We believe the leading edge of supply chain analytics to be the development of digital twins of inventory systems. These twins take the form of discrete event models that use Monte Carlo simulation to generate and optimize over the full range of operational risks. We also assert that we and our colleagues at Smart Software have played an outsized role in forging that leading edge. But we are not alone: there are a small number of other software firms around the globe who are catching up.

So, what’s next for supply chain analytics? Where is the next frontier? It might involve some sort of neural network model of a distribution system. But we’d give better odds on an extension of our leading-edge models of “single echelon” inventory systems to “multi-echelon” inventory systems.

Figures 1 and 2 illustrate the distinction between single and multiple echelon systems. Figure 1 depicts a manufacturer that relies on a Source to replenish its stock of spare parts or components. When stockouts loom, the manufacturer orders replenishment stock from the Source.

Figure 1: A single-echelon inventory system

Single echelon models do not explicitly include details of the Source. It remains mysterious, an invisible ghost whose only relevant feature is the random time it takes to respond to a replenishment request. Importantly, the Source is implicitly assumed to never itself stock out. That assumption may be “good enough” for many purposes, but it cannot be literally true. It gets handled by stuffing supplier stockout events into the replenishment lead time distribution. Pushing back on that assumption is the rationale for multiechelon modeling.

Figure 2 depicts a simple two-echelon inventory system. It shifts domains from manufacturing to distribution. There are multiple warehouses (WH’s) dependent on a distribution center (DC) for resupply. Now the DC is an explicit part of the model. It has a finite capacity to process orders and requires its own reordering protocols. The DC gets its replenishment from higher up the chain from a Source. The Source might be the manufacturer of the inventory item or perhaps a “regional DC” or something similar, but – guess what? – it is another ghost. As in the single-echelon model, this ghost has one visible characteristic: the probability distribution of its replenishment lead time. (The punch line of a famous joke in physics is “But madame, it’s turtles all the way down.” In our case, “It’s ghosts all the way up.”)

Figure 2: A two-echelon inventory system

The problem of process design and optimization is much harder with two levels. The difficulty is not just the addition of two more control parameters for every WH (e.g., a Min and a Max for each) plus the same two parameters for the DC. Rather, the tougher part is modeling the interaction among the WH’s. In the single-level model, each WH operates in its own little world and never hears “Sorry, we’re stocked out” from the ghostly Source. But in a two-level system, there are multiple WH’s all competing for resupply from their shared DC. This competition creates the main analytical difficulty: the WH’s cannot be modeled in isolation but must be analyzed simultaneously. For instance, if one DC services ten WH’s, there are 2+10×2 = 22 inventory control parameters whose values need to be calculated. In nerd-speak: It is not trivial to solve a 22-variable constrained discrete optimization problem having a stochastic objective function.

If we choose the wrong system design, we discover a new phenomenon inherent in multi-echelon systems, which we informally call “meltdown” or “catastrophe.” In this phenomenon, the DC cannot keep up with the replenishment demands of the WH’s, so it eventually creates stockouts at the warehouse level. Then the WH’s increasingly frantic replenishment requests exhaust the inventory at the DC, which starts its own panicked requests for replenishment from the regional DC. If the regional DC takes too long to refill the DC, then the whole system dissolves into a stockout tragedy.

One solution to the meltdown problem is to overdesign the DC so it almost never runs out, but that can be very expensive, which is why there is a regional DC in the first place. So any affordable system design has a DC that is just good enough to last a long time between meltdowns. This perspective implies a new type of key performance indicator (KPI), such as “Probability of Meltdown within X years is less than Y percent.”

The next frontier will require new methods and new metrics but will offer a new way to design and optimize distribution systems. Our skunk works is already generating prototypes. Watch this space.

In this blog, we will discuss today’s fast-paced and unpredictable market and the constant challenges businesses face in managing their inventory and service levels efficiently. The main subject of this discussion, rooted in the concept of “Probabilistic Inventory Optimization,” focuses on how modern technology can be leveraged to achieve optimal service and inventory targets amidst uncertainty. This approach not only addresses traditional inventory management issues but also offers a strategic edge in navigating the complexities of demand fluctuations and supply chain disruptions.

