What We’re Up Against

As a third-generation Boston Red Sox fan, I’m disinclined to take advice from any New York Yankee ballplayer, even a great one but have to agree that sometimes, you just need to make a decision.   However, wouldn’t it be better if we knew the tradeoffs associated with each decision. Perhaps one road is more scenic but takes longer while the other is more direct but boring. Then you wouldn’t have to simply “take it” but could make an informed decision based on the advantages/disadvantages of each approach.

In the supply chain planning world, the most fundamental decision is how to balance item availability against the cost of maintaining that availability (service levels and fill rates). At one extreme, you can grossly overstock and never run out until you go broke and have to close up shop from sinking all your cash into inventory that doesn’t sell.  At the other extreme, you can grossly understock and save a bundle on inventory holding costs but go broke and have to close up shop because all your customers took their business elsewhere.

There is no escaping this fundamental tension. They way to survive and thrive is to find a productive and sustainable balance. To do that requires fact-based tradeoffs based on the numbers. To get the numbers requires software.

The general drift of things is obvious. If you decide to keep more inventory, you will have more Holding Costs, lower Shortage Costs, and possibly lower Ordering Costs. Whether this costs or saves money is impossible to know without some sophisticated analysis, but usually the result is that the Total Cost goes up. But if you do invest in more inventory, something will be gained, because you will offer your customers higher Service Levels and Fill Rates. How much higher requires, as you might guess, some sophisticated analysis.

Show Me the Numbers

This blog lays out what such an analysis looks like. There is no universal solution pointing you to the “right” decision. You might think that the right decision is the one that does best by your bottom line. But to get those numbers, you would need something rarely seen: an accurate model of customer behavior with regard to service level (check out our article “How to choose a target service level”) For example, at what point will a customer walk away and take their business elsewhere?  Will it be after you stock out 1% of the time, 5% of time, 10% of the time? Will you still keep their business as long as you fill back orders quickly?  Will it be after a back order of 1 day, 2 days? 3 weeks? Will it be after this happens one time on one an important part or many times across many parts?  While modeling the precise service level that will allow you to keep your customer while minimizing costs seems like an unapproachable ideal, another type of sophisticated analysis is more pragmatic. 

Inventory optimization and forecasting software can factor all associated costs such as the cost of stocking out, cost of holding inventory, and cost of ordering inventory in order to prescribe an optimal service level target that yields the lowest total cost. However, even that “optimal” service level is sensitive to changes in the costs making the results potentially questionable.  For example, if you don’t accurately estimate the precise costs (shortage costs are the most difficult) it will be tough to definitely state something like “If I increase my on-hand inventory by an average of one unit for all items in an important product family, my company will see a net gain of $170,500.  That gain increases until I get to 4 units.  At 4 units and higher, the return declines due to excessive holding costs. So, the best decision factoring projected holding, ordering, and stockout is to increase inventory by 3 units to see a net gain of over $500,000.  

Short of that ideal, you can do something that is simpler yet still extremely valuable: Quantify the tradeoff curve between inventory cost and item availability. While you won’t necessarily know the service level you should target, you will know the costs of varying service levels.  Then you can earn your big bucks by finding a good place to be on that tradeoff curve and communicating where you at risk, where you aren’t, and setting expectations with customers and internal stakeholders.  Without the tradeoff curve to guide you, you are flying blind with no way to rationally modify stocking policy.

A Scenario to Learn From

Let’s sketch out a realistic tradeoff curve. We start with a scenario requiring a management decision. The scenario we will use and associated assumptions about demand, lead times, and costs are detailed below:

Inventory Policy

• Periodic review – Reorder decisions made every 30 days
• Order-Up-To-Level (“S”) – Varied from 30 to 60 units
• Shortage Policy – Allow backorders, no lost orders

Demand

• Demand is intermittent
• Average = 0.8 units per day
• Standard deviation = 1.2 units per day
• Largest demand in a year ≈ 9
• % of days with no demand = 53%

Lead Time

• Random at either 7, 14 or 21 days with probabilities 70%, 20% and 10%, respectively

Cost Parameters

• Holding cost = $1 per day
• Ordering Cost = $10 per order without regard to size of order
• Shortage Cost = $100 per unit not immediately shipped from stock

We imagine an inventory control policy that is known in the trade as a “periodic review” or (T,S) policy. In this instance, the Review Period (“T”) is 30 days, meaning that every 30 days the inventory position is checked and an ordering decision is made. The order quantity is the difference between the observed number of units on hand and the Order-Up-To Quantity (“S”). So, if the end-of-month inventory is 12 units and S = 20, the order quantity would be S – 12 = 20 -1 2 = 8. The next month, the order quantity is likely to be different. If the inventory ever goes negative (backorders) during a review period, the next order tries to restore equilibrium by ordering more in order to fill those backorders. For example, if the inventory is -5 (meaning 5 units ordered by not available for shipping, the next order would be S – (-5) = S + 5. Details of the hypothetical demand stream, supplier lead times, and cost elements are shown in Figure 1 below. Figure 2 show a sample of daily demand and daily inventory over five review periods. Demand is intermittent, as is often true for spare parts, and therefore difficult to plan for.

