will have more Holding Costs, lower Shortage Costs, and possibly lower Ordering Costs. Whether this costs or saves money is impossible to know without some sophisticated analysis, but usually the result is that the Total Cost goes up. But if you do invest in more inventory, something will be gained, because you will offer your customers higher Service Levels and Fill Rates. How much higher requires, as you might guess, some sophisticated analysis.

Show Me the Numbers

This blog lays out what such an analysis looks like. There is no universal solution pointing you to the “right” decision. You might think that the right decision is the one that does best by your bottom line. But to get those numbers, you would need something rarely seen: an accurate model of customer behavior with regard to service level (check out our article “How to choose a target service level”) For example, at what point will a customer walk away and take their business elsewhere?  Will it be after you stock out 1% of the time, 5% of time, 10% of the time? Will you still keep their business as long as you fill back orders quickly?  Will it be after a back order of 1 day, 2 days? 3 weeks? Will it be after this happens one time on one an important part or many times across many parts?  While modeling the precise service level that will allow you to keep your customer while minimizing costs seems like an unapproachable ideal, another type of sophisticated analysis is more pragmatic. 

Inventory optimization and forecasting software can factor all associated costs such as the cost of stocking out, cost of holding inventory, and cost of ordering inventory in order to prescribe an optimal service level target that yields the lowest total cost. However, even that “optimal” service level is sensitive to changes in the costs making the results potentially questionable.  For example, if you don’t accurately estimate the precise costs (shortage costs are the most difficult) it will be tough to definitely state something like “If I increase my on-hand inventory by an average of one unit for all items in an important product family, my company will see a net gain of $170,500.  That gain increases until I get to 4 units.  At 4 units and higher, the return declines due to excessive holding costs. So, the best decision factoring projected holding, ordering, and stockout is to increase inventory by 3 units to see a net gain of over $500,000.  

Short of that ideal, you can do something that is simpler yet still extremely valuable: Quantify the tradeoff curve between inventory cost and item availability. While you won’t necessarily know the service level you should target, you will know the costs of varying service levels.  Then you can earn your big bucks by finding a good place to be on that tradeoff curve and communicating where you at risk, where you aren’t, and setting expectations with customers and internal stakeholders.  Without the tradeoff curve to guide you, you are flying blind with no way to rationally modify stocking policy.

A Scenario to Learn From

Let’s sketch out a realistic tradeoff curve. We start with a scenario requiring a management decision. The scenario we will use and associated assumptions about demand, lead times, and costs are detailed below:

Inventory Policy

  • Periodic review – Reorder decisions made every 30 days
  • Order-Up-To-Level (“S”) – Varied from 30 to 60 units
  • Shortage Policy – Allow backorders, no lost orders

Demand

  • Demand is intermittent
  • Average = 0.8 units per day
  • Standard deviation = 1.2 units per day
  • Largest demand in a year ≈ 9
  • % of days with no demand = 53%

Lead Time

  • Random at either 7, 14 or 21 days with probabilities 70%, 20% and 10%, respectively

Cost Parameters

  • Holding cost = $1 per day
  • Ordering Cost = $10 per order without regard to size of order
  • Shortage Cost = $100 per unit not immediately shipped from stock

We imagine an inventory control policy that is known in the trade as a “periodic review” or (T,S) policy. In this instance, the Review Period (“T”) is 30 days, meaning that every 30 days the inventory position is checked and an ordering decision is made. The order quantity is the difference between the observed number of units on hand and the Order-Up-To Quantity (“S”). So, if the end-of-month inventory is 12 units and S = 20, the order quantity would be S – 12 = 20 -1 2 = 8. The next month, the order quantity is likely to be different. If the inventory ever goes negative (backorders) during a review period, the next order tries to restore equilibrium by ordering more in order to fill those backorders. For example, if the inventory is -5 (meaning 5 units ordered by not available for shipping, the next order would be S – (-5) = S + 5. Details of the hypothetical demand stream, supplier lead times, and cost elements are shown in Figure 1 below. Figure 2 show a sample of daily demand and daily inventory over five review periods. Demand is intermittent, as is often true for spare parts, and therefore difficult to plan for.

Figure 1: Different choices of inventory policy (order up to), associated costs, and service levels

Figure 2: Details of five months of system operation given one of the polices

 

Inventory Planning Software Is Our Friend

Software encodes the logic of the operation of the (T,S) system, generates many hypothetical but realistic demand scenarios, calculates how each of those scenarios plays out, then looks back on the simulated operation (here, 10 years or 3,650 consecutive days) to calculate cost and performance metrics.