Understanding and implementing inventory optimization technology is important for several reasons. First, it directly impacts a company’s ability to meet customer demands promptly, thereby affecting customer satisfaction and loyalty. Second, effective inventory management controls operational costs, reducing unnecessary stock holding and minimizing the risk of stockouts or overstocking. In an era where market conditions change rapidly, having a robust system to manage these aspects can be the difference between thriving and merely surviving.

At the heart of inventory management lies a paradox: the need to be prepared for fluctuating demand without succumbing to the pitfalls of overstocking, which can lead to increased holding costs, obsolescence, and wasted resources. Conversely, understocking can result in stockouts, lost sales, and diminished customer satisfaction, ultimately impacting a company’s reputation and bottom line. The unpredictable nature of market demands, compounded by potential supply chain disruptions and changing consumer behavior, adds complexity to this balancing act.

Technology plays a pivotal role here. Modern inventory optimization software integrates probabilistic models, sophisticated forecasting algorithms, and simulation capabilities. These systems help companies respond swiftly to changing market conditions. Furthermore, adopting such technology fosters a culture of data-driven decision-making, ensuring businesses are not merely reacting to uncertainties but proactively strategizing to mitigate their impacts.

Here are brief discussions of the relevant algorithmic technologies.

Probabilistic Inventory Optimization: Traditional inventory management approaches rely on deterministic models that assume a static, predictable world. These models falter in the face of variability and uncertainty. Enter probabilistic inventory optimization, a paradigm that embraces the randomness inherent in supply chain processes. This approach employs statistical models to represent the uncertainties in demand and supply, enabling businesses to account for a full range of possible outcomes.

Advanced Forecasting:  A cornerstone of effective inventory optimization is the ability to anticipate future demand accurately. Advanced forecasting techniques, such as [we don’t sell this outside of SmartForecasts or maybe not even there anymore, so don’t mention it], time series analysis, and machine learning, extract exploitable patterns from historical data.

Safety Stock Calculation: A Shield Against Uncertainty:

Forecasts that include estimates of their own uncertainty enable safety stock calculations. Safety stock acts as a buffer against the unpredictability of demand and supply lead times. Determining the optimal level of safety stock is a critical challenge that probabilistic models address adeptly. With the right safety stock levels, businesses can maintain high service levels, ensuring product availability without the burden of excessive inventory.

Scenario Planning: Preparing for Multiple Futures:

The future is inherently uncertain, and a single forecast can never capture all possible scenarios. Advanced methods that create a range of realistic demand scenarios are the essential form of probabilistic inventory optimization. These techniques allow businesses to explore the implications of multiple futures, from best-case to worst-case situations. By planning against these scenarios, companies can enhance their resilience in the face of market volatility.

Navigating the Future with Confidence

The uncertain landscape of today’s business environment necessitates a shift from traditional inventory management practices to more sophisticated, probabilistic approaches. By embracing the principles of probabilistic inventory optimization, companies can strike a durable balance between service excellence and cost efficiency. Integrating advanced forecasting techniques, strategic safety stock calculations, and scenario planning, supported by Smart Inventory Planning and Optimization (Smart IP&O), equips businesses to transform uncertainty from a challenge into an opportunity. Companies that embrace this approach report significant improvements in service levels, reductions in inventory costs, and enhanced supply chain agility.

For example, less critical Items forecasted to achieve 99%+ service levels represent opportunities to reduce inventory. By targeting lower service levels on less critical items, inventory will be “the right size” over time to the new equilibrium, decreasing holding costs and the value of inventory on hand. A major public transit system reduced inventory by over $4,000,000 while improving service levels.

Optimizing Inventory Levels also means savings realized on one subset of items can be reallocated to carry a broader portfolio of “in stock” items, allowing revenues to be captured that would otherwise be lost sales. A leading distributor was able to stock a broader portfolio of parts with savings used from inventory reductions and increased part availability by 18%.

​BACKGROUND

Most of Smart Software’s blogs, webinars and white papers describe the use of our software in “normal operations.” This one is about “irregular operations.”  Smart Software is in the process of adapting our products to help you cope with your own irregular ops. This is a preview.

