Taiichi Ohno of Toyota is credited with inventing Just-In-Time (JIT) manufacturing in the 1950s. JIT ensures that a manufacturer produces only what is needed, only when required, and only in the necessary amount. That innovation has since had major impacts, some good, some less so.

A recent New York Times article “How the World Ran out of Everything” describes some of the “less so” impacts.  For example, JIT has kept inventory costs very low improving return on assets.  This in turn is rewarded by Wall Street, so many companies have spent the last few decades reducing their inventories dramatically. Focused as they were on financials, many companies ignored the risks inherent in reducing inventories to the point that “lean” began to border on “emaciated.” Combined with increased globalization and new risks of supply interruption, stock-outs have abounded.

Some industries have gone too far, leaving them exposed to disruption. In a competition to get to the lowest cost, companies have inadvertently concentrated their risk, been interrupted by shortages of raw materials or components, and sometimes forced to halt assembly lines. Wall Street does not look kindly on production halts.

We all know that random events have added to the problem. First among them has been the Covid pandemic. As the pandemic has hindered factory operations and spread disarray in global shipping, many economies worldwide have been tormented by shortages of an immense range of goods — from computer chips to lumber to clothing.

The damage is compounded when more unexpected things go wrong. The Suez Canal Blockage is a prime example, obstructing the main trade route between Europe and Asia. Recently, cyberattacks have added another layer of disruption.

The reaction creates its own problems, just as the cyberattack on the Colonial Pipeline created gas shortages through panic buying. Suppliers start filling orders more slowly than usual. Manufacturers and distributors reverse course and increase inventories and diversify their suppliers to avoid future stockouts. Simply expanding warehouses may not deliver the solution, and the need to determine how much inventory to keep is more urgent every day.

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.