To reveal the tradeoff curve, we ran several computational experiments in which we varied the Order-Up-To Level, S. The plots Figure 2 show the behavior of the on-hand inventory in “richest” alternative with S = 60. In the snippet shown in Figure 2, the on-hand inventory never comes close to stocking out. You can read that too ways. One, a bit naïve, is to say “Good, we’re well protected.” The other, more aggressive, is to say, “Oh no, we’re bloated. I wonder what would happen if we reduced S.”

The Tradeoff Curve Revealed

Figure 3 shows the results of reducing S from 60 down to 30 in steps of 5 units. The table shows that Total Cost is the sum of Holding Cost, Ordering Cost, and Shortage Cost. For the (T,S) policy, the ordering cost is always the same, since an order is placed like clockwork every 30 days. But the other components of cost respond to the changes in S.

Figure 3: The experimental results and corresponding tradeoff curve showing how changing the Order-Up-To Level (“S”) impacts both Service Level and Total Annual Cost

Note that the Service Level is always lower than the Fill Rate in these scenarios. As a professor, I always think of this difference in terms of exam grading. Each replenishment cycle is like a test. Service Level is about the probability of a stockout, so it’s a like the grade on pass/fail exam with one question that must be answered perfectly. If there is no stockout in a cycle, that’s an A. If there is a stockout, that’s an F. It doesn’t matter if it’s one unit that’s not supplied or 50 – it’s still an F. But Fill Rate is like a question that is graded with partial credit. So being short one of ten units gets you 90% Fill Rate for that cycle, not 0%. It’s important to understand the difference between these two important metrics for inventory planning – check out this vlog describing service level vs. fill rate via an interactive exercise in Excel.

The plot in Figure 3 is the real news. It pairs Total Cost and Service Level for various levels of S. If you read the graph right to left, it tells us that there are dramatic cost savings to be had by reducing S with very little penalty in terms of reduced item availability. For instance, reducing S from 60 to 55 saves close to $800 per year on this one item while reducing service level just a bit from (essentially) 100% to a still-impressive 99%. Cutting S some more does the same, though not as dramatically. If you read the graph left to right, you see that moving up from S = 30 to S = 35 costs about $1,000 per year but improves Service Level from an F grade (45%) to at least a C grade (71%). After that, pushing S higher costs progressively more while gaining progressive less.

The tradeoff curve doesn’t give you an answer to how to set the Order-Up-To Level, but it does let you evaluate the costs and benefits of each possible answer. Take a minute and pretend that this is your problem: Where would you want to be along the tradeoff curve?

You may object and say you hate your choices and want to change the game. Is there escape from the curve? Not from the general curve, but you might be able to shape a less painful curve. How?

You may have other cards to play. One avenue is to try to “shape” the demand so that it is less variable. The demand plot in Figure 2 shows a lot of variability. If you could smooth out the demand, the whole tradeoff curve would shift down, making every choice less expensive. A second avenue is to try to reduce the mean and variability of supplier lead times. Achieving either would also shift the curve down to make the choice less painful. Check out our article on how suppliers influence your inventory costs

Summary

The tradeoff curve is always with us. Sometimes we may be able to make it more friendly, but we always to pick our spot along it. It is better to know what you’re getting for any choice of inventory policy than to try to guess, and the curve gives you that.  When you have an accurate estimate of that curve, you are no longer flying blind when it comes to inventory planning. 

 

 

 

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      Quantum Inventory Theory?

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      forecasting and inventory optimization

      Physicists like my Smart Software co-founder, Dr. Nelson Hartunian, tell us civilians that everything is different when we drill down to the tiniest level of the world. Physics at the quantum level is quite weird – not at all like what we experience in our usual macroscopic life. Among the oddities are “superposition”, “entanglement”, and “quantum foam.”  Weird as these phenomena are, I cannot help seeing analogs in the supposedly different world of supply chain management.

      Consider quantum superposition. Briefly, superposition means any quantum entity can be in two states at once. Schrödinger’s cat is the most famous illustration of this idea. But how many of you readers are also in a state of superposition? Don’t you find yourself being a manager of a team yet a member of your supervisor’s team, a trouble-shooter yet also a forecasting expert or an inventory optimizer and…? And doesn’t all this make you sometimes feel, like that cat, that you are simultaneously both dead and alive? Modern software can ease some of this burden by automating the tasks of demand planning and inventory optimization. The rest is up to you.

