The answer is 9,142: Understanding the influence of disruption risk on inventory decision making Deloitte Review issue 14

The question was how many units of inventory a manager should order when faced with a possible disruption in supply. The correct answer is not guesswork, but based on 150 years of theory and practice. We examine individual choices made in this critical situation—and the results are not encouraging.

The question was how many units of inventory a manager should order when faced with a possible disruption in supply. Almost no one—as in 0.3 percent—got it right.

Every day, inventory managers ask themselves “How much should I order?” The correct answer is not guesswork; it is based on more than 150 years of theory and practice.1 Referred to as the Newsvendor Approach, this method of identifying profit-maximizing inventory levels forms the bedrock of the inventory planning systems used by many companies around the world.2 The research presented in this article investigates what happens when inventory managers impose their judgment based on the recommendations of those systems—in particular, when faced with the possibility of a disruption in supply.


Supply chain risk and potential disruption continue to occupy the minds of executives worldwide. Recent research by Deloitte revealed 71 percent of approximately 600 global manufacturing and retail executives view supply chain risk as important in strategic decision making. Forty-eight percent said the frequency of negative supply chain events had increased over the last three years, and 53 percent claimed that these events had become more costly.3 Elsewhere in this issue of Deloitte Review, we consider how leaders can improve the general resilience of their companies and supply chains.4

In this article, we examine the individual choices that inventory managers make in response to potential disruptions in supply. The results are not encouraging: Virtually everyone (99.7 percent of subjects) responded suboptimally, overreacting to low probabilities of disruption and underreacting to high probabilities. Approximately 15 percent of the individuals in our study responded irrationally, reducing orders in response to potential supply disruptions instead of increasing them. Fully one-third of our subjects altered inventory recommendations for no apparent reason. This kind of performance should be worrying to leaders of US companies that, as of July 2013, held approximately $1.7 trillion in inventory.5 Proper inventory planning is, after all, critical to customer service and to overall company performance.

Past and future uncertainties: The challenge faced by inventory managers

Inventory decision making balances both past and future uncertainties. Past uncertainties include the variability of historical demand for any of the products a company offers. Future uncertainties include possible disruptions in the supply of the products or other inventory. Many inventory management systems rely on historical (past) data and use it to recommend future action (that is, order quantities). Inventory planners accept or alter these recommendations using their own judgment about how the future will unfold. Our analysis will focus on these choices. In particular, our study asks the following questions:

  1. Do individuals unnecessarily adjust from inventory system-recommended quantities (that is, do they adjust for the sake of adjusting)?
  2. Do individuals respond rationally to potential supply disruptions (that is, increase orders in response to potential shortage)?
  3. Do individuals optimally adjust quantities in response to potential supply disruptions?
  4. Does overreaction or underreaction depend on the probability of the potential disruption or the profitability of the product?

We conclude that in general managers do a poor job of making inventory decisions under these conditions, making errors in judgment that can be severe, and that many inventory management processes are, at best, naïve to the existence or mitigation of the negative effects of manager choices.

The case of Tristen Corporation

Tristen Corporation provides a good example of how inventory management processes operate in many firms.6

Tristen is a $700 million manufacturer and marketer of durable consumer products. Based in North America, the company offers over 500 core products to residential and professional users along with more than 3,000 other accessories and consumable supplies. Approximately 75 percent of production occurs internationally. The product portfolio contains a mix of stable and high-growth products. Tristen has more than 1,000 employees and sustains double-digit growth, primarily as a result of new and innovative product offerings.

Production and inventory planning is performed at Tristen’s headquarters in the United States. Ordering is supported by an inventory planning system that uses two years’ worth of SKU-level sales data to recommend inventory and order levels. Tristen’s inventory planning systems utilize a Newsvendor approach that accounts for both average historical demand and demand variation, calculating safety stocks based on a standard service level. This approach is typical across many industries.

Tristen’s cadre of inventory analysts evaluate the recommendations of the inventory planning system and finalize recommended inventory amounts, triggering planning for orders and manufacturing. Analysts consider system recommendations along with other available information (not considered by the planning algorithm) to make a final determination of inventory levels. This information sometimes suggests the possibility of shortages in supply. Here, the Tristen policy is clear. As stated by the director of inventory planning at the company:

“When supply looks as if it might be constrained, we definitely build inventory, including ‘ordering up’ when we think we might be placed on allocation.”

