Increasing Revenue by Increasing Spare Part Availability

The Smart Forecaster

 Pursuing best practices in demand planning,

forecasting and inventory optimization

Let’s start by recognizing that increased revenue is a good thing for you, and that increasing the availability of the spare parts you provide is a good thing for your customers.

But let’s also recognize that increasing item availability will not necessarily lead to increased revenue. If you plan incorrectly and end up carrying excess inventory, the net effect may be good for your customers but will definitely be bad for you. There must be some right way to make this a win-win, if only it can be recognized.

To make the right decision here, you have to think systematically about the problem. That requires that you use probabilistic models of the inventory control process.

 

A Scenario

Let’s consider a specific, realistic scenario. Quite a number of factors have an influence on the results:

  • The item: A specific low-volume spare part.
  • Demand mean: Averaging 0.1 units per day (so, highly “intermittent”)
  • Demand standard deviation: 0.35 units per day (so, highly variable or “overdispersed”).
  • Supplier average lead time: 5 days.
  • Unit cost: $100.
  • Holding cost per year as % of unit cost: 10%.
  • Ordering cost per PO cut: $25.
  • Stockout consequences: Lost sales (so, a competitive market, no backorders).
  • Shortage cost per lost sale: $100.
  • Service level target: 85% (so, 15% chance of a stockout in any replenishment cycle).
  • Inventory control policy: Periodic-review/Order-up-to (also called at (T,S) policy)

 

Inventory Control Policy

A word about the inventory control policy. The (T,S) policy is one of several that are common in practice. Though there are other more efficient policies (e.g., they don’t wait for T days to go by before making adjustment to stock), (T,S) is one of the simplest and so it is quite popular. It works this way: Every T days, you check how many units you have in stock, say X units. Then you order S-X units, which appear after the supplier lead time (in this case, 5 days). The T in (T,S) is the “order interval”, the number of days between orders; the S is the “order-up-to level”, the number of units you want to have on hand at the start of each replenishment cycle.

To get the most out of this policy, you must wisely pick values of T and S. Picking wisely means you cannot win by guessing or using simple rule-of-thumb guides like “Keep an average of 3 x average demand on hand.”  Poor choices of T and S hurt both your customers and your bottom line. And sticking too long with choices that were once good can result in poor performance should any of the factors above change significantly, so the values of T and S should be recalculated now and then.

The smart way to pick the right values of T and S is to use probabilistic models encoded in advanced software. Using software is essential when you have to scale up and pick values of T and S that are right for not one item but hundreds or thousands.

 

Analysis of Scenario

Let’s think about how to make money in this scenario. What’s the upside? If there were no expenses, this item could generate an average of $3,650 per year: 0.1 units/day x 365 days x $100/unit. Subtracted from that will be operating costs, comprised of holding, ordering and shortage costs. Each of those will depend on your choices of T and S.

The software provides specific numbers: Setting T = 321 days and S = 40 units will result in average annual operating costs of $604, giving an expected margin of $3,650 – $604 = $3,046. See Table 1, left column. This use of software is called “predictive analytics” because it translates system design inputs into estimates of a key performance indicator, margin.

Now think about whether you can do better. The service level target in this scenario is 85%, which is a somewhat relaxed standard that is not going to turn any heads. What if you could offer your customers a 99% service level? That sounds like a distinct competitive advantage, but would it reduce your margin? Not if you properly adjust the values of T and S.

Setting T = 216 days and S = 35 units will reduce average annual operating costs to $551 and increase expected margin to $3,650 – $551 = $3,099. See Table 1, right column. Here is the win-win we wanted: higher customer satisfaction and roughly 2% more revenue. This use of the software is called “sensitivity analysis” because it shows how sensitive the margin is to the choice of service level target.

