Risk aversion and implicit shortage cost explain the Anchoring and Insufficient Adjustment bias in human newsvendors
Introduction
Laboratory experiments using human newsvendors ([16] first, followed by [1], [2], [3], [10], [6], [11]) observed that they ordered less (more) than the optimal quantity in the high (low) profit margin condition. [16] showed that this bias cannot be explained exclusively by risk aversion, risk seeking, loss aversion, waste aversion, stockout aversion, or underestimation of opportunity costs. They suggested that prospect theory might be able to account for this order pattern, but this was recently [12] shown to not be the case. [16] also suggested that ex-post inventory preference could explain this behavior, but acknowledged that it was not able to account for the observed asymmetry in the low margin and high margin settings. This observed asymmetry also cannot be explained by newsvendor overconfidence as manifested by underestimating the variability of demand, as analyzed by [14]. Finally, [16] mentioned in passing that a combination of these preferences, such as risk aversion and stockout aversion, might be able to explain this bias, but did not elaborate on how such a combination could be constructed. We show that risk aversion coupled with shortage cost (sometimes referred to as loss of goodwill, as in [11]) is the only pair of causes that can comprehensively and reasonably characterize the AIA bias. After analytically establishing this result, we fit the model to data from [16] and construct the specific forms of the risk aversion function and the shortage cost value that result in their findings.
Section snippets
The newsvendor decision
The basic parameters of a typical newsvendor decision are the demand distribution (), selling price (), and purchase cost (). While the demand can be from any probability distribution, for ease of analysis and consistency with most of the existing newsvendor experiments, we assume here that the demand follows a uniform distribution. We also consider demand to be continuously distributed, in contrast to much of the existing behavioral literature that assumes it to be discretely
Proposed causes for the human bias
The following seven causes are commonly considered when explaining the AIA behavior in human newsvendor decisions.
- 1.
Risk Aversion: Utility is a non-decreasing, concave function of profit, and the newsvendor’s objective is to maximize expected utility. [5] showed that inclusion of risk aversion results in a lower order quantity for all settings of the problem parameters.
- 2.
Waste Aversion (): Any leftover inventory must be disposed of at an additional cost of , implying that the salvage
Newsvendor with risk aversion and an implicit shortage cost
We define the non-decreasing function as the utility that a decision maker receives after realizing profit . The objective function is then transformed into one of expected utility, . When the utility function is concave, it captures risk aversion. The shortage cost () quantifies the aversion to stockouts. [7] demonstrated that human subjects consider loss of goodwill even when it is not explicitly included in the task description. Inclusion of this shortage cost
Explaining AIA observations
We say that AIA exists when the following conditions are satisfied: The smallest possible penalty cost, , that explains can be computed as . Further, we compute the following quantities: In constructing
Application to Schweitzer and Cachon data
We apply the above-mentioned approach to explain the results observed in [16]. Recall that in our continuous adaptation of their setting, , , , , , , and . To achieve these order quantities, the shortage cost must satisfy: Fixing , we compute the six needed profit levels as follows:
Robustness of our result
In this section, we evaluate the robustness of our results when (i) Proposition 4 is satisfied but Proposition 6 is violated; (ii) Proposition 4 is not satisfied; and (iii) demand is normally distributed.
Conclusion
The well-documented Anchoring and Insufficient Adjustment bias in newsvendor decision making is consistent only with the combination of implicit risk aversion and shortage aversion. In order to mitigate this bias, managers should educate their decision makers to explicitly account for these aversions.
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