In this sense, Tristen is like many other companies. Its managers are compelled to make decisions based not on the certainty, but rather on the possibility of shortages. Tristen’s systems, though just as sophisticated as those of many other companies, are of little help in this regard. They only look at historical demand and are not designed to factor in the potential for future supply disruptions. Managers at Tristen are left to make these adjustments based on their understanding of future risks. It is reasonable to wonder how well-equipped they are to accomplish this task.

... the logic of choice does not provide an adequate foundation for a descriptive theory of decision making. As a result, alternative theories of choice and risk attitudes have been established that attempt to account for the intuitive judgments that individuals make. Although sometimes useful, these intuitive judgments occasionally lead to severe and systematic errors.

Decision making under uncertainty

Research in behavioral economics and behavioral operations offers ample evidence that humans frequently make poor choices in the face of uncertainty. Whereas classic economic theory suggests individuals make decisions under risk by calculating an “expected value” (that is, the average value or “utility” of all the possible outcomes weighted by their probabilities), extensive analysis of actual behavior shows systematic violation of this rule and suggests “the logic of choice does not provide an adequate foundation for a descriptive theory of decision making.”7 As a result, alternative theories of choice and risk attitudes have been established that attempt to account for the intuitive judgments that individuals make.8 Although sometimes useful, these intuitive judgments occasionally lead to severe and systematic errors.9

Inventory decisions are not immune to these anomalies. There is a wealth of evidence to suggest that managers perform poorly in manual inventory planning. Reasons for this poor performance include bias, alternative preferences, lack of experience, and even simple random errors.10 Thus, inventory planning systems play an important role in decision support. We tackled the issue of how challenges to decision making affect the performance of managers when reacting to the prospect of a future disruption that would restrict supply, a task in which inventory planning systems are generally unable to assist. Specifically, we wanted to understand how managers dealt with the threat of being put “on allocation.”

About the research

We conducted a field experiment to understand inventory manager behavior with 81 experienced supply chain managers and 41 undergraduate students majoring in supply chain management at a program ranked among the top 15 in the United States.11 Study participants were asked to plan inventory in six decision-making scenarios.

Participants were given short cases that presented the cost and profitability of a stock keeping unit (SKU). SKUs were either high-profit (90 percent gross margin) or medium-profit (60 percent gross margin). Figure 1 depicts one such case. Participants received information about the expected demand for the SKU along with the level of demand variability (standard deviation). All SKUs had the same demand profile. Key aspects of basic inventory planning (including the role of profitability, cost, expected demand, and standard deviation of demand) were explained in available video-based training.

DR_Fig1_DUP539_InventoryEach scenario offered a base case that we used to investigate our first question: Do inventory managers unnecessarily adjust system-recommended quantities? Participants were provided a system-recommended “profit-maximizing order quantity” and asked to enter the number of units they wanted to order.

We then offered “shortage risk” scenarios that allowed us to explore the influence of both SKU profitability and disruption probability on managers’ choices. Participants were asked to respond to scenarios that included one of three magnitudes of shortage risk—5 percent (low), 25 percent (moderate), and 75 percent (high)—and were informed that if a shortage did occur, they would be put on “allocation,” receiving just half of their order amount. They were then asked how many units they would like to order.12 Cases were constructed so that each level of SKU profitability was paired with each probability of disruption.

Table 1 summarizes the data for each SKU, including profit level, system-recommended optimal base case amount, disruption probability, resulting profit-maximizing optimal order quantity, and the quantity adjustment in units to move from the base case to the optimal inventory amount given the associated disruption probability. For example, Zeta is a high-profit SKU with an optimal base case quantity of 7,564. Zeta also has a moderate disruption risk (25 percent probability). Factoring in this risk increases the profit-maximizing inventory quantity to 9,142—an increase of 1,578 units over the base case.13

Table 1. Summary data on six SKU cases provided for study participants

SKU Profitability Recommended base amount Disruption probability Optimal order quantity Optimal adjustment from base amount
Gamma Medium 5,507 5% 5,571 +64
Epsilon Medium 5,507 25% 5,905 +398
Theta Medium 5,507 75% 8,552 +3,045
Delta High 7,564 5% 7,759 +195
Zeta High 7,564 25% 9,142 +1,578
Kappa High 7,564 75% 13,870 +6,306

Unnecessary adjustment to profit-maximizing inventory recommendations

Before looking into how participants responded to risk, we wanted to know how much they would order in a case that did not mention risk. Our analysis revealed that, despite being offered the profit- maximizing inventory quantity that already took into account all available information, participants altered system-generated, optimal recommendations 33 percent of the time. We found this surprising because in theory one might expect that, absent other information, inventory planners would accept an inventory quantity recommendation that is expected to maximize profit.

