Summary

Smart Software’s advanced supply chain analytics exploits multiple advanced methods. Two of the most important are “statistical bootstrapping” and “Monte Carlo simulation”. Since both involve lots of random numbers flying around, folks sometimes get confused about which is which and what they are good for. Hence, this note. Bottom line up front: Statistical bootstrapping generates demand scenarios for forecasting. Monte Carlo simulation uses the scenarios for inventory optimization.

Bootstrapping

Bootstrapping, also called “resampling” is a method of computational statistics that we use to create demand scenarios for forecasting. The essence of the forecasting problem is to expose possible futures that your company might confront so you can work out how to manage business risks. Traditional forecasting methods focus on computing “most likely” futures, but they fall short of presenting the full risk picture. Bootstrapping provides an unlimited number of realistic what-if scenarios.

Bootstrapping does this without making unrealistic assumptions about the demand, i.e., that it is not intermittent, or that it has a bell-shaped distribution of sizes. Those assumptions are crutches to make the math simpler, but the bootstrap is a procedure,  not an equation, so it doesn’t need such simplifications.

For the simplest demand type, which is a stable randomness with no seasonality or trend, bootstrapping is dead easy. To get a reasonable idea of what a single future demand value might be, pick one of the historical demands at random. To create a demand scenario, make multiple random selections from the past and string them together. Done. It is possible to add a little more realism by “jittering” the demand values, i.e., adding or subtracting a bit of additional randomness to each one, but even that is simple.

Figure 1 shows a simple bootstrap. The first line is a short sequence of historical demand for an SKU. The following lines show scenarios of future demand created by randomly selecting values from the demand history. For instance, the next three demand might be (0, 14, 6), or (2, 3, 5), etc.

Figure 1: Example of demand scenarios generated by a simple bootstrap

Higher frequency operations such as daily forecasting bring with them more complex demand patterns, such as double seasonality (e.g., day-of-week and month-of-year) and/or trend. This challenged us to invent a new generation of bootstrapping algorithms. We recently won a US Patent for this breakthrough, but the essence is as described above.

Monte Carlo Simulation

Monte Carlo is famous for its casinos, which, like bootstrapping, invoke the idea of randomness. Monte Carlo methods go back a long way, but the modern impetus came with the need to do some hairy calculations about where neutrons would fly when an A-bomb explodes.

The essence of Monte Carlo analysis is this: “Our problem is too complicated to analyze with paper-and-pencil equations. So, let’s write a computer program that codes the individual steps of the process, put in the random elements (e.g., which way a neutron shoots away), wind it up and watch it go. Since there’s a lot of randomness, let’s run the program a zillion times and average the results.”

Applying this approach to inventory management, we have a different set of randomly occurring events: e.g., a demand of a given size arrives on a random day, a replenishment of a given size arrives after a random lead time, we cut a replenishment PO of a given size when stock drops to or below a given reorder point. We code the logic relating these events into a program. We feed it with a random demand sequence (see bootstrapping above), run the program for a while, say one year of daily operations, compute performance metrics like Fill Rate and Average On Hand inventory, and “toss the dice” by re-running the program many times and averaging the results of many simulated years. The result is a good estimate of what happens when we make key management decisions: “If we set the reorder point at 10 units and the order quantity at 15 units, we can expect to get a service level of 89% and an average on hand of 21 units.” What the simulation is doing for us is exposing the consequences of management decisions based on realistic demand scenarios and solid math. The guesswork is gone.

Figure 2 shows some of the inner workings of a Monte Carlo simulation of an inventory system in four panels. The system uses a Min/Max inventory control policy with Min=10 and Max=25. No backorders are allowed: you have the good or you lose the business. Replenishment lead times are usually 7 days but sometimes 14. This simulation ran for one year.

The first panel shows a complex random demand scenario in which there is no demand on weekends, but demand generally increases each day from Monday to Friday. The second panel shows the random number of units on hand, which ebbs and flows with each replenishment cycle. The third panel shows the random sizes and timings of replenishment orders coming in from the supplier. The final panel shows the unsatisfied demand that jeopardizes customer relationships. This kind of detail can be very useful for building insight into the dynamics of an inventory system.

