# Collaborative Planning in Non-Hierarchical Networks--An Intelligent Negotiation-Based Framework
## 4 Application Case--Analysis and Results
### Application Case Description  
In order to test and validate the intelligent collaborative planning framework proposal, an application case based on the footwear sector industry was constructed. This application case scenario considered a three-stage production process. For each one of the production stages, the partner search module identified four potential partners with the relevant KPIs presented in the Table 2. The list of KPIs presented in the Table 2 is indicative and defined according to the characteristics of the business opportunity, the potential customer requirements, and the agreement of the partners invited to enter the negotiation process. In reality, the negotiation platform has more than 100 assessment KPIs that cover aspects such as collaboration degree, technical expertise, product quality, delivery, cost, flexibility, and environmental practices. Initially, the broker and the selected partners collaboratively define the criteria that will support subsequent decisions in the process, i.e., the multicriteria assessment of the plan proposals. In the present application case, the collaboration degree presents the partners' historical assessment from other partners that were involved in previous projects. The quality certification is a binary assessment (1--yes; 0--no) that establishes if the partner has a quality certification desirable for that particular product. The third criterion chosen for the application case was cost. In this case, the cost is a function of the partner's capacity model (refer to Section 4.2) and the corresponding time period for the quotation request in the negotiation process. Table 3 presents the selected criteria and the corresponding weight. Based on the weight values assigned to each evaluation criterion, the minimization process is carried out using the objective function defined in Equation (9), while ensuring the delivery deadline as a hard constraint. For each evaluation criteria, the normalized objective function is determined according to Equation (8). However, interpreting the values derived from the normalized objective function for each optimal solution, during every iteration of the negotiation process, can pose understanding problems for the various partners involved. To facilitate the multicriteria analysis and support decision making, a normalization criterion is utilized during the serialization process to assess all optimized alternative collaborative plans. In this case, linear normalization was chosen, utilizing the following transformations for cost \(C(x)\) and benefit \(B(x)\) to handle minimization and maximization criteria, respectively (see Equations (10) and (11)):  
\[C(x)=\frac{\frac{1}{x}}{\frac{1}{m_{\text{ND}}}}=\frac{m_{\text{ND}}}{x}, \tag{10}\]  
\[B(x)=\frac{x}{M_{\text{ND}}}, \tag{11}\]  
where \(m_{\text{ND}}\) and \(M_{\text{ND}}\) are the minimum and maximum objective function values of nondominated solutions found in the multi-objective optimization process. A weighted value function \(V(x)\) is computed to score all nondominated solutions found in each iteration:  
\[V(x)=W_{1}C(f_{1}(x))+W_{2}B(f_{2}(x))+W_{3}B(f_{3}(x)), \tag{12}\]  
where \(W_{1}\), \(W_{2}\), and \(W_{3}\) are the weights established with the partners; values \(f_{1}(x),f_{2}(x)\), and \(f_{3}(x)\) correspond to \(f_{s}(x)\) in Equation (8). The assessment of solutions according to the value function results in values in the interval between 0% and 100%, which characterizes the score of each one of the alternative plans. The highest value corresponds to the best collaborative plan. Table 4 presents an evaluation of five alternative plans, considering the agreed criteria, which consider the cost, collaboration degree, and quality certification. The data presented in Table 4 are based on a test case with the participation of partners from the project. In