I first heard the term “irregular operations” when serving a sabbatical tour at the U.S. Federal Aviation Administration in Washington, DC. The FAA abbreviates the term to “IROPS” and uses it to describe situations in which weather, mechanical problems or other issues disrupt the normal flow of aircraft.

Smart Inventory Optimization® (“SIO”) currently works to provide what are known as “steady state” policies for managing inventory items. That means, for instance, that SIO automatically calculates values for reorder points (ROP’s) and order quantities (OQ’s) that are meant to last for the foreseeable future. It computes these values based on simulations of daily operations that extend years into the future. If and when the unforeseeable happens, our regime change detection method reacts by removing obsolete data and allowing recalculation of the ROP’s and OQ’s.

We often note the increasing speed of business, which shortens the duration of the “foreseeable future.” Some of our customers are now adopting shorter planning horizons, such as moving from quarterly to monthly plans. One side effect of this change is that IROPS have become more consequential. If a plan is based on three simulated years of daily demand, one odd event, like a large surprise order, doesn’t matter much in the grand scheme of things. But if the planning horizon is very short, one big surprise demand can have a major effect on key performance indicators (KPI’s) computed over a shorter interval – there is no time for “averaging out”. The planner may be forced to place an emergency replenishment order to deal with the disruption. When should the order be placed to do the most good? How big should it be?

SCENARIO: NORMAL OPS

To make this concrete, consider the following scenario. Tom’s Spares, Inc. provides critical service parts to its customers, including SKU723, a replacement circuit board sold under the trade name WIDGET. Demand for WIDGET is intermittent, with less than one unit demanded per day. Tom’s Spares orders WIDGETs from Acme Products, who take either 7 or 10 days to fulfill replenishment orders.

Tom’s Spares operates with a short inventory planning horizon of 28 days. The company operates in a competitive environment with impatient customers who only grudgingly accept backorders. Tom’s policy is to set ROP’s and OQ’s to keep inventory lean while maintaining a fill rate of at least 90%. Management monitors KPI’s on a monthly basis. In the case of WIDGETS, these KPI targets are currently met using an ROP=3 and an OQ=4, resulting in an average on hand of about 4 units and average fill rate of 96%.  Tom’s Spares has a pretty good thing going for WIDGETS.

Figure 1 shows two months of WIDGET information. The top left panel shows daily unit demand. The top right shows daily units on hand. The bottom left panel shows the timing and size of replenishment orders back to Acme Products. The bottom right shows units backordered due to stockouts. In this simulation, daily demand was either 0 or 1, with one demand of 2 units. On hand units began the month at 7 and never dropped below 1, though in the next month there was a stockout resulting in a single unit on backorder. Over the two months, there were 4 replenishment orders of 4 units each sent to Acme, all of which arrived during the two-month simulation period.

GOOD TROUBLE DISRUPTS NORMAL OPS

Now we add some “good trouble” to the scenario: An unusually large order arises part way through the planning period. It’s “good” because more demand implies more revenue. But it’s “trouble” because the normal ops inventory control parameters (ROP=3, OQ=4) were not chosen to cope with this situation. The spike in demand might be so big, and so disadvantageously timed, as to overwhelm the inventory system, creating stockouts and their attendant backorders. The KPI report to management for such a month would not be pretty.

Figure 2 shows a scenario in which a demand spike of 10 units hits in the third day of the planning period. In this case, the spike puts the inventory under water for the rest of the month and creates a cascade of backorders extending into the next month. Averaging over 1,000 simulations, month 1 KPI’s show an average on hand of 0.6 units and a miserable 44% fill rate.

FIGHTING BACK WITH IRREGULAR OPERATIONS

Tom’s Spares can respond to an irregular situation with an irregular move by creating an emergency replenishment order. To do it right, they have to think about (a) when to place the order (b) how big the order should be and (c) whether to expedite the order.

The timing question seems obvious: react as soon as the order hits. However, if the customer were to provide early warning, Tom’s Spares could order early and be in better position to limit the disruption from the spike. However, if communication between Tom’s and the customer making the big order is spotty, then the customer might give Tom’s a heads-up later or not at all.

