Those of you who track hot topics will be familiar with the term “digital twin.” Those who have been too busy with work may want to read on and catch up.

What is a digital twin?

While there are several definitions of digital twin, here’s one that works well:

A digital twin is a dynamic virtual copy of a physical asset, process, system, or environment that looks like and behaves identically to its real-world counterpart. A digital twin ingests data and replicates processes so you can predict possible performance outcomes and issues that the real-world product might undergo. [Source: Unity.com]. For additional background, you might go to Mckinsey.com.

What is the difference between a digital twin (hereafter DT) and a model? Primarily, a DT gets connected to real-time data to maintain the model as an up-to-the-minute representation of the system you are working with.

Our current products might be called “slow-motion DT’s” because they are usually used with non-real-time data (though not stale data, since it is updated overnight) and applied to problems like planning the next quarter’s raw material buys or setting inventory parameters for a month or longer.

Are people using digital twins in my industry?

My impression is that the penetration of DT’s may be highest in the aerospace and nuclear industries. Most of our customers are elsewhere: in manufacturing, distribution, and public utilities such as transportation and power. Soon we’ll be offering new products that come closer to the strict definition of a DT that is connected intimately to the system it represents.

DT Preview

Most users of Smart Inventory Optimization™ (SIO) run the application periodically, typically monthly. SIO analyzes current demand for inventory items and recent supplier lead times, converting these into demand and supply scenarios, respectively. Then users either interactively (for individual items) or automatically (at scale) set inventory control parameters that will provide the long-term average performance they want, balancing the competing goals of minimizing inventory while guaranteeing a sufficient level of item availability.

Smart Supply Planner (SSP) operates in a more immediate way to react to contingencies. Any day could bring an anomalous order that spikes up demand, such as when a new customer places a surprising initial stocking order. Or a key supplier could experience a problem at its factory and be forced to delay shipment of your planned replenishment orders. In the long run, these contingencies average out and justify the recommendations coming out of SIO. However, SSP will give you a way to react in the short run to seize opportunities or dodge bullets.

At its core, SSP operates like SIO in that it is scenario driven. The differences are that it uses short planning horizons and uses real-time initial conditions as the basis for its simulations of inventory system performance. Then it will provide real-time recommendations for interventions that offset the disruption caused by the contingencies. These would include cancelling or expediting replenishment orders.

Summary

Digital twins let you try out plans “in silico” before you implement them in the factory or warehouse. At their core are mathematical models of your operation but connected to real-time data. They provide a “digital sandbox” in which you can try out ideas and get immediate predictions of how well they will work. Much more than a spreadsheet, DT’s will soon be the key tool in your inventory planning toolbox.

Some companies invest in software to help them manage their inventory, whether it’s spare parts or finished goods. But a surprising number of others play the Inventory Guessing Game every day, trusting to an imagined “Golden Gut” or to plain luck to set their inventory control parameters. But what kind of results do you expect with that approach?

How good are you at intuiting the right values? This blog post challenges you to guess the best Min and Max values for a notional inventory item. We’ll show you its demand history, give you a few relevant facts, then you can pick Min and Max values and see how well they would work. Ready?

The Challenge

Figure 1 shows the daily demand history of the item. The average demand is 2 units per day. Replenishment lead time is a constant 10 days (which is unrealistic but works in your favor). Orders that cannot be filled immediately from stock cannot be backordered and are lost. You want to achieve at least an 80% fill rate, but not at any cost. You also want to minimize the average number of units on hand while still achieving at least an 80% fill rate. What Min and Max values would produce an 80% fill rate with the lowest average number of units on hand? [Record your answers for checking later. The solution appears below at the end of the article.]

Computing the Best Min and Max Values

The way to determine the best values is to use a digital twin, also known as a Monte Carlo simulation. The analysis creates a multitude of demand scenarios and passes them through the mathematical logic of the inventory control system to see what values will be taken on by key performance indicators (KPI’s).

