​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

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 95^th 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 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

Customer as Teacher

Our customers are great teachers who have always helped us bridge the gap between textbook theory and practical application of forecasting and demand planning. Our latest bit of schooling concerns “blanket orders” and how to account for them as part of the demand planning process. 

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 incorporate blanket orders into the demand planning process and details how to adjust stocking targets accordingly.

Demand Planning with Blanket Orders is 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.

How to Incorporate Blanket Orders when Demand Planning 

A blanket policy does have advantages, but rigidity is its Achilles heel.  Demand 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 inventory 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 demand planning process that accounts for blanket orders properly 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.

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.

The Covid19 pandemic has placed unusual stress on public transit agencies. This stress forces agencies to look again at their spare parts planning processes, which is a key driver up ensuring uptime and balancing service parts inventory costs.

This blog focuses on bus systems and their practices for spare parts management and planning. However, there are lessons here for other types of public transit, including rail and light rail.

Back in 1995, the Transportation Research Board (TRB) of the National Research Council published a report that still has relevance. System-Specific Spare Bus Ratios: A Synthesis of Transit Practice stated

The purpose of this study was to document and examine the critical site-specific variables that affect the number of spare vehicles that bus systems need to maintain maximum service requirements. … Although transit managers generally acknowledged that right-sizing the fleet actually improves operations and lowers cost, many reported difficulties in achieving and consistently maintaining a 20 percent spare ratio as recommended by FTA… The respondents to the survey advocated that more emphasis be placed on developing improved and innovative bus maintenance techniques, which would assist them in minimizing downtime and improving vehicle availability, ultimately leading to reduced spare vehicles and labor and material costs.

Grossly simplified guidelines like “keep 20% spare buses” are easy to understand and measure but grossly mask more detailed tactics that can provide more tailored policies that better steward taxpayer dollars spent on spare parts while ensuring the highest levels of availability. If operational reliability can be improved for each bus, then fewer spares are needed.

One way to keep each bus up and running more often is to improve the management of inventories of spare parts – specifically by forecasting service parts usage and the required replenishment policies more accurately. Here is where modern supply chain management can make a significant contribution. The TRB noted this in their report:

Many agencies have been successful in limiting reliance on excess spare vehicles. Those transit officials agree that several factors and initiatives have led to their success and are critical to the success of any program [including] … Effective use of advanced technology to manage critical maintenance functions, including the orderly and timely replacement of parts… Failure to have available service parts and other components when they are needed will adversely affect any maintenance program.

As long as managers are cognizant of the issues and vigilant about what tools are available to them, the probability of buses [being] ‘out for no stock’ will greatly diminish.”

Effective spare parts inventory management requires a balance between “having enough” and “having too much.” What modern service parts planning software can do is make visible the tradeoff between these two goals so that transit managers can make fact-based decisions about spare parts inventories.

There are enough complications in finding the right balance to require moving beyond simple rules of thumb such as “keep ten days’ worth of demand on hand” or “reorder when you are down to five units in stock.” Factors that drive these decisions include both the average demand for a part, the volatility of that demand, the average replenishment lead time (which can be a problem when the part arrives by slow boat from Germany), the variability in lead time, and several cost factors: holding costs, ordering costs, and shortage costs (e.g., lost fares, loss of public goodwill).

Innovative supply chain analytics and spare parts planning software uses advanced probabilistic forecasting and stochastic optimization methods to manage these complexities and provide greater parts availability at lower cost. For instance, Minnesota’s Metro Transit documented a 4x increase in return on investment in the first six months of implementing a new system. To read more about how public transit agencies are exploiting innovative supply chain analytics, see:

• Optimizing Parts Management at BC Transit
• Smart Software and Metro Transit
• Smart Software Helps Metro-North Railroad Keep the Trains Running On-Time

I’ve stood in front of thousands of students. They’ve been more or less young, more or less technical, more or less experienced – and more or less interested.  I’ve done this as a university faculty member since 1972, first at Massachusetts Institute of Technology, then at Harvard University, finally in the School of Engineering at Rensselaer Polytechnic Institute. Between Harvard and RPI I dropped out of academia temporarily to co-found Smart Software with Charlie Smart and Nelson Hartunian. So since then, I’ve also been busy training business users to exploit the power of advanced analytics for forecasting and inventory optimization.

As I write this, I’ve just returned to my office at RPI after introducing first-year Industrial Engineering students to the basic concepts of inventory management. If they stick with the program, they will go on to take required courses in supply chain, system simulation, statistical analysis, and optimization. I told them stories about how useful they will be to their companies should they decide to make a career in the world of supply chain. If I’d had more time, I would have mentioned how capable they will be when they graduate relative to many of their corporate peers. These freshmen and ready and willing to stay the course, soaking up all the techniques and theories we can throw at them, and honing their practical skills in summer jobs or coop assignments.

What I didn’t tell them is that many of them will have to work to keep their intensity when they are on the job. It’s a sad truth that, for whatever reason, many inventory practitioners settle into a kind of stasis that impedes their companies’ ability to exploit the latest technologies, such as cloud-based advanced demand forecasting and inventory optimization. Gather enough of such people in one place and agility and improved efficiency go out the window.

I think one of the factors that dulls people is that the process of implementation frequently feels painfully incremental and prolonged. It often begins with a sobering inventory of relevant data, its correctness, and its currency. Then it moves to an often-awkward discovery that there really is no systematic process in place and the subsequent need to design a good one going forward. Next is the need to learn to use a new software suite. That step involves learning new vocabulary, some level of probabilistic thought, an ability to interpret new graphs and tables, not to mention a new software interface.  All this takes time and effort.

We’ve found that a few things help new customers stay the course. One is having a champion among management, an executive sponsor, who can vouch for the commercial importance of a successful implementation while ensuring the users are supported with continuing education.  A second is identifying and training a super-user or two having unusual combinations of technical and communication skills.  A third is breaking the training into bite-sized chunks and testing for comprehension after each chunk and repeating this process until it is clear that the new concepts, vocabulary, and process are fully absorbed. But all those maneuvers will come to naught without management being all-in and ready to stay the course.  Inventory planning practices in place for many years are not going to be replaced entirely over a three-month implementation process.  You’ve got to want it to get it.