Supply Chain Math: Don’t Bring a Knife to a Gunfight

Whether you understand it in detail yourself or rely on trustworthy software, math is a fact of life for anyone in inventory management and demand forecasting who is hoping to remain competitive in the modern world.

At a conference recently, the lead presenter in an inventory management workshop proudly proclaimed that he had no need for “high-fallutin’ math”, which was explained to mean anything beyond sixth-grade math.

Math is not everyone’s first love. But if you really care about doing your job well, you can’t approach the work with a grade school mentality. Supply chain tasks like demand forecasting and inventory management are inherently mathematical. The blog associated with edX, a premier site for online college course material, has a great post on this topic, at https://www.mooc.org/blog/how-is-math-used-in-supply-chain. Let me quote the first bit:

Math and the supply chain go hand and hand. As supply chains grow, increasing complexity will drive companies to look for ways to manage large-scale decision-making. They can’t go back to how supply chains were 100 years ago—or even two years ago before the pandemic. Instead, new technologies will help streamline and manage the many moving parts. The logistics skills, optimization technologies, and organizational skills used in supply chain all require mathematics.

Our customers don’t need to be experts in supply chain math, they just need to be able to wield the software that contains the math. Software combines users’ experience and subject matter expertise to produce results that make the difference between success and failure. To do its job, the software can’t stop at sixth-grade math; it needs probability, statistics, and optimization theory.

It’s up to us software vendors to package the math in such a way that what goes into the calculations is all that is relevant, even if complicated; and that what comes out is clear, decision-relevant, and defensible when you must justify your recommendations to higher management.

Sixth-grade math can’t warn you when the way you propose to manage a critical spare part will mean a 70% chance of falling short of your item availability target. It can’t tell you how best to adjust your reorder points when a supplier calls and says, “We have a delivery problem.” It can’t save your skin when there is a surprisingly large order and you have to quickly figure out the best way to set up some expedited special orders without busting the operating budget.

So, respect the folk wisdom and don’t bring a knife to a gunfight.

 

 

The Supply Chain Blame Game: Top 3 Excuses for Inventory Shortage and Excess
  1. Blaming Shortages on Lead Time Variability
    Suppliers will often be late, sometimes by a lot. Lead time delays and supply variability are supply chain facts of life, yet inventory carrying organizations are often caught by surprise when a supplier is late.  An effective inventory planning process embraces these facts of life and develops policies that effectively account for this uncertainty.  Sure, there will be times when lead time delays come out of nowhere.  But most often the stocking policies like reorder points, safety stocks, and Min/Max levels aren’t recalibrated often enough to catch changes in the lead time over time.  Many companies only review the reorder point after it has been breached, instead of recalibrating after each new lead time receipt.  We’ve observed situations where the Min/Max settings are only recalibrated annually or are even entirely manual.  If you have a mountain of parts using old Min/Max levels and associated lead times that were relevant a year ago, it should be no surprise that you don’t have enough inventory to hold you until the next order arrives. 

 

  1. Blaming Excess on Bad Sales/Customer Forecasts
    Forecasts from your customers or your sales team are often intentionally over-estimated to ensure supply, in response to past inventory shortages where they were left out to dry. Or, the demand forecasts are inaccurate simply because the sales team doesn’t really know what their customer demand is going to be but are forced to give a number. Demand Variability is another supply chain fact of life, so planning processes need to do a better job account for it.  Why should rely on sales teams to forecast when they best serve the company by selling? Why bother playing the game of feigning acceptance of customer forecasts when both sides know it is often nothing more than a WAG?  A better way is to accept the uncertainty and agree on a degree of stockout risk that is acceptable across groups of items.  Once the stockout risk is agreed to, you can generate an accurate estimate of the safety stock needed to counter the demand variability.  The catch is getting buy-in, since you may not be able to afford super high service levels across all items.  Customers must be willing to pay a higher price per unit for you to deliver extremely high service levels.  Sales people must accept that certain items are more likely to have backorders if they prioritize inventory investment on other items.  Using a consensus safety stock process ensures you are properly buffering and setting the right expectations.  When you do this, you free all parties from having to play the prediction game they were not equipped to play in the first place. 

