Head to Head: Which Service Parts Inventory Policy is Best?

Our customers have usually settled into one way to manage their service parts inventory. The professor in me would like to think that the chosen inventory policy was a reasoned choice among considered alternatives, but more likely it just sort of happened. Maybe the inventory honcho from long ago had a favorite and that choice stuck. Maybe somebody used an EAM or ERP system that offered only one choice. Perhaps there were some guesses made, based on the conditions at the time.

The Competitors

Too seldom, businesses make these choices in haphazard ways. But modern service parts planning software lets you be more systematic about your choices. This post demonstrates that proposition by making objective comparisons among three popular inventory policies:  Order Up To, Reorder Point/Order Quantity, and Min/Max.  I discussed each of these policies in this video blog.

  • Order Up To. This is a periodic review policy where every T days, on-hand inventory is tallied and an order of random size is placed to bring the stock level back up to S units.
  • Q, R or Reorder Point/Order Quantity. Q, R is a continuous review policy where every day, inventory is tallied. If there are Q or fewer units on hand, an order of fixed size is placed for R more units.
  • Min, Max is another continuous review policy where every day, inventory is tallied. If there are Min or fewer units on hand, an order is placed to bring the stock level back up to Max units.

Inventory theory says these choices are listed in increasing order of effectiveness. The first option, Order Up To, is clearly the simplest and cheapest to implement, but it closes its eyes to what’s going on for long periods of time.  Imposing a specified passage of time in between orders makes it, in theory, less flexible. In contrast, the two continuous review options keep an eye on what’s happening all the time, so they can react to potential stockouts quicker. The Min/Max option is, in theory, more flexible than the option that uses a fixed reorder quantity because the size of the order dynamically changes to accommodate the demand.

That’s the theory. This post examines evidence from head-to-head comparisons to check the theory and put concrete numbers on the relative performance of the three policies.

The Meaning of “Best”

How should we keep score in this tournament? If you are a regular reader of this Smart Forecaster blog, you know that the core of inventory planning is a tug-of-war between two opposing objectives: keeping inventory lean vs keeping item availability metrics such as service level high.

To simplify things, we will compute “one number to rule them all”: the average operating cost. The winning policy will be the one with the lowest average.

This average is the sum of three components: the cost of holding inventory (“holding cost”), the cost of ordering replenishment units (“ordering cost”) and the cost of losing a sale (“shortage cost”). To make things concrete, we used the following assumptions:

  • Each service part is valued at $1,000.
  • Annual holding cost is 10% of item value, or $100 per year per unit.
  • Processing each replenishment order costs $20 per order.
  • Each unit demanded but not provided costs the value of the part, $1,000.

For simplicity, we will refer to the average operating cost as simply “the cost”.

Of course, the lowest average cost can be achieved by getting out of the business. So the competition required a performance constraint on item availability: Each option had to achieve a fill rate of at least 99%.

The Alternatives Duke it Out

A key element of context is whether stockouts result in losses or backorders. Assuming that the service part in question is critical, we assumed that unfilled orders are lost, which means that a competitor fills the order. In an MRO environment, this will mean additional downtime due to stockout.

To compare the alternatives, we used our predictive modeling engine to run a large number of Monte Carlo simulations.  Each simulation involved specifying the parameter values of each policy (e.g., Min and Max values), generating a demand scenario, feeding that into the logic of the policy, and measuring the resulting cost averaged over 365 days of operation. Repeating this process 1,000 times and averaging the 1,000 resulting costs gave the final result for each policy.  

To make the comparison fair, each alternative had to be designed for its best performance. So we searched the “design space” of each policy to find the design with the lowest cost. This required repeating the process described in the previous paragraph for many pairs of parameter values and identifying the pair yielding the lost average annual operating cost.

Using the algorithms in Smart Inventory Optimization (SIOTM) we made head-to-head-to-head comparisons under the following assumptions about demand and supply:

  • Item demand was assumed to be intermittent and highly variable but relatively simple in that there was neither trend nor seasonality, as is often true for service parts. Daily mean demand was 5 units with a large standard deviation of 13 units. Figure 1 shows a sample of one year’s demand. We have chosen a very challenging demand pattern, in which some days have 10 to even 20 times the average demand.

Daily part demand was assumed to be intermittent and very spikey.

Figure 1: Daily part demand was assumed to be intermittent and very spikey.


  • Suppliers’ replenishment lead times were 14 days 75% of the time and 21 days otherwise. This reflects the fact that there is always uncertainty in the supply chain.


And the Winner Is…

Was the theory right? Kinda’ sorta’.

Table 1 shows the results of the simulation experiments. For each of the three competing policies, it shows the average annual operating cost, the margin of error (technically, an approximate 95% confidence interval for the mean cost), and the apparent best choices for parameter values.

Results of the simulated comparisons

Table 1: Results of the simulated comparisons

For example, the average cost for the (T,S) policy when T is fixed at 30 days was $41,680. But the Plus/Minus implies that the results are compatible with a “true” cost (i.e., the estimate from an infinite number of simulations) of anywhere between $39,890 and $43,650. The reason there is so much statistical uncertainty is the extremely spikey nature of demand in this example.