Deeper exploration reveals more about these deviations. Table 2 reports the proportion of respondents choosing the exact system-recommended optimal order quantity, as well as those who chose to deviate from that recommendation by either increasing or decreasing their actual order amounts.

Table 2. Summary of adjustments from optimal (optimal, above, below) in the risk-free base case

SKU Profitability Choosing optimal Above optimal Below optimal
Gamma, Epsilon, Theta Medium 68.3% 19.4% 12.3%
Delta, Zeta, Kappa High 65.0% 15.8% 19.1%
Note: Since the disruption probability was not offered, the only difference between SKUs/cases was the profitability level.

Participants who deviated from the system-recommended amount did so with a weakly discernible pattern. Adjustments for medium-profit SKUs (Gamma, Epsilon, and Theta) frequently leaned toward increasing the order quantity rather than toward decreasing it below the optimal level. Statistical tests reveal this to be a significant difference.

Research in behavioral economics and behavioral operations offers an explanation for this pattern. Prospect Theory, a cornerstone of behavioral economic thought, argues that loss aversion is an inherent attribute of decision makers.14 Inventory management studies have found the concept of loss is credibly associated with the idea of stocking out of product and losing sales. For low- and medium-profitability products, where stocking rates tend to be lower, this “stockout aversion” leads to a greater tendency to overstock.

Getting to 9,142

The inventory quantity approach we adopted for this research is one of the simplest algorithms used in the field called “The Single Period Model.”15 In it, the inventory order quantity is calculated as a function of a known service level, average expected demand, and the standard deviation of demand (a measure of demand variability). Mathematically, optimal inventory is derived as follows:

Q = μ + Ζσ

Where Q is optimal order quantity, μ is average historical demand, σ is the standard deviation of demand and Z is an adjustment factor derived from the application of the desired service level to a normal distribution.

In all cases, average demand (μ) is 5,000 units and standard deviation (σ) is 2,000 units. For SKUs Delta, Zeta, and Kappa, the desired service level is stated to be 90 percent, which translates to a Z value of 1.2815566.16 Therefore, optimal base case inventory for these SKUs is:


In the case of Zeta, there is a 25 percent risk of a disruption that would result in the company receiving only 3,782 units; so there is a rational incentive to “order up” to account for the possibility. We calculate profit-maximizing inventory in this case through simulation using a linear optimization technique that balances the consequences of over- and under-ordering for each possible outcome. In the case of SKU Zeta, this optimal is 9,142 units.

The trend for high-profit SKUs appears to be in the opposite direction, though our statistical tests discourage that conclusion because deviations tend to be small, even if they occur more frequently than for the medium profit SKUs. The “stockout aversion” effect is potentially reduced for higher-profit products due to their higher natural stocking levels and the tendency of participants to put more effort into achieving an optimal decision given the higher stakes involved.17

Irrational response to potential disruptions in supply

The analysis of participant responses to the base case reveals a tendency toward irrational behavior even when disruption is not presented as a possibility. After all, why would someone deviate from a profit-maximizing quantity unless compelled to do so? We now turn to the question of whether this pattern of behavior extends to circumstances where disruption is an explicit possibility. Our experiment allowed us to test reactions at several different probability and profitability levels. In general, we are interested in the pattern of responses as these factors vary. First, however, we must ask a more basic question: Are managers’ reactions rational to the extent that they are even directionally correct in response to possible supply disruption?

For the purposes of our investigation, we defined a rational response as one in which inventory managers increased their order in response to the possibility of a disruption in supply (or at least did not decrease it). Recall that in the event of a disruption, participants were told that they would only receive half the amount of inventory they ordered (for example, in the case featured in figure 1, they were told that if they ordered 7,564 units and the disruption occurred they would receive only 3,782). Therefore, decreasing an order when faced with disruption would count as an irrational response.