 

  1. Blaming Problems on Bad Data
    “Garbage In/Garbage Out” is a common excuse for why now is not the right time to invest in planning software. Of course, it is true that if you feed bad data into a model, you won’t get good results, but here’s the thing:  someone, somewhere in the organization is planning inventory, building a forecast, and making decisions on what to purchase. Are they doing this blindly, or are they using data they have curated in a spreadsheet to help them make inventory planning decisions? Hopefully, the latter.  Combine that internal knowledge with software, automating data import from the ERP, and data cleansing.  Once harmonized, your planning software will provide continually updated, well-structured demand and lead time signals that now make effective demand forecasting and inventory optimization possible.  Smart Software cofounder Tom Willemain wrote in an IBF newsletter that “many data problems derive from data having been neglected until a forecasting project made them important.” So, start that forecasting project, because step one is making sure that “what goes in” is a pristine, documented, and accurate demand signal.

 

 

Managing Inventory amid Regime Change

​If you hear the phrase “regime change” on the news, you immediately think of some fraught geopolitical event. Statisticians use the phrase differently, in a way that has high relevance for demand planning and inventory optimization. This blog is about “regime change” in the statistical sense, meaning a major change in the character of the demand for an inventory item.

An item’s demand history is the fuel that powers demand planners’ forecasting machines. In general, the more fuel the better, giving us a better fix on the average level, the volatility, the size and frequency of any spikes, the shape of any seasonality pattern, and the size and direction of any trend.

But there is one big exception to the rule that “more data is better data.” If there is a major shift in your world and new demand doesn’t look like old demand, then old data become dangerous.

Modern software can make accurate forecasts of item demand and suggest wise choices for inventory parameters like reorder points and order quantities. But the validity of these calculations depends on the relevance of the data used in their calculation. Old data from an old regime no longer reflect current reality, so including them in calculations creates forecast error for demand planners and either excess stock or unacceptable stockout rates for inventory planners.

That said, if you were to endure a recent regime change and throw out the obsolete data, you would have a lot less data to work with. This has its own costs, because all the estimates computed from the data would have greater statistical uncertainty even though they would be less biased. In this case, your calculations would have to rely more heavily on a blend of statistical analysis and your own expert judgement.

At this point, you may ask “How can I know if and when there has been a regime change?” If you’ve been on the job for a while and are comfortable looking at timeplots of item demand, you will generally recognize regime change when you see it, at least if it’s not too subtle. Figure 1 shows some real-world examples that are obvious.

Figure 1 Four examples of regime change in real-world item demand

Figure 1: Four examples of regime change in real-world item demand

 

Unfortunately, less obvious changes can still have significant effects. Moreover, most of our customers are too busy to manually review all the items they manage even once per quarter. When you get beyond, say, 100 items, the task of eyeballing all those time series becomes onerous. Fortunately, software can do a good job of continuously monitoring demand for tens of thousands of items and alerting you to any items that may need your attention. Then too, you can arrange for the software to not only detect regime change but also automatically exclude from its calculations all data collected before the most recent regime change, if any. In other words, you can get both automatic warning of regime change and automatic protection from regime change.

For more on the basics of regime change, see our previous blog on the topic: https://smartcorp.com/blog/demandplanningregimechange/  

 

An Example with Numbers in It

If you would like to learn more, read on to see a numerical example of how much regime change can alter the calculation of a reorder point for a critical spare part. Here is a scenario to illustrate the point.

Scenario

  • Goal: calculate the reorder point needed to control the risk of stockout while waiting for replenishment. Assume the target stockout risk is 5%.
  • Assume the item has intermittent daily demand, with many days of zero demand.
  • Assume daily demand has a Poisson distribution with an average of 1.0 units per day.
  • Assume the replenishment lead time is always 30 days.
  • The lead time demand will be random, so it will have a probability distribution and the reorder point will be the 95th percentile of the distribution.
  • Assume the effect of regime change is to either raise or lower the mean daily demand.
  • Assume there is one year of daily data available for estimating the mean daily unit demand.

 

Figure 2 Example of change in mean demand and sample of random daily demand

Figure 2 Example of change in mean demand and sample of random daily demand

 

Figure 2 shows one form of this scenario. The top panel shows that the average daily demand increases from 1.0 to 1.5 after 270 days. The bottom panel shows one way that a year’s worth of daily demand might appear. (At this point, you may be feeling that calculating all this stuff is complicated, even for what turns out to be a simplified scenario. That is why we have software!)