Software can also help you visualize the complex, random dynamics of inventory movements. A by-product of the analysis that populated Table 1 are graphs showing the random paths taken by stock as it decreases over a replenishment cycle. Figure 1 shows a selection of 100 random scenarios for the scenario in which the service level target is 99%. In the figure, only 1 of the 100 scenarios resulted in a stockout, confirming the accuracy of the choice of order-up-to-level.

 

Summary

Management of spare parts inventories is often done haphazardly using gut instinct, habit, or obsolete rule-of-thumb. Winging it this way is not a reliable and reproducible path to higher margin or higher customer satisfaction. Probability theory, distilled into probability models then encoded in advanced software, is the basis for coherent, efficient guidance about how to manage spare parts based on facts: demand characteristics, lead times, service level targets, costs and the other factors. The scenarios analyzed here illustrate that it is possible to achieve both higher service levels and higher margin. A multitude of scenarios not shown here offer ways to achieve higher service levels but lose margin. Use the software.

Scenarios with different service level targets

Stock on hand during one replenishment cycle

 

 

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    1. Scale-dependent error
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    3. Relative error
    4 .Scale-free error

    Remark: Scale-dependent metrics are expressed in the units of the forecasted variable. The other three are expresses as percentages.

     

    1. Scale-dependent error metrics

    • Mean Absolute Error (MAE) aka Mean Absolute Deviation (MAD)
    • Median Absolute Error (MdAE)
    • Root Mean Square Error (RMSE)
    • These metrics express the error in the original units of the data.
      • Ex: units, cases, barrels, kilograms, dollars, liters, etc.
    • Since forecasts can be too high or too low, the signs of the errors will be either positive or negative, allowing for unwanted cancellations.
      • Ex: You don’t want errors of +50 and -50 to cancel and show “no error”.
    • To deal with the cancellation problem, these metrics take away negative signs by either squaring or using absolute value.

     

    2. Percentage error metric

    • Mean Absolute Percentage Error (MAPE)
    • This metric expresses the size of the error as a percentage of the actual value of the forecasted variable.
    • The advantage of this approach is that it immediately makes clear whether the error is a big deal or not.
    • Ex: Suppose the MAE is 100 units. Is a typical error of 100 units horrible? ok? great?
    • The answer depends on the size of the variable being forecasted. If the actual value is 100, then a MAE = 100 is as big as the thing being forecasted. But if the actual value is 10,000, then a MAE = 100 shows great accuracy, since the MAPE is only 1% of the actual.

     

    3. Relative error metric

    • Median Relative Absolute Error (MdRAE)
    • Relative to what? To a benchmark forecast.
    • What benchmark? Usually, the “naïve” forecast.
    • What is the naïve forecast? Next forecast value = last actual value.
    • Why use the naïve forecast? Because if you can’t beat that, you are in tough shape.

     

    4. Scale-Free error metric

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      • They do both use the naïve forecast, but this metric uses errors in forecasting the demand history, while the MdRAE uses errors in forecasting future values.
      • This matters because there are usually many more history values than there are forecasts.
      • In turn, that matters because this metric would “blow up” if all the data were zero, which is less likely when using the demand history.

     

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    The special problem of intermittent demand

    • “Intermittent” demand has many zero demands mixed in with random non-zero demands.
    • MAPE gets ruined when errors are divided by zero.
    • MdRAE can also get ruined.
    • MdSAE is less likely to get ruined.

     

    Recap and remarks

    • Forecast metrics are necessary aids for monitoring and improving forecast accuracy.
    • There are two major classes of metrics: absolute and relative.
    • Absolute measures (MAE, MdAE, RMSE) are natural choices when assessing forecasts of one item.
    • Relative measures (MAPE, MdRAE, MdSAE) are useful when comparing accuracy across items or between alternative forecasts of the same item or assessing accuracy relative to the natural variability of an item.
    • Intermittent demand presents divide-by-zero problems which favor MdSAE over MAPE.
    • When assessing forecasts of multiple items, it often makes sense to use weighted averages, weighting items differently by volume or revenue.
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