The size of the special order seems obvious too: pre-order the required number of units. But that works best if Tom’s Spares knows when the demand spike will hit. If not, it might be a good idea to order extra to limit the duration of any backorders. In general, the less early warning provided, the larger the order Tom’s should make. This relationship could be explored with simulation, of course.

The arrival of the replenishment order could be left to the usual operation of Acme Products. In the simulations above, Acme was equally likely to respond in 7 or 14 days. For a 28-day planning horizon, taking a risk on getting a 14-day response might be asking for trouble, so it may be especially worthwhile for Tom’s to pay Acme for expedited shipping. Maybe overnight, but possibly something cheaper but still relatively fast.

We explored a few more scenarios using simulation. Table 1 shows the results. Scenarios 1-4 assume a surprise additional demand of 10 units arrives on Day 3, triggering an immediate order for  additional replenishment. The size and lead time of the replenishment order varies.

Scenario 0 shows that doing nothing in response to the surprise demand leads to an abysmal 41% fill rate for that month; not shown is that this result sets of the next month for continued poor performance. Regular operations won’t do well. The planner must do something to respond to the anomalous demand.

Doing something in response involves making a one-time emergency replenishment order. The planner must choose the size and timing of that order. Scenarios 1 and 3 depict “half sized” replenishments. Scenarios 1 and 2 depict overnight replenishments, while scenarios 3 and 4 depict guaranteed one week response.

The results make clear that immediate response is more important than the size of the replenishment order for restoring the Fill Rate. Overnight replenishment produces fill rates in the 70% range, while one-week replenishment lead time drops the fill rate into the mid-50% to mid-60% range.

TAKEAWAYS

Inventory management software is expanding from its traditional focus on normal ops to an additional focus on irregular ops (IROPS). This evolution has been made possible by the development of new statistical methods for generating demand scenarios at a daily level.

We considered one IROPS situation: surprise arrival of an anomalously large demand. Daily simulations provided guidance about the timing and size of an emergency replenishment order. Results from such an analysis provide inventory planners with critical backup by estimating the results of alternative interventions that their experience suggests to them.

This video blog holds essential insights for those working with the complexities of inventory management. The session focuses on striking the right balance within the inventory tradeoff curve, inviting viewers to understand the deep-seated importance of this equilibrium. If you’ve ever had to manage stock, you’ll know it feels like a bit of a tug-of-war. On one side, you’re pulling towards less inventory, which is great for saving money but can leave your customers high and dry. On the other, you’re considering more inventory, which keeps your customers happy but can be a pain for your budget. To make a smart choice in this ongoing tug-of-war, you need to understand where your current inventory decisions place you on this tradeoff curve. Are you at a point where you can handle the pressure, or do you need to shuffle along to a more comfortable spot?

If you can’t answer this question, it means that you still rely on outdated methods, risking the potential for surplus inventory or unmet customer needs. Watch the video so you can see exactly where you are on this curve and understand better about whether you want to stay put or move to a more optimal position.

And if you decide to move, we’ve got the tools to guide you. Smart IP&O’s advanced “what-if” analysis enables businesses to precisely evaluate the impact of different inventory strategies, such as adjustments to safety stock levels or changes in reorder points, on their balance between holding costs and service levels. By simulating demand scenarios and inventory policies, Smart IP&O provides a clear visualization of potential financial outcomes and service level implications, allowing for data-driven strategic decisions. This powerful tool ensures businesses can achieve an optimal balance, minimizing excess inventory and related costs while maintaining high service levels to meet customer demand efficiently.  

​In this video blog, we explore the critical roles of Descriptive, Predictive, and Prescriptive Analytics in inventory management, highlighting their essential contributions to driving supply chain optimization through strategic foresight and insightful data analysis.

​These analytics foster a dynamic, responsive, and efficient inventory management ecosystem by enabling inventory managers to monitor current operations, anticipate future developments, and formulate optimal responses. We’ll walk you through how Descriptive Analytics keeps you informed about current operations, Predictive Analytics helps you anticipate future demands, and Prescriptive Analytics guides your strategic decisions for maximum efficiency and cost-effectiveness.

By the end of the video, you’ll have a solid understanding of how to leverage these analytics to enhance your inventory management strategies. These are not just tools but a new way of thinking about and approaching inventory optimization with the support of modern software.