Results Study II

Table 3.4 shows the average order trajectories and the 95% confidence intervals for each treatment. We observe a higher level of orders and wider confidence intervals in treatments with higher step in the final customer demand and longer time to build supplier capacity. During the first three periods, the system is in equilibrium given that the supplier is able to satisfy retailers’ orders and retailers are able to satisfy customers’ demand on time. Once the final customer demand increases, retailers face a backlog very quickly, causing the probability of receiving duplicated orders to increase. The presence of backlog and inflated final customer demand lead to an increase in retailers’ orders. With time, the supplier builds capacity to meet the increase in retailers’ demand, so that the supplier capacity increases and surpasses retailers’ orders. When the supplier capacity is large enough, she is able to satisfy retailers’ demand, and with backlogs at the desired levels, final customers can cancel duplicated orders.

In addition, Table 3.4 shows the average retailers’ orders and standard deviation of subjects’

decisions and Appendix 3.2 shows the p-values that evaluate the significance difference of subject behavior between experimental treatments. Results show that despite the oscillations in subjects’

decisions, the average orders in treatments with the same step in final customer demand are not significantly different. This is because subjects can backlog unsatisfied orders until enough capacity becomes available, which means that in the long term, retailers will be able to reduce their backlog and satisfy their customers’ orders.

Subjects deviate from optimal trajectories in all treatments. Results show that subjects’ ordering behavior fluctuates around the optimal trajectory in all treatments during the whole simulation horizon.

Taking into account the different treatment variables analyzed in this study, we quantify the effect of each experimental variable on retailers’ orders deviations (see Table 3.5). We compared the average deviation from the subjects’ orders with respect to the optimal trajectories. Deviations are computed as the sum of absolute values of the difference between subjects’ decisions and the optimal ordering trajectory. Initially, as shown in Table 3.4, Table 3.5 shows that there is a significant difference between subjects decisions and optimal ordering quantities for all experimental variables (all deviations are significantly different from zero).

Table 3.5. Mean comparisons among treatment variables

Variable Variable Values Deviation

p-value increase the probability of duplications from 0.1 to 0.4 (Diff=0.1-=0.4=-0.66; p-value=.06). In addition, higher step in final customer demand and a higher time to build capacity also lead to a significant increase in the deviations from the optimal trajectory (Diffstep=5-step=20=-3.91; p-value=.00; Diff=1-=4 =-2.59; p-value=.00).

Now, in order to understand the effect of these experimental variables on the bullwhip effect, the differences in subjects’ behavior should be analyzed in terms of ordering variance and the ability of the supplier to respond to retailers’ orders. Therefore, to get a better understanding of the difference in subjects’ performance, we need to compare the standard deviations of subjects’ orders among treatments. To make a clean comparison among the different treatments, we analyze the standard deviation of the difference between subjects’ orders and the optimal trajectories. In this way, we will discount the expected variance of the optimal solutions. Table 3.6 shows the standard deviations of these deviations from the optimal ordering trajectories in each treatment and Appendix 3.3 shows the p-values obtained by performing comparison tests under the hypothesis of equality of standard deviations between treatments.

Results show a switch in the deviations as we increase the time to build suppliers’ capacity. For the cases where we have short time to build capacity ( =1), an increase in the probability of

duplications lead to less variation in subjects’ orders (p-value<.01 for comparisons of T3 vs. T7 and T4 vs. T8). However, for the cases where we have long time to build capacity ( =4), there is not decrease in the variability of subjects’ orders. For T5 and T9, there is not significant difference (p-value=0.82), and for T6 and T10, there is a significant increase in orders’ variability (p-value<.01).

In addition, as we expected, an increase in the step of the final customer demand leads to a higher level of variation in subjects’ orders in three out of four cases. Therefore, more aggressive change in final customer demand lead to more unstable retailers’ orders and more instabilities for the whole supply chain.

Finally, due to the stationarity of the final customer demand, the ability of the supplier to build capacity and the full information subjects receive about the system, we were expecting a complete reduction of the bullwhip effect during the last periods of the experiment. Therefore, we extract the last 10 periods of the experiments (after 24) of our data and compared them with the first periods (before 24) to analyze the evolution of the bullwhip effect, i.e. the ordering variance, in these two time frames.

We chose the last 10 periods, because we expect orders had reached the equilibrium at that moment.

Table 3.6. Standard deviation of subjects’ orders by experimental treatment

Proportional allocation

Table 3.6 shows the estimations of the standard deviations of the deviations of subjects’ decisions before and after period 24. Results show a small reduction in the standard deviation in almost all treatments (p-values<.01), except in T7 (p-value=.36) and T9 (p-value=.13), where there is not even a significant reduction of the order variability.