Figure 1: Different choices of inventory policy (order up to), associated costs, and service levels

Figure 2: Details of five months of system operation given one of the polices

Inventory Planning Software Is Our Friend

Software encodes the logic of the operation of the (T,S) system, generates many hypothetical but realistic demand scenarios, calculates how each of those scenarios plays out, then looks back on the simulated operation (here, 10 years or 3,650 consecutive days) to calculate cost and performance metrics.

To reveal the tradeoff curve, we ran several computational experiments in which we varied the Order-Up-To Level, S. The plots Figure 2 show the behavior of the on-hand inventory in “richest” alternative with S = 60. In the snippet shown in Figure 2, the on-hand inventory never comes close to stocking out. You can read that too ways. One, a bit naïve, is to say “Good, we’re well protected.” The other, more aggressive, is to say, “Oh no, we’re bloated. I wonder what would happen if we reduced S.”

The Tradeoff Curve Revealed

Figure 3 shows the results of reducing S from 60 down to 30 in steps of 5 units. The table shows that Total Cost is the sum of Holding Cost, Ordering Cost, and Shortage Cost. For the (T,S) policy, the ordering cost is always the same, since an order is placed like clockwork every 30 days. But the other components of cost respond to the changes in S.

Figure 3: The experimental results and corresponding tradeoff curve showing how changing the Order-Up-To Level (“S”) impacts both Service Level and Total Annual Cost

Note that the Service Level is always lower than the Fill Rate in these scenarios. As a professor, I always think of this difference in terms of exam grading. Each replenishment cycle is like a test. Service Level is about the probability of a stockout, so it’s a like the grade on pass/fail exam with one question that must be answered perfectly. If there is no stockout in a cycle, that’s an A. If there is a stockout, that’s an F. It doesn’t matter if it’s one unit that’s not supplied or 50 – it’s still an F. But Fill Rate is like a question that is graded with partial credit. So being short one of ten units gets you 90% Fill Rate for that cycle, not 0%. It’s important to understand the difference between these two important metrics for inventory planning – check out this vlog describing service level vs. fill rate via an interactive exercise in Excel.

The plot in Figure 3 is the real news. It pairs Total Cost and Service Level for various levels of S. If you read the graph right to left, it tells us that there are dramatic cost savings to be had by reducing S with very little penalty in terms of reduced item availability. For instance, reducing S from 60 to 55 saves close to $800 per year on this one item while reducing service level just a bit from (essentially) 100% to a still-impressive 99%. Cutting S some more does the same, though not as dramatically. If you read the graph left to right, you see that moving up from S = 30 to S = 35 costs about $1,000 per year but improves Service Level from an F grade (45%) to at least a C grade (71%). After that, pushing S higher costs progressively more while gaining progressive less.

The tradeoff curve doesn’t give you an answer to how to set the Order-Up-To Level, but it does let you evaluate the costs and benefits of each possible answer. Take a minute and pretend that this is your problem: Where would you want to be along the tradeoff curve?

You may object and say you hate your choices and want to change the game. Is there escape from the curve? Not from the general curve, but you might be able to shape a less painful curve. How?

You may have other cards to play. One avenue is to try to “shape” the demand so that it is less variable. The demand plot in Figure 2 shows a lot of variability. If you could smooth out the demand, the whole tradeoff curve would shift down, making every choice less expensive. A second avenue is to try to reduce the mean and variability of supplier lead times. Achieving either would also shift the curve down to make the choice less painful. Check out our article on how suppliers influence your inventory costs

Summary

The tradeoff curve is always with us. Sometimes we may be able to make it more friendly, but we always to pick our spot along it. It is better to know what you’re getting for any choice of inventory policy than to try to guess, and the curve gives you that.  When you have an accurate estimate of that curve, you are no longer flying blind when it comes to inventory planning. 