Table 1 says that, in this example, the three policies fall in line with expectations. However, more useful conclusions would be:

  1. The three policies are remarkably similar in average cost. By clever choice of parameter values, one can get good results out of any of the three policies.
  2. Not shown in Table 1, but clear from the detailed simulation results, is that poor choices for parameter values can be disastrous for any policy.
  3. It is worth noting that the periodic review (T,S) policy was not allowed to optimize over possible values of T. We fixed T at 30 to mimic what is common in practice, but those who use the periodic review policy should consider other review periods. An additional experiment fixed the review period at T = 7 days. The average cost in this scenario was minimized at $36,551 ± $1,668 with S = 343. This result is better than that using T = 30 days.
  4. We should be careful about over-generalizing these results. They depend on the assumed values of the three cost parameters (holding, ordering and shortage) and the character of the demand process.
  5. It is possible to run experiments like those shown here automatically in Smart Inventory Optimization. This means that you too would be able to explore design choices in a rigorous way.




Leveraging ERP Planning BOMs with Smart IP&O to Forecast the Unforecastable

​In a highly configurable manufacturing environment, forecasting finished goods can become a complex and daunting task. The number of possible finished products will skyrocket when many components are interchangeable. A traditional MRP would force us to forecast every single finished product which can be unrealistic or even impossible. Several leading ERP solutions introduce the concept of the “Planning BOM”, which allows the use of forecasts at a higher level in the manufacturing process. In this article, we will discuss this functionality in ERP, and how you can take advantage of it with Smart Inventory Planning and Optimization (Smart IP&O) to get ahead of your demand in the face of this complexity.

Why Would I Need a Planning BOM?

Traditionally, each finished product or SKU would have a rigidly defined bill of materials. If we stock that product and want to plan around forecasted demand, we would forecast demand for those products and then feed MRP to blow this forecasted demand from the finished good level down to its components via the BOM.

Many companies, however, offer highly configurable products where customers can select options on the product they are buying. As an example, recall the last time you bought a personal computer. You chose a brand and model, but from there, you were likely presented with options: what speed of CPU do you want? How much RAM do you want? What kind of hard drive and how much space? If that business wants to have these computers ready and available to ship to you in a reasonable time, suddenly they are no longer just anticipating demand for that model—they must forecast that model for every type of CPU, for all quantities of RAM, for all types of hard drive, and all possible combinations of those as well! For some manufacturers, these configurations can compound to hundreds or thousands of possible finished good permutations.

Planning BOM emphasizing the large numbers of permutations Laptops Factory Components

There may be so many possible customizations that the demand at the finished product level is completely unforecastable in a traditional sense. Thousands of those computers may sell every year, but for each possible configuration, the demand may be extremely low and sporadic—perhaps certain combinations sell once and never again.

This often forces these companies to plan reorder points and safety stock levels mostly at the component level, while largely reacting to firm demand at the finished good level via MRP. While this is a valid approach, it lacks a systematic way to leverage forecasts that may account for anticipated future activity such as promotions, upcoming projects, or sales opportunities. Forecasting at the “configured” level is effectively impossible, and trying to weave in these forecast assumptions at the component level isn’t feasible either.


Planning BOM Explained

This is where Planning BOMs come in. Perhaps the sales team is working a big b2b opportunity for that model, or there’s a planned promotion for Cyber Monday. While trying to work in those assumptions for every possible configuration isn’t realistic, doing it at the model level is totally doable—and tremendously valuable.

The Planning BOM can use a forecast at a higher level and then blow demand down based on predefined proportions for its possible components. For example, the computer manufacturer may know that most people opt for 16GB of RAM, and far fewer opt for the upgrades to 32 or 64. The planning BOM allows the organization to (for example) blow 60% of the demand down to the 16GB option, 30% to the 32GB option, and 10% to the 64GB option. They could do the same for CPUs, hard drives, or any other customizations available.  

Planning BOM Explained with computer random access memory ram close hd


The business can now focus their forecast at this model level, leaving the Planning BOM to figure out the component mix. Clearly, defining these proportions requires some thought, but Planning BOMs effectively allow businesses to forecast what would otherwise be unforecastable.


The Importance of a Good Forecast

Of course, we still need a good forecast to load into an ERP system. As explained in this article, while ERP  can import a forecast, it often cannot generate one and when it does it tends to require a great deal of hard to use configurations that don’t often get revisited resulting in inaccurate forecasts.  It is therefore up to the business to come up with their own sets of forecasts, often manually produced in Excel. Forecasting manually generally presents a number of challenges, including but not limited to:

  • The inability to identify demand patterns like seasonality or trend
  • Overreliance on customer or sales forecasts
  • Lack of accuracy or performance tracking

No matter how well configured the MRP is with your carefully considered Planning BOMs, a poor forecast means poor MRP output and mistrust in the system—garbage in, garbage out. Continuing along with the “computer company” example, without a systematic way of capturing key demand patterns and/or domain knowledge in the forecast, MRP can never see it.