      A second quantum analog is entanglement. Briefly, entanglement is the linkage between two elements of a system. They can be light years apart, yet changing one part of an entangled system will instantaneously change the other part. This bugged Albert Einstein, who derided it as “spooky action as a distance.” In our regular world, demand planning and inventory optimization are entangled, since the process of inventory optimization sits on top of the process of demand forecasting. Modern software links the two in an efficient interface.

      Finally, the quantum foam – one of my favorite ideas. As I understand it, quantum foam is a substitute for empty space: there is no empty space, rather a constant bubbling of “vacuum energy” accompanied by a flux of “virtual particles” being born out of nothing and then disappearing back into nothing. In the supply chain world, the analogs of virtual particles are customer orders. Often it seems that they pop up with no warning out of thin air, and sometimes they disappear by cancellation in an equally random and mysterious process. This kind of demand fluctuation is the basis for all the theory of inventory control. Modern software therefore begins with probability models of customer demand. Those models then have implications for such tangible quantities as safety stocks, reorder points, and order quantities.

      Does it really help demand planners and inventory managers to think about these ideas from quantum physics? Well, it’s a bit of fun to see the analogies to our regular world of work. And they do remind us of more macroscopic matters: the basic concepts of the need to deal with more than one task simultaneously, the linkage between forecasting and inventory management, and randomness as the fundamental feature of the supply chain.

       

       

       

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          Stop Leaking Money with Manual Inventory Controls

          The Smart Forecaster

           Pursuing best practices in demand planning,

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          An inventory professional who is responsible for 10,000 items has 10,000 things to stress over every day. Double that for someone responsible for 20,000 items.

          In the crush of business, routine decisions often take second place to fire-fighting: dealing with supplier hiccups, straightening out paperwork mistakes, recovering from that collision between a truck and the loading dock.

          In the meantime, however, your company’s accumulated inventory control policies keep on doing what they do, even if they are leaking money. A good manager will make time to listen to the “background noise” even when he or she hears loud crashing in the warehouse.

          Consider the current settings for your inventory control parameters (e.g., reorder points and order quantities). It’s easy to think of these as “fire and forget” decisions. But these settings usually accumulate over time and end up comprising a mish-mash of forgotten judgement calls that may be misaligned with your current operating environment. Many factors can drift away from their previous levels, such as supplier lead times, ordering costs, or average item demand. These changes can force invisible tradeoffs that are not to your best advantage.

          It’s wise to revisit these control settings now and then to see if it’s possible to align your day-to-day operations with current realities. Of course, it would be infeasible for a busy manager to manually calculate the effects of changing the control settings on, say, 10,000 items. But that’s what modern inventory optimization and demand planning software is for: making large scale analytical tasks feasible. Such software will allow you to automatically process new information and compute adjustments at scale. The result will be easy wins – many of which would otherwise go unrealized.  And continuously saving a little here and there adds up to significant dollars when you are managing thousands of items.

          Consider this example. Company A uses a periodic review inventory system. Every 30 days, they check on-hand inventory for all their items and decide how much replenishment stock to order. Each of their 10,000 items has a specified Order-Up-To Level that determines the size of their replenishment orders.

          For instance, suppose Item 1234 has an Order-Up-To Level of 74, determined by factoring in the average item demand of 1.0 units per day, an average replenishment lead time of 8 days, and a target fill rate of 90% for this item. The choice of 74 as the Order-Up-To Level lets Company A meet its 90% fill rate target for Item 1234, but it also results in an average on hand inventory level of 40 units. At $1,500 per unit, this item alone represents $45,000 of inventory investment.

          Now supposed that average item demand were to drift up from 1.0 to 1.2 units/day. Without anyone noticing, the fill rate for Item 1234 would drop to 82%!

          Now suppose demand were to shift in the other direction and drift down to 0.8 units/day. As with the increase in average demand from 1.0 to 1.2 units/day, this kind of change is difficult to see when looking at a plot (see Figure 1) but can have a significant operational impact. In this case, the fill rate would zoom to a generous 96% but on hand inventory would also zoom: from 40 units to 46. Those six extra units would represent $9,000 in excess inventory.

          Figure 1: Samples of daily demand with two different average values.  The difference in demand is unnoticeable to the naked eye but if not accounted for will have a large operational impact on inventory spend and service levels

          Now imagine similar small shifts happening unnoticed across a full fleet of 10,000 inventory items. The total financial impact of all such shifts would be sufficient to get onto the radar of any CFO.  Trying to keep on top of this turbulence would be impossible if done manually but modern inventory optimization software could calculate the proper adjustments automatically as frequently as your company can handle, even daily helping you realize substantial improvements in service levels, inventory efficiency, while lowering stockout and holding costs!

           

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