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.

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.

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.

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.

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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.

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

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.

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.

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.

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/