Analysis

Successful calculation of the proper reorder point will depend on when regime change happens and how big a change occurs. We simulated regime changes of various sizes at various times within a 365 day period. Around a base demand of 1.0 units per day, we studied shifts in demand (“shift”) of ±25% and ±50% as well as a no change reference case. We located the time of the change (“t.break”) at 90, 180, and 270 days. In each case, we computed two estimates of the reorder point: The “ideal” value given perfect knowledge of the average demand in the new regime (“ROP.true”), and the estimated value of mean demand computed by ignoring the regime change and using all the demand data for the past year (“ROP.all”).

Table 1 shows the estimates of the reorder point computed over 100 simulations. The center block is the reference case, in which there is no change in the daily demand, which remains fixed at 1 unit per day. The colored block at the bottom is the most extreme increasing scenario, with demand increasing to 1.5 units/day either one-third, one-half, or two-thirds of the way through the year.

We can draw several conclusions from these simulations.

ROP.true: The correct choice for reorder point increases or decreases according to the change in mean demand after the regime change. The relationship is not a simple linear one: the table spans a 600% range of demand levels (0.25 to 1.50) but a 467% range of reorder points (from 12 to 56).

ROP.all: Ignoring the regime change can lead to gross overestimates of the reorder point when demand drops and gross underestimates when demand increases.  As we would expect, the later the regime change, the worse the error. For example, if demand increases from 1.0 to 1.5 units per day two-thirds of the way through the year without being noticed, the calculated reorder point of 43 units would fall 13 units short of where it should be.

A word of caution: Table 1 shows that basing the calculations of reorder points using only data from after a regime change will usually get the right answer. What it doesn’t show is that the estimates can be unstable if there is very little demand history after the change. Therefore, in practice, you should wait to react to the regime change until a decent number of observations have accumulated in the new regime. This might mean using all the demand history, both pre- and post-change, until, say, 60 or 90 days of history have accumulated before ignoring pre-change data.

 

Table 1 Correct and Estimated Reorder Points for different regime change scenarios

Table 1 Correct and Estimated Reorder Points for different regime change scenarios

Blanket Orders

Customer as Teacher

Our customers are great teachers who have always helped us bridge the gap between textbook theory and practical application. A prime example happened over twenty years ago, when we were introduced to the phenomenon of intermittent demand, which is common among spare parts but rare among the finished goods managed by our original customers working in sales and marketing. This revelation soon led to our preeminent position as vendors of software for managing inventories of spare parts. Our latest bit of schooling concerns “blanket orders.”

Expanding the Inventory Theory Textbook

Textbook inventory theory focuses on the three most used replenishment policies: (1) Periodic review order-up-to policy, designated (T, S) in the books (2) Continuous review policy with fixed order quantity, designated (R, Q) and (3) Continuous review order-up-to policy, designated (s, S) but usually called “Min/Max.” Our customers have pointed out that their actual ordering process often includes frequent use of “blanket orders.” This blog focuses on how to adjust stocking targets when blanket orders are used.

Blanket Orders are Different

Blanket orders are contracts with suppliers for fixed replenishment quantities arriving at fixed intervals. For example, you might agree with your supplier to receive 20 units every 7 days via a blanket order rather than 60 to 90 units every 28 days under the Periodic Review policy. Blanket orders contrast even more with the Continuous Review policies, under which both order schedules and order quantities are random.

In general, it is efficient to build flexibility into the restocking process so that you order only what you need and only order when you need it. By that standard, Min/Max should make the most sense and blanket policies should make the least sense.

The Case for Blanket Policies

However, while efficiency is important, it is never the only consideration. One of our customers, let’s call them Company X, explained the appeal of blanket policies in their circumstances. Company X makes high-performance parts for motorcycles and ATV’s. They turn raw steel into cool things.

But they must deal with the steel. Steel is expensive. Steel is bulky and heavy. Steel is not something conjured overnight on a special-order basis. The inventory manager at Company X does not want to place large but random-sized orders at random times. He does not want to baby-sit a mountain of steel. His suppliers do not want to receive orders for random quantities at random times. And Company X prefers to spread out its payments. The result: Blanket orders.

