Upstream Supply Flexibility
4.4 Study 1: Base Case with Continuous De- De-mandDe-mand
Recall that customer demand in this study is uniformly distributed between 100 and 200 units. For a risk-neutral profit maximizer this would imply a theoretical indifference mark-up δRN∗ = 1.01 (from Equation 4.2).
4.4.1 Results
Figure 4.5 plots the average valuation of each subject in the Neutral frame (x-axis) and the Operations Frame (y-(x-axis), in the Free Order and the Fixed Order treatments. Table 4.1 provides the corresponding sample averages (standard deviations in parentheses) and the results from hypothesis tests. In Figure 4.5, Hypothesis 4.1 implies ˆδ = δ∗RN= 1.01 and thus data along the solid horizontal line (for Operations Frame) and along the solid vertical line (for Neutral frame).
Hypothesis 4.2’postulates no differences under the two frames and thus implies data along the 45 line. Hypothesis 4.3 implies the average willingness-to-pay in the Fixed Order treatment above that in the Free Order treatment.
What we observe in Figure 4.5 is data along the solid vertical line, but gen-erally above the solid horizontal line. Hypotheses tests (Table 4.1) confirm that the average willingness-to-pay is above 1.01 in the Operations Frame treatments (both Free and Fixed Order conditions). The average willingness-to-pay is not significantly different from 1.01 in the Neutral Frame treatments. Thus, we can reject Hypothesis 4.1 (Risk neutrality) for the Operations Frame, but not for the Neutral Frame.
Table 4.1: Summary of average willingness-to-pay estimates (standard devia-tions in parantheses) and hypothesis tests
Figure 4.5: Distribution of valuations {δiN F, δOFi } (Note: Neutral Frame is Fixed Order in both treatments)
Overvaluing flexibility in the Operations Frame does not necessarily indicate a biased perception of the value of flexibility per se. We recognize that a subject might be consciously willing to pay more than warranted by plain expected profit considerations. E.g., intrinsic (and unobservable) attitudes towards risk could potentially explain what appears to be overvaluation of flexibility. However, results of the Neutral Frame control treatment indicate that this is not the case. When presented with only the distributions of profits, subjects’ implicit valuation of flexibility is amazingly close to the risk-neutral prediction of δ∗RN= 1.01, but significantly lower than in the Operations Frame.
The data in Figure 4.5 are located mostly above the 45 line. The relative overvaluation of flexibility in the Operations Frame with respect to the Neutral Frame benchmark, δˆδˆN FOF, amounts to 47% in the Free Order treatment and 79% in the Fixed Order treatment. By comparing average willingness-to-pay for flexibility within subjects, in the Operations Frame (explicit revelation of δˆ∗) and the Neutral Frame (which explicitly offers profit distributions based on ˆδ∗), we are in a position to rule out intrinsic preferences towards stochastic distribution of profits as a reason for overvaluation of flexibility. We therefore reject Hypothesis 4.2.
We now test the validity of Hypothesis 4.3, which states that the willingness-to-pay for flexibility in Fixed Order should not be lower than in Free Order. Re-call that the intuitive reasoning behind this hypothesis is that being constrained to a quantity that is not the most preferred one makes the flexible option of ordering LATER more valuable, resulting in an increased willingness-to-pay.
Figure 4.5 and Table 4.1 show that subjects indeed pay more, on average, in
the Fixed Order than in the Free Order treatment, consistent with Hypothesis 4.3, although the differences are not statistically significant.
Lastly, we look at the order quantities participants choose with the NOW option. Theoretically, the parameters of our setting controlled for the anchoring-on-mean-demand bias reported in previous studies, since the expected-profit maximizing quantity under NOW equals mean demand. In the Free Order treatment the average order quantity is 144 when participants choose NOW, which is slightly below the risk-neutral optimum q∗RN = 150 (Wilcoxon, p = 0.051).
4.4.2 Discussion
In the Operations Frame and Free Order condition participants are willing to pay wholesale prices for the LATER option that are on average 52% above the risk-neutral benchmark, and this overpayment is even higher, at 84%, in the Fixed Order condition. These overpayments translate to leaving 10% of expected profit on the table in the Free Order condition, and 16% in the Fixed Order condition. In contrast, we observe no overpayment for the equivalent option in the Neutral Frame. Why are participants willing to pay different amounts for flexibility in the Operations and Neutral Frames? We consider two potential explanations.
The first explanation relates to the fact that in the Neutral Frame partici-pants face a simpler problem than they do in the Operations Frame, because in the Neutral Frame they make decisions about the profit distributions from the two options presented to them directly. In the Operations Frame, however, they have to construct these profit distributions from problem parameters first. We term this the cognitive effort hypothesis.
While the latter can explain differences between the Operations and the Neutral Frame, there is no a priori reason to assume that limited capabilities or willingness to construct the correct prospects would bias the valuation of flexibility in any specific direction. Overvaluation is putting too much weight on the positive aspect of increased flexibility (namely a better match between supply and demand) while undervaluation is putting too much weight on the negative aspect (namely paying a higher per-unit price). Shedding more light on this issue, our second explanation for the results implies psychological aspects of the LATER option increasing its value, beyond the expected profit. One such aspect may have to do with the fact that the LATER option allows participants to avoid any ex post decision regret from failing to match supply and demand.
The following, admittedly highly simplistic model, captures this logic. Suppose participants experience some disutility from ex-post inventory error, f (|q−D|) (Schweitzer and Cachon 2000). Assuming f0(·) > 0 and f (0) = 0, this disutility is meaningless when ordering LATER (where q = D) but decreases the expected utility from ordering NOW,
UN OW=E [u (πN OW(q)) −f (|q−D|)] (4.3)
The willingness-to-pay for full flexibility then increases relative to a newsvendor that does not anticipate future regret from an order decision.
Theorem 8. The willingness-to-pay for flexibility, δ∗, is higher if the decision maker experiences and anticipates disutility from the ex-post inventory error,
|q − D|.
Even though anticipated regret is minimized at the profit maximal order quantity (because regret is minimized at mean demand which is qRN∗ , given our parameters, see Schweitzer and Cachon 2000), it may well be that the impact of decision regret is even stronger in our setting than in previous newsvendor ex-periments without a decision postponement option. This is because the ex-ante presence of such an option may render regret from ex-post inventory error from a newsvendor order decision very salient. When foregoing the option to order LATER a decision maker is more likely to engage in self-recrimination, which is a strong antecedent variable for decision regret (Sugden 1985). Anticipated de-cision regret becomes a valid behavioral explanation for apparent overvaluation of flexibility since the Operations Frame provides the decision maker with an appropriate frame-of-mind for regret behavior. Clearly, such a frame-of-mind is non-existent in the Neutral Frame. This implies a lower valuation of flexibility since regret behavior captured in (4.3) is meaningless under this frame. We term this the framing and regret hypothesis.
The framing, regret, and cognitive effort explanations offered above are not mutually exclusive. We designed Study 2 to measure whether overvaluing flexi-bility in the Operations Frame persists in a cognitively less challenging setting.
To do this, we simplify the problem in the Operations Frame by allowing cus-tomer demand to take only three values: 100, 150 and 200. If we continue to observe overvaluing flexibility in this simpler setting, it will provide additional evidence that behavioral factors, such as the desire to avoid anticipated decision regret, are causing flexibility to be overvalued.