Our findings offer a reason for leaders to be concerned. On average, across all six SKUs, responders acted irrationally 15.1 percent of the time. The proportion of respondents registering reactions in the expected direction ranges between 82.0 percent (Epsilon) and 89.3 percent (Theta) as seen in table 3. Statistical tests confirm this is a significant number and estimate that the true level of irrational response could run, in some cases, as high as 28.6 percent.18 The actual impact of such errors on company performance will likely be highly dependent on the unique attributes of the specific products and companies involved. However, estimates are possible. In our simulations, for example, the average irrational disruption response in the case of Zeta was an 18 percent decrease in order quantity (instead of an optimal 21 percent increase), leading to a 25 percent decrease in expected profitability and a 100 percent increase in lost sales relative to optimal, should the disruption occur.19

Table 3: Proportion of "rational" reactions to potential supply and demand disruptions (99% C.I.)

Variable Mean 99% Conf. interval
Gamma 86.1% 76.1% 92.2%
Delta 86.1% 76.1% 92.3%
Epsilon 82.0% 71.4% 89.2%
Zeta 82.8% 72.4% 98.9%
Theta 89.3% 80.0% 94.6%
Kappa 82.8% 72.4% 89.8%

Understanding why these managers behave irrationally presents a challenge. Our interpretation of the data is that they may have erred in the face of increased uncertainty and decision complexity. Though the complexity of the scenarios we presented did increase with the introduction of a chance of disruption, we still view the circumstances as a reasonable approximation of the reality that inventory managers face. That said, decisions of this particular type (inventory ordering and replenishment) have been accepted as complex.20 Moreover, nearly 70 years of management and administrative theory articulate managers’ limitations when it comes to complex decision making.21Researchers have demonstrated an inverse relationship between such complexity and decision quality.22 Although this type of irrational behavior does not appear to be a hallmark of inventory decision making, it certainly appears with startling frequency, affecting an estimated one in seven decisions where supply disruption is a possibility.

Even rational managers respond suboptimally to the possibility of disruption

The suboptimality of inventory managers’ decision making continues as we turn our focus to their response to different levels of disruption risk. This is true even when we restrict our analysis to those who previously responded rationally by avoiding unnecessary adjustment to the base case and who adjusted in the proper direction in response to potential supply disruptions.23 Across all the responses we examined, the failure rate when making adjustments in response to potential shortages was 99.7 percent.24

Table 4 presents the aggregated results of our participants’ performance. In summary:

  • Overreaction at low probabilities—Participants dramatically overreacted when confronted with low probability disruptions of either supply or demand. For example, when confronted with a 5 percent chance of a 50 percent cut in supply, participants’ orders for SKU “Gamma” averaged 387 percent of the optimal adjustment.
  • Underreaction at high probabilities—Participants demonstrated a strong tendency to underreact when the probability of supply disruption was high. For example, on a high-margin product (Kappa), participants’ adjustment in the face of a 75 percent probability of a 50 percent cut in supply averaged just 55 percent of the optimal adjustment.

Table 4. Summary of optimal and actual adjustments in response to supply disruption probabilities

SKU Profitability Disruption probability Optimal quantity after adjustment Optimal adjustment Actual adjustment Adjustment actual/optimal (%)
Gamma Medium 5% 5,571 64 246 387%
Delta High 5% 7,759 195 593 303%
Epsilon Medium 25% 5,905 398 914 230%
Zeta High 25% 9,142 1,578 1,847 117%
Theta Medium 75% 8,552 3,045 2,578 85%
Kappa High 75% 13,870 6,306 3,455 55%

That managers perform so poorly on this task is troubling but not surprising. Behavioral economic and operations theory predict it. In particular, studies using Prospect Theory have demonstrated a tendency for decision makers to overweight “boundary conditions” while simultaneously underweighting mid-range probabilities.25 Specifically, “an increase from 0 percent to 5 percent appears to have a larger effect than an increase from 30 percent to 35 percent, which also appears smaller than an increase from 95 percent to 100 percent.” Overweighting is particularly evident with low probability outcomes.26

We see this insight playing out in our experiments. As the probability of supply disruption increases from “impossible” to “possible,” managers respond by overreacting to risk. At the 5 percent disruption probability level, participants’ adjustments average 387 percent of optimal for our medium-profit SKU (Gamma) and 303 percent of optimal for our high-profit SKU (Delta).

Consistent with the theory, overreactions diminish as the probability of disruption increases from 5 percent to 25 percent. At this level, the overreaction relative to optimal for the medium-profit SKU (Epsilon) is still a statistically significant 230 percent. For the high-profit SKU (Zeta), the difference from optimal is insignificant (just 17 percent above optimal). At the highest level of disruption probability, underweighting of prospects is clearly in effect. Participants significantly underreact in the case of both medium- and high-profit SKUs. The medium-profit (Theta) adjustment falls 15 percent short of optimal, and the high-profit adjustment falls 45 percent short.