Figure 2: Details of a Monte Carlo simulation

Figure 2 shows only one of the countless ways that the year could play out. Generally, we want to average the results of many simulated years. After all, nobody would flip a coin once to decide if it were a fair coin. Figure 3 shows how four key performance metrics (KPI’s) vary from year to year for this system. Some metrics are relatively stable across simulations (Fill Rate), but others show more relative variability (Operating Cost= Holding Cost + Ordering Cost + Shortage Cost). Eyeballing the plots, we can estimate that the choices of Min=10, Max=25 leads to an average Operating cost of around $3,000 per year, a Fill Rate of around 90%, a Service Level of around 75%, and an Average On Hand of about 10

Figure 3: Variation in KPI’s computed over 1,000 simulated years

In fact, it is now possible to answer a higher level of management question. We can go beyond “What will happen if I do such-and-such?” to “What is the best thing I can do to achieve a fill rate of at least 90% for this item at the lowest possible cost?” The mathemagic  behind this leap is yet another key technology called “stochastic optimization”, but we’ll stop here for now. Suffice it to say that Smart’s SIO&P software can search the “design space” of Min and Max values to automatically find the best choice.

Managing spare parts presents numerous challenges, such as unexpected breakdowns, changing schedules, and inconsistent demand patterns. Traditional forecasting methods and manual approaches are ineffective in dealing with these complexities. To overcome these challenges, this blog outlines key strategies that prioritize service levels, utilize probabilistic methods to calculate reorder points, regularly adjust stocking policies, and implement a dedicated planning process to avoid excessive inventory. Explore these strategies to optimize spare parts inventory and improve operational efficiency.

Bottom Line Upfront

​1.Inventory Management is Risk Management.

2.Can’t manage risk well or at scale with subjective planning – Need to know service vs. cost.

3.It’s not supply & demand variability that are the problem – it’s how you handle it.

4.Spare parts have intermittent demand so traditional methods don’t work.

5.Rule of thumb approaches don’t account for demand variability and misallocate stock.

6.Use Service Level Driven Planning  (service vs. cost tradeoffs) to drive stock decisions.

7.Probabilistic approaches such as bootstrapping yield accurate estimates of reorder points.

8.Classify parts and assign service level targets by class.

9.Recalibrate often – thousands of parts have old, stale reorder points.

10.Repairable parts require special treatment.

Do Focus on the Real Root Causes

Intermittent Demand

• Slow moving, irregular or sporadic with a large percentage of zero values.
• Non-zero values are mixed in randomly – spikes are large and varied.
• Isn’t bell shaped (demand is not Normally distributed around the average.)
• At least 70% of a typical Utility’s parts are intermittently demanded.

Normal Demand

• Very few periods of zero demand (exception is seasonal parts.)
• Often exhibits trend, seasonal, or cyclical patterns.
• Lower levels of demand variability.
• Is bell-shaped (demand is Normally distributed around the average.)

Don’t rely on averages

• OK for determining typical usage over longer periods of time.
• Often forecasts more “accurately” than some advanced methods.
• But…insufficient for determining what to stock.

Don’t Buffer with Multiples of Averages

Example:  Two equally important parts so let’s treat them the same.
We’ll order more  when On Hand Inventory ≤ 2 x Avg Lead Time Demand.

Do use Service Level tradeoff curves to compute safety stock

Standard Normal Probabilities

OK for normal demand. Doesn’t work with intermittent demand!

Don’t use Normal (Bell Shaped) Distributions

• You’ll get the tradeoff curve wrong:

– e.g., You’ll target 95% but achieve 85%.

– e.g., You’ll target 99% but achieve 91%.

• This is a huge miss with costly implications:

– You’ll stock out more often than expected.

– You’ll start to add subjective buffers to compensate and then overstock.

– Lack of trust/second-guessing of outputs paralyzes planning.

Why Traditional Methods Fail on Intermittent Demand: 

Traditional Methods are not designed to address core issues in spare parts management.

Need: Probability distribution (not bell-shaped) of demand over variable lead time.

• Get: Prediction of average demand in each month, not a total over lead time.
• Get: Bolted-on model of variability, usually the Normal model, usually wrong.

Need: Exposure of tradeoffs between item availability and cost of inventory.

• Get: None of this; instead, get a lot of inconsistent, ad-hoc decisions.

Do use Statistical Bootstrapping to Predict the Distribution:

Then exploit the distribution to optimize stocking policies.

How does Bootstrapping Work?

24 Months of Historical Demand Data.

Bootstrap Scenarios for a 3-month Lead Time.

Bootstrapping Hits the Service Level Target with nearly 100% Accuracy!