We built a digital twin for this problem and systematically exercised it with 1,085 pairs of Min and Max values. For each pair, we simulated 365 days of operation a total of 100 times. Then we averaged the results to assess the performance of the Min/Max pair in terms of two KPI’s: fill rate and average on hand inventory.

Figure 2 shows the results. The inherent tradeoff between inventory size and fill rate is clear in the figure: if you want a higher fill rate, you have to accept a larger inventory. However, at each level of inventory there is a range of fill rates, so the game is to find the Min/Max pair that yields the highest fill rate for any given size inventory.

A different way to interpret Figure 2 is to focus on the dashed green line marking the target 80% fill rate. There are many Min/Max pairs that can hit near the 80% target, but they differ in inventory size from about 6 to about 8 units. Figure 3 zooms in on that region of Figure 2 to show  quite a number of Min/Max pairs that are competitive.

We sorted the results of all 1,085 simulations to identify what economists call the efficient frontier. The efficient frontier is the set of most efficient Min/Max pairs to exploit the tradeoff between fill rate and units on hand. That is, it is a list of Min/Max pairs that provide the least cost way to achieve any desired fill rate, not just 80%. Figure 4 shows the efficient frontier for this problem. Moving from left to right, you can read off the lowest price you would have to pay (as measured by average inventory size) to achieve any target fill rate. For example, to achieve a 90% fill rate, you would have to carry an average inventory of about 10 units.

Figures 2, 3, and 4 show results for various Min/Max pairs but do not display the values of Min and Max behind each point. Table 1 displays all the simulation data: the values of Min, Max, average units on hand and fill rate. The answer to the guessing game is highlighted in the first line of the table: Min=7 and Max=13¹. Did you get the right answer, or something close²? Did you maybe get onto the efficient frontier?

Conclusions

Maybe you got lucky, or maybe you do indeed have a Golden Gut, but it’s more likely you didn’t get the right answer, and it’s even more likely you didn’t even try. Figuring out the right answer is extremely difficult without using the digital twin. Guessing is unprofessional.

One step up from guessing is “guess and see”, in which you implement your guess and then wait a while (months?) to see if you like the results. That tactic is at least “scientific”, but it is inefficient.

Now consider the effort to work out the best (Min,Max) pairs for thousands of items. At that scale, there is even less justification for playing the Inventory Guessing Game. The right answer is to play it… Smart³.

¹ This answer has a bonus, in that it achieves a bit more than 80% fill rate at a lower average inventory size than the Min/Max combination that hit exactly 80%. In other words, (7,13) is on the efficient frontier.

² Because these results come from a simulation instead of an exact mathematical equation, there is a certain margin of error associated with each estimated fill rate and inventory level. However, because the average results were based on 100 simulations each 365 days long, the margins of error are small. Across all experiments, the average standard errors in fill rate and mean inventory were, respectively, only 0.009% and 0.129 units.

³ In case you didn’t know this, one of the founders of Smart Software was … Charlie Smart.

Balancing Act

Managing inventory, like managing anything, involves balancing competing priorities. Do you want a lean inventory? Yes! Do you want to be able to say “It’s in stock” when a customer wants to buy something? Yes!

But can you have it both ways? Only to a degree. If you lean into leaning your inventory too aggressively, you risk stockouts. If you stamp out stockouts, you create inventory bloat. You are forced to find a satisfactory balance between the two competing goals of lean inventory and high item availability.

Striking a Balance

How do you strike that balance? Too many inventory planners “guestimate” their way to some kind of answer. Or they work out a smart answer once and hope that it has a distant sell-by date and keep using it while they focus on other problems. Unfortunately, shifts in demand and/or changes in supplier performance and/or shifts in your own company’s priorities will obsolete old inventory plans and put you right back where you started.

