4.2.2. Analysis of Experiments Results
(1) Analysis of the auctions results under risk aversion
Under risk aversion of 4PL integrator, in first-stage, FSSA has the same score for each 3PL supplier, and in the second stage, EA starts with the starting score 0.1. The second-stage auction process is shown in
Table 9.
(2) Analysis of the auctions results under risk neutral
Under risk neutrality of 4PL integrator, in first stage, 3PL supplier 10 has a maximum score 5 × 10
−4, and in the second stage the EA starts with 0.1. The second-stage auction process is shown in
Table 10. Summary of the auction results under different risk attitude is shown in
Table 11.
In
Table 11, the 3PL supplier with the highest score under the current risk attitude is selected by the two-stage auction. The cost score of 3PL supplier 7 is the highest when the 4PL integrator is risk averse, this result is same as in
Table 3. The cost score of 3PL supplier 10 is the highest when the 4PL integrator is risk neutral, this result is same as in
Table 4. So, the effectiveness of the two-stage auction is verified.
When the 4PL integrator is risk averse, the highest score of 3PL supplier under FSSA is 0 (see
Table 6), and the highest score of 3PL supplier under two-stage auction is 0.7651. When the 4PL integrator is risk neutral, the highest score of the 3PL supplier under FSSA is 5 × 10
−4 (see
Table 8), and the highest score of the 3PL supplier under the two-stage auction is 0.7717. Hence, the two-stage auction obtained a higher score than the simple FSSA, that is, the 4PL integrator gained higher utility under two-stage auction.
Comparing the two-stage auction with EA, the starting score in the EA is the score corresponding to the reserved point published by the 4PL integrator. When the delivery date reservation value is 230 and the price reservation value is 390, the initial score under risk aversion can be obtained according to Equation (1), which is −2.045. According to Equation (2), the initial score under risk neutral is −1. The two-stage auction starts at 0.1, the 4PL integrator can design the starting score of the second stage EA more accurately because of the FSSA in the first stage, so the auction round is reduced, and the 4PL integrator obtains higher auction efficiency. The two-stage auction combines the advantages of the two auction methods, 4PL integrator can choose the 3PL supplier by first performing the FSSA and then the EA.
Table 11 also shows that the utility of 4PL integrator under risk neutral is 0.7717, which is higher than the utility of 4PL integrator under risk averse, which is 0.7651. Because when 4PL integrator auction is under risk aversion, for the same profit and loss value, 4PL integrator will psychologically magnify the negative utility of losses, thus concealing the positive utility brought by benefits. 4PL integrator are not psychologically allowed to have expected losses, that is, requirements
. Although 4PL integrator did not feel the loss, but in fact, they ignored part of the benefits, 4PL integrator shows irrational behavior. Therefore, 4PL integrator maintains a risk neutral rational attitude in auction, which can bring higher utility to itself.
4.2.3. Analysis on Incomplete Attribute Weight Information
This section considers a situation of incomplete information in the auction process, specifically, the attribute weights in the 4PL integrator’s scoring function are considered. The attribute weight truly reflects the preference of the 4PL integrator. If the information is not fully disclosed, the core information of the customer can be effectively protected from the leak, effectively preventing the false suppliers who are not satisfied with the business from exploring the business information in the name of auction cooperation. Moreover, the degree of disclosure of attribute weight information directly affects the bids of 3PL suppliers and thus affects their score [
40]. Therefore, this paper studies the incomplete disclosure of attribute weight information. Different from the complete information auction, that the attribute weight information is fully announced. Under the incomplete information situation, the attribute weight of the 4PL integrator is reserved for the 3PL supplier, which is released in the form of interval. At the same time, the risk aversion of the 4PL integrator is still considered.
Based on surveys of enterprises and literatures [
40], the initial data about the delivery date weight and price weight are designed. Usually, the weights are value of points under the situation of complete information. However, the auction is under the situation of incomplete information, the values of the weights are not determined values or are uncertain values. Therefore, this section applies a form of interval to describe this kind of uncertainty, and then applies Formulas (2)–(4) to calculate the values of the delivery date weight and price weight, respectively. According to the published attribute weight range of 4PL integrator from small to large, three specific cases are designed to test the influence of the incomplete information on the auction results. These specific cases are called Case I, II, III, respectively.
(1) Case I
Assume that the 4PL integrator publishes the delivery date weight and price weight in the range
,
. Then the 4PL integrator announces a large delivery date weight and price weight
,
, then the 4PL integrator announces a small delivery date weight and price weight
,
, as shown in
Figure 2.
Then according to Formulas (2)–(4), the combination of these four intervals can generate the point weight as , .
(2) Case II
Assume that the 4PL Integrator publishes the delivery date weight and price weight in the range
. Then the 4PL integrator announces a large delivery date weight and price weight
, then the 4PL integrator announces a small delivery date weight and price weight
, which is shown in
Figure 3.
Then according to Formulas (2)–(4), the combination of these four intervals can generate the point weight , .
(3) Case III
Assume that the 4PL integrator publishes the delivery date weight and price weight in the range
,
. Then the 4PL integrator announces a large delivery date weight and price weight
,
, then the 4PL integrator announces a small delivery date weight and price weight
, which is shown in
Figure 4.
Then according to Formulas (2)–(4), the combination of these four intervals will estimate the point weight , .
For the above estimated point weights, the two-stage auction is implemented. The results of calculation are divided into two parts: (1) The auction results under risk aversion; (2) the auction results under risk neutrality.
4.2.4. Comparative Analysis
The experimental results for the three cases are compared and summarized in
Table 12. It can be seen from
Table 12 that the auction winner is the 3PL supplier with the highest cost score under the current 4PL integrator’s risk attitude. The 3PL supplier 7 is the winner under risk aversion of 4PL integrator, which also can be found in
Table 3. The 3PL supplier 10 is the winner under risk neutral of 4PL integrator, which also can be seen in
Table 4.
The transaction price and the delivery date of the 3PL supplier winner are summarized in
Table 13.
Formula (6) is used to calculate the utility of the 4PL integrator under risk aversion, and
Table 14 is obtained. The results in
Table 14 are also shown in
Figure 5.
The highest utility of 4PL integrator for risk neutral auctions is obtained at , .
Formula (6) is used to calculate the utility of the transaction result in the risk-neutral 4PL integrator, and
Table 15 is obtained. The results in
Table 15 are shown in
Figure 6.
Figure 5 shows that the highest utility of 4PL integrator under risk neutral is obtained at
. The highest utility of 4PL integrator for risk neutral auctions is obtained at
.
Figure 6 shows that the highest utility of 4PL integrator under risk neutral is obtained at
,
. So, the highest utility of 4PL integrator under risk aversion and risk neutrality is not at complete information auctions, i.e., at
. So 4PL integrator will not get higher utility under complete information auctions. Therefore, the 4PL integrator can reserve the auction information appropriately before the auction.