• National Warehousing Operation.

Task: Forecast inventory stocking levels for 12,000 intermittently demanded SKUs at 95% & 99% service levels

Results:

At 95% service level, 95.23% did not stock out.

At 99% service level, 98.66% did not stock out.

This means you can rely on output to set expectations and confidently make targeted stock adjustments that lower inventory and increase service.

Set Target Service Levels According to Order Frequency & Size

Recalibrate Reorder Points Frequently

• Static ROPs cause excess and shortages.
• As lead time increases, so should the ROP and vice versa.
• As usage decreases, so should the ROP and vice versa.
• Longer you wait to recalibrate, the greater the imbalance.
• Mountains of parts ordered too soon or too late.
• Wastes buyers’ time placing the wrong orders.
• Breeds distrust in systems and forces data silos.

Do Plan Rotables (Repair Parts) Differently

Summary

1.Inventory Management is Risk Management.

2.Can’t manage risk well or at scale with subjective planning – Need to know service vs. cost.

3.It’s not supply & demand variability that are the problem – it’s how you handle it.

4.Spare parts have intermittent demand so traditional methods don’t work.

5.Rule of thumb approaches don’t account demand variability and misallocate stock.

6.Use Service Level Driven Planning  (service vs. cost tradeoffs) to drive stock decisions.

7.Probabilistic approaches such as bootstrapping yield accurate estimates of reorder points.

8.Classify parts and assign service level targets by class.

9.Recalibrate often – thousands of parts have old, stale reorder points.

10.Repairable parts require special treatment.

Reveal how forecasts are used with these 4 questions.

Often companies will insist that they “don’t use forecasts” to plan inventory.  They often use reorder point methods and are struggling to improve on-time delivery, inventory turns, and other KPIs. While they don’t think of what they are doing as explicitly forecasting, they certainly use estimates of future demand to develop reorder points such as min/max.

Regardless of what it is called, everyone tries to estimate future demand in some way and uses this estimate to set stocking policies and drive orders. To improve inventory planning and make sure you aren’t over/under ordering and creating large stockouts and inventory bloat, it is important to understand exactly how your organization uses forecasts. Once this is understood, you can assess whether the quality of the forecasts can be improved.

Try getting answers to the following questions. It will reveal how forecasts are being used in your business – even if you don’t think you use forecasts.

1.  Is your forecast a period-by-period estimate over time that is used to predict what on-hand inventory will be in the future and triggers order suggestions in your ERP system?

2. Or is your forecast used to derive a reorder point but not explicitly used as a per-period driver to trigger orders? Here, I may predict we’ll sell 10 per week based on the history, but we are not loading 10, 10, 10, 10, etc., into the ERP. Instead, I derive a reorder point or Min that covers the two-period lead time + some amount of buffer to help protect against stock out. In this case, I’ll order more when on hand gets to 25.

3. Is your forecast used as a guide for the planner to help subjectively determine when they should order more?  Here, I predict 10 per week, and I assess the on-hand inventory periodically, review the expected lead time, and I decide, given the 40 units I have on hand today, that I have “enough.” So, I do nothing now but will check back again in a week.

4. Is it used to set up blanket orders with suppliers? Here, I predict 10 per week and agree to a blanket purchase order with the supplier of 520 per year. The orders are then placed in advance to arrive in quantities of 10 once per week until the blanket order is consumed.

Once you get the answers, you can then ask how the estimates of demand are created.  Is it an average? Is it deriving demand over lead time from a sales forecast?  Is there a statistical forecast generated somewhere?  What methods are considered? It will also be important to assess how safety stocks are used to protect against demand and supply variability.  More on all of this in a future article.

I’ll bet your maintenance and repair teams would be ok with incurring higher stock out risks one some spare parts if they knew that the inventory reduction savings would be used to spread out the inventory investment more effectively to other parts and boost overall service levels.

I’ll double down that your Finance team, despite always being challenged with lowering costs, would support a healthy inventory increase if they could clearly see that the revenue benefits from increased uptime, fewer expedites, and service level improvements clearly outweighed the additional inventory costs and risk.

A spare parts tradeoff curve will enable service parts planning teams to properly communicate the risks and costs of each inventory decision.  It is mission critical for parts planning and the only way to adjust stocking parameters proactively and accurately for each part.  Without it, planners, for all intents and purposes, are “planning” with blinders on because they won’t be able to communicate the true tradeoffs associated with stocking decisions.

