# Manufacturer Channel Encroachment and Evolution in E-Platform Supply Chain: An Agent-Based Model
## 3 Model
### Consumers' Behaviour  
There are N consumers in the supply chain network. They obtain information on the selling price of products from different channels and choose a manufacturer to maximise utility. The consumers' state chart is shown in Figure 4. In the _Initial_ state, the consumer does not act and waits for the manufacturers to set the price. After manufacturers release their prices, consumers enter the _Getinfo_ state by randomly selecting x + y manufacturers on the e-commerce platform and the direct sales channel to obtain information on the goods' prices and subsequently calculate the utility. Here x and y denote the consumer's channel preference. In the baseline model, x = y. In the scenario where channel preferences \begin{table}
\begin{tabular}{c c} \hline \hline
**Expression** & **Explanation** \\ \hline \(P_{i}^{t}=RP_{Hi}^{t}+DP_{i}^{t}\) & Profit for manufacturer \(i\) in period \(t\) \\ \(RP_{i}^{t}=RP_{Hi}^{t}+RP_{Li}^{t}\) & Profit of the retail channel for manufacturer \(i\) in period \(t\) \\ \(RP_{Hi}^{t}=\left((1-\alpha)*RP_{Hi}^{t}-C_{H}\right)*Q_{RHi}^{t}\) & Profit of the high-quality product in the retail channel for manufacturer \\ \(RP_{Li}^{t}=\left((1-\alpha)*RP_{Li}^{t}-C_{L}\right)*Q_{RLi}^{t}\) & Profit of the low-quality product in the retail channel for manufacturer \(i\) \\ \(DP_{i}^{t}=DP_{Hi}^{t}+DP_{Li}^{t}-C\) & Profit of the direct sales channel for manufacturer \(i\) in period \(t\) \\ \(DP_{Hi}^{t}=\left(DP_{Hi}^{t}-C_{H}\right)*Q_{DHi}^{t}\) & Profit of the high-quality product in the direct sales channel for manufacturer \(i\) in period \(t\) \\ \(DP_{Li}^{t}=\left(DP_{Li}^{t}-C_{H}\right)*Q_{DLi}^{t}\) & Profit of the low-quality product in the direct sales channel for manufacturer \(i\) in period \(t\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Profit expressions. \begin{table}
\begin{tabular}{c c} \hline \hline
**Notation** & **Explanation** \\ \hline C & Channel maintenance costs per period \\ \(\alpha\) & The commission of the e-platform \\ \(RP_{mi}^{t}\) & The retail price of high/low-quality product for manufacturer \(i\) in period \(t\). (\(m=\) H, L) \\ \(DP_{mi}^{t}\) & The direct sales price of high/low-quality product for manufacturer \(i\) in period \(t\). (\(n=\) H, L) \\ \(C_{m}\) & The production costs per unit of high/low-quality product (\(m=\) H, L) \\ \(Q_{Rmi}^{t}\) & The retail sales volume of high/low-quality product for manufacturer \(i\) in period \(t\). (\(m=\) H, L) \\ \(Q_{Dmi}^{t}\) & The direct sales volume of high/low-quality product for manufacturer \(i\) in period \(t\). (\(m=\) H, L) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Notations. are considered, x > y. This will be explained in a later section. In the _Buy_ period, the consumers choose the manufacturer that will yield the highest utility and give the purchase information back to the manufacturers. In the _Waiting_ period, the consumers wait for the manufacturers to update the price using the genetic algorithm, after which they move on to the next period. The following objective function is obtained by modelling the consumers' behaviour using the Cobb-Douglas utility function, with reference to [PERSON] et al. [32]. \[ \begin{array}{l}\text{Maximize }U_{j}^{t}=\left(q_{Hi}^{t}\right)^{\alpha_{j}} \left(q_{Li}^{t}\right)^{\beta_{j}}\\ \text{s.t. }q_{Hi}^{t}p_{Hi}^{t}+q_{Li}^{t}p_{Li}^{t}\leq B_{j}\end{array}  \tag{2}\]  
The consumers' demand function is obtained using the Lagrange multiplier method as follows. \[ \begin{cases}q_{Hi}^{t*}=\frac{\alpha_{j}B_{j}}{(\alpha_{j}+\beta_{j})p_{Hi}^{ t*}}\\ q_{Li}^{t*}=\frac{\beta_{j}B_{j}}{(\alpha_{j}+\beta_{j})p_{Li}^{t}}\end{cases}  \tag{3}\]  
\(U_{j}^{t}\) is the utility of consumer \(j\) in period \(t\). \(q_{Hi}^{t}\) and \(q_{Li}^{t}\) denote the number of high-quality and low-quality products purchased from the manufacturer \(i\), respectively. \(\alpha_{j}\) and \(\beta_{j}\) denote consumer \(j\)'s quality preferences for high- and low-quality products, respectively, \(\alpha_{j}+\beta_{j}=1\).