It is inevitable that every plan has a shelf life and has to be updated. However, it is definitely not best practice to replace one guess with another. Instead, each planning cycle should exploit modern supply chain software to replace guesswork with fact-based analysis using probability math.

Know Thyself

The one thing that software cannot do is compute a best answer without knowing your priorities. How much do you prioritize lean inventory over item availability? Software will predict the levels of inventory and availability caused by any decisions you make about how to manage each item in your inventory, but only you can decide whether any given set of key performance indicators is consistent with what you want.

Knowing what you want in a general sense is easy: you want it all. But knowing what you prefer when comparing specific scenarios is more difficult. It helps to be able to see a range of realizable possibilities and mull over which seems best when they are laid out side by side.

See What’s Next

Supply chain software can give you a view of the tradeoff curve. You know in general that lean inventory and high item availability trade off against each other, but seeing item-specific tradeoff curves sharpens your focus.

Why is there a curve? Because you have choices about how to manage each item. For instance, if you check inventory status continuously, what values will you assign to the Min and Max values that govern when to order replenishments and how much to order. The tradeoff curve arises because choosing different Min and Max values leads to different levels of on hand inventory and different levels of item availability, e.g., as measured by fill rate.

A Scenario for Analysis

To illustrate these ideas, I used a digital twin  to estimate how various values of Min and Max would perform in a particular scenario. The scenario focused on a notional spare part with purely random demand having a moderately high level of intermittency (37% of days having zero demand). Replenishment lead times were a coin flip between 7 and 14 days. The Min and Max values were systematically varied: Min from 20 to 40 units, Max from Min+1 units to 2xMin units. Each (Min,Max) pair was simulated for 365 days of operation a total of 1,000 times, then the results averaged to estimate both the average number of on hand units and the fill rate, i.e., percentage of daily demands that were satisfied immediately from stock. If stock was not available, it was backordered.

Results

The experiment produced two types of results:

• Plots showing the relationship between Min and Max values and two key performance indicators: Fill rate and average units on hand.
• A tradeoff curve showing how the fill rate and units on hand trade off against each other.

Figure 1 plots on hand inventory as a function of the values of Min and Max. The experiment yielded on hand levels ranging from near 0 to about 40 units.  In general, keeping Min constant and increasing Max results in more units on hand. The relationship with Min is more complex: keeping Max constant,  increasing Min first adds to inventory but at some point reduces it.

Figure 2 plots fill rate as a function of the values of Min and Max.  The experiment yielded fill rate levels ranging from near 0% to 100%.  In general, the functional relationships between the fill rate and the values of Min and Max mirrored those in Figure1.

Figure 3 makes the key point, showing how varying Min and Max produces a perverse pairing of the key performance indicators. Generally speaking, the values of Min and Max that maximize item availability (fill rate)  are the same values that maximize inventory cost (average units on hand). This general pattern is represented by the blue curve. The experiments also produced some offshoots from the blue curve that are associated with poor choices of Min and Max, in the sense that other choices dominate them by producing the same fill rate with lower inventory.

Conclusions

Figure 3 makes clear that your choice of how to manage an inventory item forces you to trade off inventory cost and item availability. You can avoid some inefficient combinations of Min and Max values, but you cannot escape the tradeoff.

The good side of this reality is that you do not have to guess what will happen if you change your current values of Min and Max to something else. The software will tell you what that move will buy you and what it will cost you. You can take off your Guestimator hat and do your thing with confidence.

Figure 1 On Hand Inventory as a function of Min and Max values

Figure 2 Fill Rate as a function of Min and Max values

Figure 3 Tradeoff curve between Fill Rate and On Hand Inventory

I’ll start with a confession: I’m an algorithm guy. My heart lives in the “engine room” of our software, where lightning-fast calculations zip back and forth across the AWS cloud, generating demand and supply scenarios used to guide important decisions about demand forecasting and inventory management.

