Physical goods. We still need them. In fact, despite our much-ballyhooed move to a digital world, per-capita consumption of durable goods in the USA has almost doubled in the past decade and quadrupled in the last generation.¹ We continue to demand more goods, for less money. And an important way to achieve ever more efficiency gains is by continually improving our supply chain management practices, such as by optimizing our inventory management. Achieving efficiencies becomes all the more important in the face of new or changing tariffs – these tariffs can themselves alter the locations at which safety inventory should be held.

Every Operations Management professional is taught how much safety inventory to hold to manage uncertainty in demand. However, almost never is the professional taught how to decide where to hold that safety inventory in a supply chain (e.g., at which location or supplier). This is an important, high-level, strategic decision that likely involves multiple firms, and possibly also requires coordination across company divisions. For example, consider the five stages in the simplified pharmaceutical example of Figure 1; the five stages are 1) production step A at a supplier; 2) production step B at the manufacturer; 3) packaging into bottles and into blister packs at the manufacturer; 4) shipping and clearing customs at a port and subsequent shipping to a single distribution center; and 5) shipping to four hospitals (two receive the bottles and two opt for the blister packs). The question then becomes, should safety inventory be held at (i.e., just after) all stages? Or is it safe to hold it only at the final stage? Or only at the “key stages” in the supply chain? We offer a simple-to-use framework to answer these questions. We’ll also discuss how to use the framework in conjunction with the concepts of postponement and preponement.

Our framework assumes that the end stage must hold safety inventory to ensure a predetermined service level, such as a 98% fill rate at retailing (recognizing that the end stage need not be defined as retailing). However, the other stages need not necessarily hold safety inventory. How does one decide? The more stages at which safety inventory is held, the less safety inventory that is needed at the end stage. Since holding finished goods inventory at the end stage is more expensive than holding work-in-process inventory, this incentivizes the holding at more stages. However, holding inventory at more stages requires more inventory in total (the firm doesn’t take advantage of time-pooling). This incentivizes the holding at fewer stages. Our framework balances these competing objectives. As mentioned previously, achieving this balance may involve the cooperation of multiple firms within the supply chain. Having said that, a key advantage of our framework is that the decisions can be somewhat (but not entirely) decoupled – each stage only needs information at its own stage and the downstream stage¹. By using our relatively straightforward framework, safety against shortages can often be achieved without the need for each firm (and/or each stage) to hold safety stock.

Figure 1: Simplified 5 stage supply chain (pictograms generated with hotpot.ai).

To reiterate, we address the higher-level, more-strategic question of where to hold safety stock. Others have already addressed the question of how much to hold, if the holding locations are known – hold the amount needed to ensure the desired service level, considering the time interval during which the safety inventory must offer protection.²

The Framework of Where in the Supply Chain to Hold Safety Inventory

To apply our framework, each stage only needs to compare its processing time with that of the downstream stage, along with the value of each item at its own stage versus that of the downstream stage. The intuition is that there is a greater incentive to hold safety inventory before a stage that adds significant value to the product (this reduces the holding cost), and there is a greater incentive to hold inventory after a stage that has a long processing time (this minimizes the time interval during which the safety inventory must provide protection against uncertainty). These are key insights to remember, even if the framework described herein cannot be implemented rigorously.

To show how the framework is applied, let’s continue with the parsimonious example of Figure 1. Stages 1 and 3 are non-fan-out points, so at those stages we apply Figure 2. We’ll define a fan-out point later and show how to apply the framework at such stages. To apply Figure 2 at stage 1, we need to find the x and y values to enter onto the graph of Figure 2. The x-value is the ratio of the product value just after stage 2 divided by that just after stage 1. From Figure 1 we find this to be ($4 / $1) = 4. The y-value is the ratio of the processing time at stage 2 divided by that at stage 1. From Figure 1 we find this to be (3 weeks / 2 weeks) = 1.5. The x-y coordinates of (4, 1.5) are located at the point IMAGE 2, which is in the ‘Hold’ region. Thus stage 1 should hold safety inventory. Similarly, applying Figure 2 at stage 3, we find x-y coordinates of (1.2, 2). Since this is located in the ‘Do not hold’ region, stage 3 should not hold safety inventory.

Figure 2: Hold safety inventory at a non-fan-out stage?

