Upstream Supply Flexibility
4.3 Experimental Design
4.3.1 Implementation and Parameterization: All Studies
In all studies demand is uniformly distributed with support on [100;200]. The price and cost parameters are p = 12 and w = 6. Under these circumstances the expected profit maximizing newsvendor order q∗RN equals mean demand µ = 150. This effectively controls for the anchoring bias which describes the empirically observed tendency to order closer to mean demand relative to the optimal order quantity.
Our experiment follows a 2x2x2 mixed design. There are two between-subject variables, Free Order vs. Fixed Order (discussed in Section 4.3.2), and
Continuous Demand vs. Discrete Demand.11 Additionally, there is one within-subject variable, Operations Frame vs. Neutral Frame, discussed in Section 4.3.3. Figure 4.2 gives an overview of the different treatment variables (detailed instructions are provided in Appendix B.2).
Figure 4.2: Roadmap to experiments
4.3.2 Elicitation Procedure with Free or Fixed Order
The main decision throughout the experiment concerned choices between or-dering NOW and oror-dering LATER. The pivotal quantity to test our research hypotheses is an estimate of each subject’s willingness-to-pay for full supply flexibility. We elicit this indifference mark-up, ˆδ, on the regular wholesale price w, by use of an adaptive choice-based method (see Appendix A.2). Figure 4.3 shows snapshots of a typical decision screen presented to the participants in the course of the experiment.
I order „NOW“ I am indifferent I order „LATER“
Choice-Based Adaption
I order „NOW“ I am indifferent I order „LATER“
Profit-maximizing quantity
Choice-Based Adaption (b) Fixed Order
Figure 4.3: Screenshots (Operations Frame)
11Note that, technically, we do not consider a continuous demand distribution since we allow only integer values. In our terminology, Continuous Demand encompasses all integer quantities on the support of the demand distribution, whereas Discrete Demand considers only a subset of these.
In both between-subject treatments participants chose either to order NOW or to order LATER in each round12, with the unit wholesale price of the former option being unchanged at 6 throughout the experiment.
In the Free Order treatment (Figure 4.3(a)), the order decision under the NOW option is complex, but under the LATER option it is trivial because ordering q = D is transparently the best course of action. If decision-makers are averse to the cognitive effort required in the NOW option, their value for the LATER option should increase. To control for this asymmetry between the two options in the required cognitive effort, we conducted Fixed Order treat-ments in which the newsvendor order was fixed at the profit-maximal quantity q∗RN = 150 (Figure 4.3(b)). Of course, if q∗6= 150, the value of postponement should be higher under the Fixed Order than under the Free Order (Theorem 7 and Hypothesis 4.3). For the Free Order treatment, when choosing NOW, the participant had to enter an order quantity, and then press a button to randomly generate the quantity demanded. When choosing LATER, the participant had to press a button to randomly generate the quantity demanded, and then enters an order quantity. For the Fixed Order treatment, when choosing NOW the participant’s order was automatically set to 150 units, which coincides with the expected profit maximizing order.
After order quantity and demand had materialized, the computer screen displayed revenue, costs and the resulting profit for the round. Based on choices in previous rounds, the wholesale price for the option LATER, w + δ, was adjusted by the computer by use of a bi-section algorithm. If, at a given mark-up δ, a subject indicated a preference for ordering NOW (LATER), the mark-mark-up was increased (decreased) until the subject indicated indifference. We present the details of the algorithm in Appendix A.
4.3.3 Control for Preferences towards Risky Prospects
Apart from an empirical estimate of the indifference mark-up ˆδ, testing our re-search hypotheses requires a normative benchmark δ∗ according to (4.2), which is easy to compute for a risk neutral profit maximizer, but generally depends on the unobservable utility function u (). This makes it cumbersome to test Hypothesis 4.2 directly. In order to control for risk attitude as a potential driver of willingness-to-pay for flexibility, we introduced a Neutral Frame to our experiment, along the line of reasoning in Chapter 3.
Note that the newsvendor problem is naturally described by a context-specific set of prices, costs, and quantities. The implicit assumption the preva-lent supply chain models is that a decision maker, in order to make an optimal decision, is both willing and able to construct profit distributions associated with these parameters. Likewise, the time notion of ordering NOW or LATER in the Operations Frame is essentially immaterial from a decision-theoretic perspective because both options simply represent distributions of final wealth. The Neutral Frame displays these profit distributions directly (see Figure 4.4(b) where lot-tery ”A” is technically equivalent to ordering NOW in the Operations Frame) and thus provides us with an estimate for a subject’s valuation of flexibility, δˆN F, without this valuation being biased by any of the contextual factors as
12In later periods they could also indicate indifference between NOW and LATER. In this case the computer randomly picked one of the two options to be played.
in the Operations Frame. Since the two different frames offer identical, but differently framed, profit distributions, they entail a simple decision theoretic prediction which holds for every theory of choice under uncertainty working on the distributions of final wealth, captured in the following auxiliary hypothesis to test Hypothesis 4.2.
HYPOTHESIS 4.2’. Choices and the implied indifference markups ˆδOF (Oper-ations Frame) and ˆδN F (Neutral Frame) should be identical.
Using a within-subject design allows us to construct for each subject an individ-ual over-/undervaluation score δˆδˆOFN F. Each subject performed, on two occasions (separated by a week), both the Operations Frame and the Neutral Frame, in that order. The Neutral Frame was offered only in its Fixed Order version, depicted in Figure 4.4(b), since this version entails choice between only two risky prospects (one newsvendor order quantity and one postponement option), whereas the corresponding Free Order treatment would entail the cumbersome simultaneous display of 102 profit distributions (101 possible newsvendor order quantities plus one postponement option).
I order „NOW“ I am indifferent I order „LATER“
Equivalent to ordering
(a) Operations frame
I choose „A“ I am indifferent I choose „B“
0
Equivalent to ordering LATER Equivalent to ordering NOW
(b) Neutral frame
Figure 4.4: Screenshots (Fixed Order quantity)
4.3.4 Subject Payment
We recruited 79 subjects through a computerized system at the University of Mannheim.13 All sessions were conducted at the laboratory of the Collaborative Research Center 504. Participants read written instructions and were briefed orally. To ensure that participants understood the logic of the experiment, each participant had to answer a number of problem-related quiz questions on the computer screen before being allowed to start the actual experiment. Data from 4 participants consistently violating dominance by choosing to order NOW even when the option LATER came at no additional costs, were dropped.
Each subject participated in two sessions, a week apart, Operations Frame in week 1 and Neutral Frame in week 2. We employed the random lottery
13Participants were students at the University of Mannheim, over 75% German, and most others from other European countries, 40% were female and 60% male, 44% undergraduates and 56% graduate students. The average age of the participants was 24, and the vast majority were majoring in business, economics, or social sciences.
procedure to determine subjects’ payoffs on each of the two occasions. After participants completed the indifference price elicitation part of the study, a com-puter randomly picked two rounds for payment. Additionally, subjects earned a fixed amount of 2e for completing a post-experiment questionnaire in week 1.
Subjects were paid after completion of both sessions (using a conversion factor of 0.0025 from laboratory tokens to e). The average payoff was 14.65e with a standard deviation of 2.85e.