But I recognize that the target of all that beautiful, furious calculation is the brain of the boss, the person responsible for making sure that customer demand is satisfied in the most efficient and profitable way. So, this blog is about Smart Operational Analytics (SOA), which creates reports for management. Or, as they are called in the military, sit-reps.

All the calculations guided by the planners using our software ultimately get distilled into the SOA reports for management. The reports focus on five areas: inventory analysis, inventory performance, inventory trending, supplier performance, and demand anomalies.

Inventory Analysis

These reports keep tabs on current inventory levels and identify areas that need improvement. The focus is on current inventory counts and their status (on hand, in transit, in quarantine), inventory turns, and excesses vs shortages.

Inventory Performance

These reports track Key Performance Indicators (KPIs) such as Fill Rates, Service Levels, and inventory Costs. The analytic calculations elsewhere in the software guide you toward achieving your KPI targets by calculating Key Performance Predictions (KPPs) based on recommended settings for, e.g., reorder points and order quantities. But sometimes surprises occur, or operating policies are not executed as recommended, so there will always be some slippage between KPPs and KPIs.

Inventory Trending

Knowing where things stand today is important, but seeing where things are trending is also valuable. These reports reveal trends in item demand, stockout events, average days on hand, average time to ship, and more.

Supplier Performance

Your company cannot perform at its best if your suppliers are dragging you down. These reports monitor supplier performance in terms of the accuracy and promptness of filling replenishment orders. Where you have multiple suppliers for the same item, they let you compare them.

Demand Anomalies

Your entire inventory system is demand driven, and all inventory control parameters are computed after modeling item demand. So if something odd is happening on the demand side, you must be vigilant and prepare to recalculate things like mins and maxes for items that are starting to act in odd ways.

Summary

The end point for all the massive calculations in our software is the dashboard showing management what’s going on, what’s next, and where to focus attention. Smart Inventory Analytics is the part of our software ecosystem aimed at your company’s C-Suite.

Figure 1: Some sample reports in graphical form

Over forty years ago, Smart Software consisted of three friends working to start a company in a church basement. Today, our team has expanded to operate from multiple locations across Massachusetts, New Hampshire and Texas, with team members in England, Spain, Armenia and India. Like many of you in your jobs,  we have found ways to make distributed teams work for us and for you.

This note is about a different kind of teamwork: the collaboration between you and our software that happens at your fingertips. I often write about the software itself and what goes on “under the hood”. This time, my subject is how you should best team up with the software.

Our software suite, Smart Inventory Planning and Optimization (Smart IP&O™) is capable of massively detailed calculations of future demand and the inventory control parameters (e.g., reorder points and order quantities) that would most effectively manage that demand. But your input is required to make the most of all that power. You need to team up with the algorithms.

That interaction can take several forms. You can start by simply assessing how you are doing now. The report writing functions in Smart IP&O (Smart Operational Analytics™) can collate and analyze all your transactional data to measure your Key Performance Indicators (KPIs), both financial (e.g., inventory investment) and operational (e.g., fill rates).

The next step might be to use SIO (Smart Inventory Optimization™), the inventory analytics within SIP&O, to play “what-if” games with the software. For example, you might ask “What if we reduced the order quantity on item 1234 from 50 to 40?” The software grinds the numbers to let you know how that would play out, then you react. This can be useful, but what if you have 50,000 items to consider? You would want to do what-if games for a few critical items, but not all of them.

The real power comes with using the automatic optimization capability in SIO. Here you can team with the algorithms at scale. Using your business judgement, you can create “groups”, i.e., collections of items that share some critical features. For example, you might create a group for “critical spare parts for electric utility customers” consisting of 1,200 parts. Then again calling on your business judgement, you could specify what item availability standard should apply to all the items in that group (e.g., “at least 95% chance of not stocking out in a year”). Now the software can take over and automatically work out the best reorder points and order quantities for every one of those items to achieve your required item availability at the lowest possible total cost. And that, dear reader, is powerful teamwork.