The Fatal Flaw in Blanket Policies

For Company X, blanket orders are intended to even out replenishment buys and avoid unwieldy buildups of piles of steel before they are ready for use. But the logic behind continuous review inventory policies still applies. Surges in demand, otherwise welcome, will occur and can create stockouts. Likewise, pauses in demand can create excess demand. As time goes on, it becomes clear that a blanket policy has a fatal flaw: only if the blanket orders exactly match the average demand can they avoid runaway inventory in either direction, up or down. In practice, it will be impossible to exactly match average demand. Furthermore, average demand is a moving target and can drift up or down.

Hybrid Blanket Policies to the Rescue

A blanket policy does have advantages, but rigidity is its Achilles heel.  Planners will often improvise by adjusting future orders to handle changes in demand but this doesn’t scale across thousands of items.  To make the replenishment policy robust against randomness in demand, we suggest a hybrid policy that begins with blanket orders but retains flexibility to automatically (not manually) order additional supply on an as-need basis. Supplementing the blanket policy with a Min/Max backup provides for adjustments without manual intervention. This combination will capture some of the advantages of blanket orders while protecting customer service and avoiding runaway inventory.

Designing a hybrid policy requires choice of four control parameters. Two parameters are the fixed size and fixed timing of the blanket policy. Two more are the values of Min and Max. This leaves the inventory manager facing a four-dimensional optimization problem.  Advanced inventory optimization software will make it possible to evaluate choices for the values of the four parameters and to support negotiations with suppliers when crafting blanket orders.

 

 

Optimizing Inventory around Suppliers´ Minimum Order Quantities

Recently, I had an interesting conversation with an inventory manager and the VP Finance. We were discussing the benefits of being able to automatically optimize both reorder points and order quantities. The VP Finance was concerned that given their large supplier required minimum order quantities, they would not be able to benefit.  He said his suppliers held all the power, forcing him to accept massive minimum order quantities and tying his hands. While he felt bad about this, he saw a silver lining: He didn’t have to do any planning. He would accept a large inventory investment, but his customer service levels would be exceptional.  Perhaps the large inventory investment was assumed to be the cost of doing business.

I pushed back and pointed out that he was not as powerless as he felt. He still had control of the other half of the procurement process: while he couldn’t control how much to order, he could control when to order by adjusting the reorder point. In other words, there is always room for careful quantitative analysis in inventory management, even when you have one hand tied behind your back.

An Example

To put some numbers behind my argument, I created a scenario then analyzed it using our methodology to show how consequential it can be to use inventory optimization software even in constrained situations. In this scenario, item demand averages 2.2 units per day but varies significantly by day of week. Let’s say the imaginary supplier insists on a minimum order quantity of 500 units (way out of proportion to demand) and fills replenishment orders in either three days or ten days in equal proportions (quite inconsistent). To spread the blame around, let’s also suppose that the imaginary supplier’s imaginary customer uses a foolish rule that the reorder point should be 10% of the minimum order quantity. (Why this rule? Too many companies use simple/simplistic rules of thumb in lieu of proper analysis.)

So, we have a base case in which the order quantity is 500 units, and the reorder point is 50 units. In this case, the fill rate is 100%, but the average number of units on hand is a whopping 330. If the customer would simply lower the reorder point from 50 to 15, the fill rate would still be 99.5%, but the average stock on hand would drop by 11% to 295 units. Using the one hand not tied behind his back, the inventory manager could cut his inventory investment by more than 10%, which would be a noticeable win.

Incidentally, if the minimum order quantity were abolished, the customer would be free to arrive at a new and much better solution. Setting the order quantity to 45 and the reorder point to 25 would achieve a 99% fill rate at the cost of a daily on-hand level of only 35 units: nearly a 90% reduction in inventory investment: a major improvement over the status quo.

Postscript

These calculations are possible using our software, which can make visible the otherwise unknown relationships between inventory system design choices (e.g., order quantity and reorder point) and key performance indicators (e.g., average units on hand and fill rate).  Armed with this ability to conduct these calculations, alternative arrangements with the supplier may now be considered. For example, what if, in exchange for paying a higher price per unit, the supplier agreed to a lower MOQ. Using the software to conduct an analysis of the key performance indicators using the “what if” costs and MOQs would reveal the cost per unit and MOQ that would be needed to develop a more profitable deal.   Once identified, all parties stand to benefit.  The supplier now generates a better margin on sales of its products, and the buyer holds considerably less inventory yielding a holding cost reduction that dwarfs the added cost per unit.  Everyone wins.