For example, if a proposed increase to the min/max levels of an important commodity group of service parts is recommended, how do you know whether the increase is too high or too low or just right?  How can you fine-tune the change for thousands of spares?  You won’t and you can’t.  Your inventory decision making will rely on reactive, gut feel, and broad-brush decisions causing service levels to suffer and inventory costs to balloon.

So, what exactly is a spare parts tradeoff curve anyway?

It’s a fact-based, numerically driven prediction that details how changes in stocking levels will influence inventory value, holding costs, and service levels.  For each unit change in inventory level there is a cost and a benefit.  The spare parts tradeoff curve identifies these costs and benefits across different stocking levels. It lets planners discover the stock level that best balances the costs and benefits for each individual item.

Here are two simplified examples. In Figure 1, the spare parts tradeoff curve shows how the service level (probability of not stocking out) changes depending on the reorder level.  The higher the reorder level, the lower the stockout risk.  It is critical to know how much service you are gaining given the inventory investment.  Here you may be able to justify that an inventory increase from a reorder point of 35 to 45 is well worth the investment of 10 additional units of stock because service levels jumps from just under 70% to 90%, cutting your stockout risk for the spare part from 30% to 10%!

​

Figure 1: Cost versus Service Level

Figure 2: Service Level versus Size of Inventory

In this example (Figure 2), the tradeoff curve exposes a common problem with spare parts inventory.  Often stock levels are so high that they generate negative returns.  After a certain stocking quantity, each additional unit of stock does not buy more benefit in the form of a higher service level.  Inventory decreases can be justified when it is clear the stock level is well past the point of diminishing returns. An accurate tradeoff curve will expose the point where it is no longer advantageous to add stock.

By leveraging #probabilisticforecasting to drive parts planning, you can communicate these tradeoffs accurately, do so at scale across hundreds of thousands of parts, avoid bad inventory decisions, and balance service levels and costs.  At Smart Software, we specialize in helping spare parts planners, Directors of Materials Management, and financial executives managing MRO, spare parts, and aftermarket parts to understand and exploit these relationships.

Every organization that runs equipment needs spare parts. All of them must cope with issues that are generic no matter what their business. Some of the problems, however, are industry specific. This post discusses one universal problem that manifested in a nuclear plant and one that is especially acute for any electric utility.

The Universal Problem of Data Quality

We often post about the benefits of converting parts usage data into smart inventory management decisions. Advanced probability modeling supports generation of realistic demand scenarios that feed into detailed Monte Carlo simulations that expose the consequences of decisions such as choices of Min and Max governing the replenishment of spares.

However, all that new and shiny analytical tech requires quality data as fuel for the analysis. For some public utilities of all kinds, record keeping is not a strong suit, so the raw material going into analysis can be corrupted and misleading. We recently chanced upon documentation of a stark example of this problem at a nuclear power plant (see Scala, ­­­­­­­Needy and Rajgopal: Decision making and tradeoffs in the management of spare parts inventory at utilities. American Association of Engineering Management, 30th ASEM National Conference, Springfield, MO. October 2009). Scala et al. documented the usage history of a critical part whose absence would result in either a facility de-rate or a shutdown. The plant’s usage record for that part spanned more than eight years of data. During that time, the official usage history reported nine events in which positive demand occurred with sizes ranging from one to six units each. There were also five events marked by negative demands (i.e., returns to warehouse) ranging from one to three units each. Careful sleuthing discovered that the true usage occurred in just two events, both with demand of two units. Obviously, calculating the best Min/Max values for this item requires accurate demand data.

The Special Problem of Health and Safety

In the context of “regular” businesses, shortages of spare parts can damage both current revenue and future revenue (related to reputation as a reliable supplier). For an electric utility, however, Scala et al. noted a much greater level of consequence attached to stockouts of spare parts. These include not only a heightened financial and reputational risk but also risks to health and safety: “Ramifications of not having a part in stock include the possibility of having to reduce output or quite possibly, even a plant shut down. From a more long-term perspective, doing so might interrupt the critical service of power to residential, commercial, and/or industrial customers, while damaging the company’s reputation, reliability, and profitability. An electric utility makes and sells only one product: electricity. Losing the ability to sell electricity can be seriously damaging to the company’s bottom line as well its long-term viability.”

All the more reason for electric utilities to be leaders rather than laggards in the deployment of the most advanced probability models for demand forecasting and inventory optimization.