Now let’s consider the fan-out points at stages 2 and 4. A stage is a fan-out-point if it is the last stage at which a product is generic – after the fan-out point, there are multiple variants of the product. The multiple variants can be different SKUs, or they can be the same SKU but be located at different retail stores (thus a distribution center is a fan-out point). See, for example, the Hewlett-Packard case⁴ or the Benetton example⁵. A stage is more incentivized to hold safety inventory if it’s a fan-out point, because of the pooling principle (the risk associated with demand uncertainty is pooled across multiple product variants). Thus, the boundary between ‘Hold’ and ‘Do not hold’ is elevated toward the upper-left, as shown in Figure 3. Furthermore, the more product variants that are created at the fan-out point, the more incentive the stage has to hold safety inventory. However, while it might seem intuitive to hold safety inventory of the common product at the fan-out point stage⁶, our framework shows that this is not always advisable. A final insight is that the ‘Hold’ area gets progressively smaller (larger) the shorter (the longer) the supply chain. However, this effect is relatively smaller than the effect of the number of variants at the fan-out point and therefore not shown.

In our pharmaceutical example, stage 2 is a fan-out point, because at stage 3 (the packaging stage), the product splits into two distinct product offerings. And stage 4 is a fan-out point, because at stage 5, each of the two package sizes is diverted to two distinct geographic locations (hospitals). We now use Figure 3 to determine whether stages 2 and/or 4 should hold safety inventory. We do so by again finding the x-y coordinates to be used in Figure 3, based on the product values, and processing times, at each stage, as given in Figure 1. The x-y coordinates for stages 2 and 4 are plotted in Figure 3, showing that stage 2 should not hold safety inventory, even though it is a fan-out point, while stage 4 should hold safety inventory because it is a fan-out point. Thus, in our pharmaceutical example, stages 1 and 4 (along with stage 5) should hold safety inventories, while stages 2 and 3 should not. It is safe to not hold safety inventory at 2 of the 5 stages!

Figure 3: Framework on whether to hold safety inventory at any stage.

What Happens Under Postponement or Preponement?

Currently, the second (manufacturing) stage is a fan-out stage, since there are two variants downstream at packaging, stage 3). Let’s say that after discussions with the four hospitals it was determined that all hospitals could accommodate bottles. Thus, the fan-out is postponed, and stage 2 is no longer a fan-out point. The bottles are shipped to the single distribution center, such that stage 4 is the only fan-out point from which the four hospitals are served. The optimal configuration of where to hold safety inventory remains the same, but now stage 4 can hold the common product and benefit even more from the risk pooling effect. The safety inventory holding costs would be almost 40% higher if safety inventory were held everywhere in the configuration of Figure 1.

Finally, consider what happens if we prepone the push-pull point (i.e., the final stage at which safety inventory is held – inventory is pushed to that point, and then pulled the rest of the way only when demand materializes). In Figure 1, the push-pull point is at the hospital, since that is the final stage where safety inventory is held, in anticipation of patient demand. Let’s say the hospital network now decides to have multiple ‘milk-runs’ daily, between the distribution center and the hospitals, such that safety stock at the hospitals is negligible and can effectively be ignored (see Figure 4). Holding inventory everywhere, under the configuration of Figure 1, would be well over double this new holding cost. Of course, this comes at the expense of more frequent and smaller shipments, so further analysis is needed.

Figure 4: Supply chain after post- and preponement (pictograms generated with hotpot.ai).

Discussion

The question of where to hold safety inventory in a supply chain is a higher-level, more-strategic decision, for which the answer – until now – has been elusive. We offer a straightforward framework to aid executives in making this decision. The framework is also beneficial in helping managers think about the impact of postponing the fan-out point, or preponing the push-pull point. This relatively easy-to-use framework shows that the supply chain can be safe even if it does not hold safety inventory at every stage. The framework further facilitates strategic reconfigurations, which are needed in these uncertain times in order to achieve supply chain resiliency.

References

1. U.S. Bureau of Economic Analysis, “Real personal consumption expenditures per capita: Goods: Durable goods”, retrieved from FRED, Federal Reserve Bank of St. Louis; January 25, 2024.
2. Bert van der Rhee, Günther M. Schmidt, and Jeroen van Orden, “Hold Safety Inventory before, at, or after the Fan-Out Point?,” Production and Operations Management 26, no. 5 (2017): 817–835.
3. Kenneth F. Simpson, “In-Process Inventories,” Operations Research 6, no. 6 (1958): 863–873.
4. Laura Kopczak and Hau L. Lee, “Hewlett-Packard Company DeskJet Printer Supply Chain (A),” Case GS-3A (Stanford, CA: Stanford Graduate School of Business, 2004), 5. 
5. Hau L. Lee and Christopher S. Tang, “Modeling the Costs and Benefits of Delayed Product Differentiation,” Management Science 43, no. 1 (1997): 40–53.
6. Karl Ulrich et al., “Managing Product Variety: A Study of the Bicycle Industry,” in Managing Product Variety, ed. Teck-Hua Ho and Christopher S. Tang (Boston: Kluwer Academic Publishers, 1998), 177.