Differences between high-profit and medium-profit SKUs are often significant. In absolute terms, the adjustment in units for high-profit SKUs is always higher, significantly so at the 5 and 25 percent disruption levels. However, the adjustment “relative to optimal” is always lower, significantly so at the higher (25 and 75 percent) disruption probabilities. This result echoes the conservatism in adjusting high-profit quantities that first surfaced in Table 2 (related to unnecessary adjustment). The adjustment response drops off much more rapidly for the higher-profit product, leading to significantly better performance at the 25 percent disruption level but significantly worse performance at the highest level of disruption

The final decision on inventory quantity is often subject to individual judgment, and individuals make significant errors in arriving at those judgments. Leaders should consider enhanced process- and technology-based solutions to improve decision making.

So what does it all mean?

There are several implications for executives responsible for operations and inventory planning:

  • Evidence suggests that a higher-than-expected percentage of inventory planning system recommendations may be unnecessarily (and suboptimally) adjusted by inventory managers. This phenomenon affected 33 percent of the ordering decisions in our study.
  • Beyond unnecessary adjustments, there is a sufficient number of irrational adjustments (reducing orders in response to potential shortages) to warrant concern. This result affected 15.1 percent of ordering decisions.
  • Inventory managers demonstrate near-universal failure to optimally adjust to prospective disruptions in supply. The success rate was just 0.3 percent, with overreactions ranging to 387 percent in some cases.

The effect of these errors on business performance varies. In some cases, performance and profitably may not be impacted much if inventory holding costs are low and the impact of lost sales negligible. In other cases, the consequences could be significant. For example in the high probability (75 percent chance of disruption) case for the high-profit Kappa, the average response would result in a 6 percent reduction in expected profitability, and a 321 percent increase in expected lost unit sales should disruption occur.

Managers are rightly concerned about the possibility of supply chain disruption, with a particular focus on “black swan” events—low probability, high magnitude disruptions. Given this context, it is reasonable to suspect that a great many inventory managers are “adjusting” levels in order to accommodate low probabilities of disruption. To the extent that we recognize “ordering up” as a valid tactic, our research suggests that dramatic overreaction may result. At a minimum, it is likely to be worth it for operations leaders to investigate the incidence of unnecessary adjustment and overreaction to low probability disruptions within their own companies.

Where disruption is viewed as likely, executives should acknowledge that simple instructions to build buffers based on estimated probabilities and magnitudes are likely to be insufficient. Our inventory planners demonstrated a strong tendency to underreact in these cases.

Importantly, supply chain leaders should recognize that even their own judgment is suspect. Senior leaders are as likely to succumb to decision making biases as are their staffs. Executives are advised to pursue more formal approaches to understand the potential impact of both high- and low-probability disruptions.

In summary, participants in our study demonstrated poor ability to account for the possibility of disruption in their inventory ordering decisions. Factors such as the profitability of the products in question and the type and probability of the disruption appear to play a role in the adjustments they make; yet they do not lead to profit-maximizing choices.

As issues related to supply chain risk continue to garner the attention of senior executives, this study provides an empirical link to the likely impact of their risk assessments on the operational aspects of their businesses. In particular, the findings reported here:

  • Reinforce the importance of accurately assessing risk probabilities across the supply chain and sensitizing leaders to the differential impact of varying risk potentials on operational reactions (for instance, the tendency to overreact or underreact).
  • Alert executives to the possible insufficiency of the inventory management processes on which they rely. The final decision on inventory quantity is often subject to individual judgment, and individuals make significant errors in arriving at those judgments. Leaders should consider enhanced process- and technology-based solutions to improve decision making.
  • Suggest that individuals may adjust inventory simply for the sake of making an adjustment. If the company has a set policy for statistically determining optimal inventory levels, these levels should not be adjusted without good reason (for example, specific expectations not factored into the statistical model). This once again points to a possible need for process- or technology-based monitoring or interventions to avoid costly inventory errors.

Overall, the findings presented here offer a perspective for company leaders on the influence of cognitive bias and error on operational and business performance. They also provide important insights into just one of the many aspects of human bias and cognitive limitation and the possible impact of such flawed thinking on company performance.