Due to the complexity of decision making, it is difficult to directly obtain or effectively evaluate optimal results and various kinds of analysis. In order to specifically compare the difference between the profits of the three firms in the case with collaboration and without collaboration, we conducted a group of numerical studies to explore the change of the optimal profit between the case with collaboration and without collaboration under different conditions. Based on this, we derived some practical results to guide the behaviors of the three firms.
4.1. Influences of Price Competition Intensity and PSLS
We considered the price competition intensity and PSLS as two key factors in our study. Therefore, we analyzed their influences on the specific optimal decisions of the three firms. In the case with collaboration, we considered the influence of the price competition intensity and PSLS on the optimal decisions. In the case without collaboration, because the PSLS did not exist, we only analyzed the influence of the price competition intensity on the optimal decisions.
Figure 6 depicts how the optimal decisions change with the increase of price competition intensity in the case without collaboration. Note that the values of
and
and
and
, respectively, were very close, so they almost overlap in the figure. In
Figure 6, we find that all decision variables increase exponentially with respect to price competition intensity. It means that the price competition intensity had a great positive impact on the pricing of the three firms and the logistics service efforts of the two retailers in the case without collaboration. It is evident that an increase in price competition intensity reinforces the firms’ inclination to utilize additional advantages to attract consumers. Consequently, they exert more efforts in providing logistics services to bolster market demand, as demonstrated by firms such as Suning and JD. However, in a highly competitive market, raising one’s own product price may seem counterintuitive. This could be attributed to three reasons. Firstly, when there is fierce price competition in the market, the demand remains relatively fixed while the supply is limited. Consequently, each channel feels the pressure to compete and seeks to increase profits by raising prices. Secondly, when one channel increases its price, other channels may perceive it as a signal that the channel offers a better product or service quality or can achieve a higher profitability. In order to maintain their competitive positions, other channels may follow suit and raise their own prices to remain competitive. Thirdly, the brand effect also plays a role. In a market with intense price competition, firms may use the brand effect to differentiate their products. Raising prices can be seen as a strategy to enhance perceived product quality or uniqueness, leading consumers to associate higher prices with higher quality or added value. Other channels may adopt a similar strategy, increasing their prices to create a comparable brand image. For instance, HEYTEA employed this strategy initially.
Figure 7 and
Figure 8 depicts how the optimal decisions change with the increase of the PSLS and price competition intensity in the case with collaboration. In
Figure 7 and
Figure 8, we find that in the case with collaboration, the impact of the competition intensity on the optimal decisions is as great as that in the case without collaboration. The reasons for the changes are similar to those in the case without collaboration. However, the PSLS is linearly positively correlated with the optimal decisions, and the growth rates of the optimal decisions regarding PSLS vary.
always increases the fastest with the increase of PSLS. When
is small,
increases the slowest with the increase of PSLS. When
is larger than a certain value,
increases the slowest with the increase of PSLS. This occurs because when the price of shared logistics services (PSLS) increases, retailer 2 raises its selling price to safeguard its profit and offset the higher cost associated with PSLS. In response, retailer 1 and the manufacturer also adjust their prices to align with retailer 2’s increase. Additionally, as the PSLS rises, retailer 1 needs to exert a greater effort in providing logistics services to justify the higher charges.
4.2. Win-Win Conditions With Collaboration
In this section, we explore the win-win conditions of the manufacturer, retailer 1, and retailer 2. We focused on ascertaining the impacts of the PSLS and on the optimal decisions and profit improvements of the three firms when the retailers collaborated, since the PSLS and were vital determining factors between the retailers that did not consider external channels (the manufacturer).
We first discuss the influences of the PSLS and on the optimal decision change. Since only appeared when there was no collaboration, we did not consider that decision. At the same time, was an exogenous variable in a certain time and space determined by the external environment, while the PSLS was an endogenous variable determined by the negotiation among firms. Therefore, we investigated the influence of on the PSLS threshold in different logistics sensitivities of consumers in different regions.
Let , , , and . We differentiated the change in the optimal decisions with respect to the PSLS, and we obtained some conclusions. when , when , when , and when . There was a certain similarity between the changes in these four optimal decisions and the PSLS, so we discuss them together. It can be observed that when the PSLS exceeds the thresholds corresponding to these four optimal decisions changes, the values of all four optimal decisions changes increase as the PSLS increases, and vice versa.
Figure 9 clearly shows the impact of
on the PSLS thresholds. The upper region of each line is the range in which the profit of the relevant optimal decisions increases in the case with collaboration. In
Figure 9, we find that with the increase of the price competition intensity, the threshold of
decreases, while the threshold of
and
increases. However, the threshold of
is always higher than the thresholds of
and
. Because
always increases when
is greater than zero, the threshold line for
does not appear in the
Figure 9.
The core concern of firms is to improve their own profits, which is also the premise of collaboration. Next, we study the profit changes of the three firms after collaboration under the joint action of the PSLS and . Let , , and . We differentiated the changes in the profits with respect to PSLS, and we obtained some conclusions. when or . It indicates that as the PSLS increases, the optimal profit change for the manufacturer first increases, then decreases, and then increases again. when or . It indicates that when the price competition intensity is low, the optimal profit for retailer 1 first decreases, then increases, and then decreases again as the PSLS increases. However, when the price competition intensity is high, the optimal profit for retailer 1 first increases, then decreases, and then increases again as the PSLS increases. when or . It indicates that as the PSLS increases, the optimal profit change for the manufacturer first increases, then decreases, and then increases again.