Extend ERP  with Smart IP&O

Smart IP&O is designed to extend your ERP system with a number of integrated demand planning and inventory optimization solutions. For example, it can generate statistical forecasts automatically for large numbers of items, allows for intuitive forecast adjustments, tracks forecast accuracy, and ultimately allows you to generate true consensus-based forecasts to better anticipate the needs of your customers.

Thanks to highly flexible product hierarchies, Smart IP&O is perfectly suited to forecasting at the Planning BOM level so you can capture key patterns and incorporate business knowledge at the levels that matter most. Furthermore you can analyze and deploy optimal safety stock levels at any level of your BOM.



Finding Your Spot on the Tradeoff Curve

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.



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.



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 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 2 Fill Rate as a function of Min and Max values



Figure 3 Tradeoff curve between Fill Rate and On Hand Inventory

Figure 3 Tradeoff curve between Fill Rate and On Hand Inventory




Why MRO Businesses Should Care About Excess Inventory

Do MRO companies genuinely prioritize reducing excess spare parts inventory? From an organizational standpoint, our experience suggests not necessarily. Boardroom discussions typically revolve around expanding fleets, acquiring new customers, meeting service level agreements (SLAs), modernizing infrastructure, and maximizing uptime. In industries where assets supported by spare parts cost hundreds of millions or generate significant revenue (e.g., mining or oil & gas), the value of the inventory just doesn’t raise any eyebrows, and organizations tend to overlook massive amounts of excessive inventory.

Consider a public transit agency.  In most major cities, the annual operating budgets will exceed $3 billion.  Capital expenses for trains, subway cars, and infrastructure may reach hundreds of millions annually. Consequently, a spare parts inventory valued at $150 million might not grab the attention of the CFO or general manager, as it represents a small percentage of the balance sheet.  Moreover, in MRO-based industries, many parts need to support equipment fleets for a decade or more, making additional stock a necessary asset. In some sectors like utilities, holding extra stock can even be incentivized to ensure that equipment is kept in a state of good repair.

We have seen concerns about excess stock arise when warehouse space is limited. I recall, early in my career, witnessing a public transit agency’s rail yard filled with rusted axles valued at over $100,000 each.  I was told the axles were forced to be exposed to the elements due to insufficient warehouse space. The opportunity cost associated with the space consumed by extra stock becomes a consideration when warehouse capacity is exhausted. The primary consideration that trumps all other decisions is how the stock ensures high service levels for internal and external customers.  Inventory planners worry far more about blowback from stockouts than they do from overbuying.  When a missing part leads to an SLA breach or downed production line, resulting in millions in penalties and unrecoverable production output, it is understandable.

Asset-intensive companies are missing one giant point. That is, the extra stock doesn’t insulate against stockouts; it contributes to them. The more excess you have, the lower your overall service level because the cash needed to purchase parts is finite, and cash spent on excess stock means there isn’t cash available for the parts that need it.  Even publicly funded MRO businesses, like utilities and transit agencies, acknowledge the need to optimize spending, now more than ever.  As one materials manager shared, “We can no longer fix problems with bags of cash from Washington.”  So, they must do more with less, ensuring optimal allocation across the tens of thousands of parts they manage.

This is where state-of-the-art inventory optimization software comes in, predicting the required inventory for targeted service levels, identifying when stock levels yield negative returns, and recommending reallocations for improved overall service levels.  Smart Software has helped asset intensive MRO based businesses optimize reorder levels across each part for decades. Give us a call to learn more. 



Spare Parts Planning Software solutions

Smart IP&O’s service parts forecasting software uses a unique empirical probabilistic forecasting approach that is engineered for intermittent demand. For consumable spare parts, our patented and APICS award winning method rapidly generates tens of thousands of demand scenarios without relying on the assumptions about the nature of demand distributions implicit in traditional forecasting methods. The result is highly accurate estimates of safety stock, reorder points, and service levels, which leads to higher service levels and lower inventory costs. For repairable spare parts, Smart’s Repair and Return Module accurately simulates the processes of part breakdown and repair. It predicts downtime, service levels, and inventory costs associated with the current rotating spare parts pool. Planners will know how many spares to stock to achieve short- and long-term service level requirements and, in operational settings, whether to wait for repairs to be completed and returned to service or to purchase additional service spares from suppliers, avoiding unnecessary buying and equipment downtime.

Contact us to learn more how this functionality has helped our customers in the MRO, Field Service, Utility, Mining, and Public Transportation sectors to optimize their inventory. You can also download the Whitepaper here.



White Paper: What you Need to know about Forecasting and Planning Service Parts


This paper describes Smart Software’s patented methodology for forecasting demand, safety stocks, and reorder points on items such as service parts and components with intermittent demand, and provides several examples of customer success.


    Constructive Play with Digital Twins

    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.


    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.


    Are You Playing the Inventory Guessing Game?

    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.]

    Are You Playing the Inventory Guessing Game-1

    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?


    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.

    Are You Playing the Inventory Guessing Game-111

    Are You Playing the Inventory Guessing Game-Table 1