Physicists like my Smart Software co-founder, Dr. Nelson Hartunian, tell us civilians that everything is different when we drill down to the tiniest level of the world. Physics at the quantum level is quite weird – not at all like what we experience in our usual macroscopic life. Among the oddities are “superposition”, “entanglement”, and “quantum foam.”  Weird as these phenomena are, I cannot help seeing analogs in the supposedly different world of supply chain management.

Consider quantum superposition. Briefly, superposition means any quantum entity can be in two states at once. Schrödinger’s cat is the most famous illustration of this idea. But how many of you readers are also in a state of superposition? Don’t you find yourself being a manager of a team yet a member of your supervisor’s team, a trouble-shooter yet also a forecasting expert or an inventory optimizer and…? And doesn’t all this make you sometimes feel, like that cat, that you are simultaneously both dead and alive? Modern software can ease some of this burden by automating the tasks of demand planning and inventory optimization. The rest is up to you.

A second quantum analog is entanglement. Briefly, entanglement is the linkage between two elements of a system. They can be light years apart, yet changing one part of an entangled system will instantaneously change the other part. This bugged Albert Einstein, who derided it as “spooky action as a distance.” In our regular world, demand planning and inventory optimization are entangled, since the process of inventory optimization sits on top of the process of demand forecasting. Modern software links the two in an efficient interface.

Finally, the quantum foam – one of my favorite ideas. As I understand it, quantum foam is a substitute for empty space: there is no empty space, rather a constant bubbling of “vacuum energy” accompanied by a flux of “virtual particles” being born out of nothing and then disappearing back into nothing. In the supply chain world, the analogs of virtual particles are customer orders. Often it seems that they pop up with no warning out of thin air, and sometimes they disappear by cancellation in an equally random and mysterious process. This kind of demand fluctuation is the basis for all the theory of inventory control. Modern software therefore begins with probability models of customer demand. Those models then have implications for such tangible quantities as safety stocks, reorder points, and order quantities.

Does it really help demand planners and inventory managers to think about these ideas from quantum physics? Well, it’s a bit of fun to see the analogies to our regular world of work. And they do remind us of more macroscopic matters: the basic concepts of the need to deal with more than one task simultaneously, the linkage between forecasting and inventory management, and randomness as the fundamental feature of the supply chain.

In my previous post in this series on essential concepts, “What is ‘A Good Forecast’”, I discussed the basic effort to discover the most likely future in a demand planning scenario. I defined a good forecast as one that is unbiased and as accurate as possible. But I also cautioned that, depending on the stability or volatility of the data we have to work with, there may still be some inaccuracy in even a good forecast. The key is to have an understanding of how much.

This topic, managing uncertainty, is the subject of post by my colleague Tom Willemain, “The Average is not the Answer”. His post lays out the theory for responsibly confronting the limits of our predictive ability. It’s important to understand how this actually works.

As I briefly touched on at the end of my previous post, our approach begins with something called a “sliding simulation”. We estimate how accurately we are predicting the future by using our forecasting techniques on an older portion of history, excluding the most recent data. We can then compare what we would have predicted for the recent past with our actual real world information about what happened. This is a reliable method to estimate how closely we are predicting future demand.

Safety stock, a carefully measured buffer in inventory level we stock above our prediction of most likely demand, is derived from the estimate of forecast error coming out of the “sliding simulation”. This approach to dealing with the accuracy of our forecasts efficiently balances between ignoring the threat of the unpredictable and costly overcompensation.

In more technical detail: the forecasts errors that are estimated by this sliding simulation process indicate the level of uncertainty. We use these errors to estimate the standard deviation of the forecasts. Now, with regular demand, we can assume the forecasts (which are estimates of future behavior) are best represented by a bell-shaped probability distribution—what statisticians call the “normal distribution”. The center of that distribution is our point forecast. The width of that distribution is the standard deviation of the “sliding simulation” forecast from the known actual values—we obtain this directly from our forecast error estimates.

Once we know the specific bell shaped curve associated with the forecast, we can easily estimate the safety stock buffer that is needed. The only input from us is the “service level” that is desired, and the safety stock at that service level can be ascertained. (The service level is essentially a measure of how confident we need to be in our inventory stocking levels, with increasing confidence requiring corresponding expenditures on extra inventory.) Notice, we are assuming that the correct distribution to use is the normal distribution. This is correct for most demand series where you have regular demand per period. It fails when demand is sporadic or intermittent.

In the next piece in this series, I’ll discuss how Smart Forecasts deals with estimating safety stock in those cases of intermittent demand, when the assumption of normality is incorrect.

Nelson Hartunian, PhD, co-founded Smart Software, formerly served as President, and currently oversees it as Chairman of the Board. He has, at various times, headed software development, sales and customer service.