Where ,
,
,
Figure 10 shows the range of profit improvement of the manufacturer and the retailers under the retailers’ collaboration. There are three main regions in the figure (other regions may exist, but they are small enough to be ignored). Region I represents that the profits of retailer 1 and retailer 2 have been improved with collaboration. In the retail industry, Walmart and Target are competitors. However, they also collaborate when they need to lower supply chain costs and improve efficiency. They jointly formed a procurement organization named Common Purchasing LLC to save on purchasing costs and enhance their competitiveness in the global procurement market. This collaboration reduced the bargaining power and pricing power of manufacturers, as the two retailers joined forces, potentially leading to a decrease in manufacturers’ profits. As this collaboration affects other participants in the supply chain, manufacturers may take action to safeguard their interests. Region II represents that the profits of the three firms have been improved with collaboration. In the strategic partnership between Best Buy and Target, they optimized their supply chain by jointly procuring, sharing logistics, and sharing data, resulting in increased profits for both firms. Manufacturers also benefited from a higher volume of wholesale sales and spillover sharing of data. Region III represents that the profits of the manufacturers and retailer 2 have been improved with collaboration. In the collaboration between Walgreens and Rite Aid, Walgreens provided a logistics network while Rite Aid offered lower procurement costs. After the collaboration, the manufacturers obtained higher profits from larger wholesale sales, while Rite Aid gained cost advantages through shared logistics and procurement, resulting in increased profits. However, due to the higher logistics costs borne by Walgreens and the cost advantage gained by Rite Aid from lower procurement prices, Walgreens’ profits suffered losses. As can be seen from
Figure 10, the Pareto improvement region exists, and the range is quite large. In addition, the PSLSs are generally not so expensive as to reach hundreds of CNY. Therefore, region II is rarely implemented. We can conclude from the above information, in a nutshell, when the retailers collaborate, the three firms have a great chance of achieving win-win results.
4.4. Extensions on the Partial Collaboration
We discussed the scenarios of full collaboration and noncollaboration. However, achieving full collaboration between the retailers is an ideal scenario, yet it is often challenging to attain in practice. Therefore, we propose the concept of partial collaboration to better inform real-world decision-making. The aim of this subsection is to determine the optimal level of collaboration among firms that maximizes their benefits. By doing so, we seek to provide recommendations on how firms should strategically collaborate with other firms in their supply chain to maximize their benefits. Partial collaboration means that some products of the firms adopt the logistics and procurement mode before the collaboration, while some products adopt the logistics and procurement mode after the collaboration. Based on the above description, we introduce the collaboration coefficient
(
) to represent the collaboration level between retailer 1 and retailer 2. For the two firms,
represents the proportion of products adopting the collaborative mode, and
represents the proportion of products not adopting the collaborative mode. Therefore, the market demands of channels are as follows:
The demand functions of the manufacturer and retailer 1, as in (
13) and (14), are the same as in (
1) and (5), respectively. The demand function of retailer 2, as in (15), consists of five components. The first three components are consistent with those in (3). The fourth component is the increased demand for self-built logistics services to transport products which adopt the noncollaborative mode. The fifth component is the increased demand for JD’s logistics services, which provides products that adopt the collaborative mode.
The profits of the channel members can be expressed as follows:
By observing Equations (
16)–(
18), in the case of a partial collaboration, the profit function of each firm is equal to the profit function in the case with collaboration multiplied by the collaboration coefficient plus the profit function in the case without collaboration multiplied by the noncollaboration coefficient
.
Next, we focus on the effect of the collaboration coefficient on profit changes. Based on the previous discussion, it is known that collaboration is often achieved when all three firms can benefit from it and achieve a profit increase. Therefore, in our subsequent analysis, we followed this basic condition for achieving collaboration and focused on the impact of the level of collaboration on the profits of the three firms. We set 10, , so all three firms could be Pareto improved in the case with collaboration. Thus, it was easy to find out how the level of collaboration affected the change in profits.
In order to simplify the calculation process, we directly put the parameter assignment result into the profit function and obtained the optimal decisions.
Theorem 4. In the case with partial collaboration, the optimal decisions and equilibrium values are summarized in Table 6. Figure 12 depicts the influence of the collaboration coefficient on the profits of the three firms. In
Figure 12, we can find that with the increase of the collaboration coefficient, the profits of all three firms increase. It indicates that the manufacturers and retailers are more inclined to achieve a complete collaboration rather than a partial collaboration between the retailers when the collaboration can make the three firms achieve a Pareto improvement.
From the perspective of profit growth, with the increase in the cooperation coefficient, retailer 2 experiences the largest profit improvement as the collaboration deepens, while the increase in profit for the manufacturer is not as significant. Therefore, in practical operations, we suggest that retailer 2 takes more proactive actions to drive the formation and deepening of the collaboration since minor profit improvements may not generate strong desires for collaboration from other firms.