multi-product and multi-period mathematical model for sustainable supplier selection and development

Supply chain management has become a significant challenge for decision-makers in today's competitive and dynamic economic environment. The presence of various suppliers with different quality levels, high production and transportation costs, and customer expectations regarding product quality have led to the entry of suppliers that meet acceptable criteria. Moreover, the modern view of the supply chain has shifted from traditional models toward sustainable supply chains, emphasizing environmental, social, and economic standards. Supplier development represents a collaboration between manufacturers and suppliers. After manufacturers assess their suppliers based on development-related criteria, it is essential to implement and execute development programs for the suppliers to remain on the manufacturer's list. Given existing constraints, it is not economically feasible for manufacturers to select a large number of suppliers. Therefore, the issues of supplier selection and development become crucial. Identifying the factors influencing supplier selection and development under these conditions is highly important. Moreover, the entry of new suppliers into the supply chain can create a competitive environment where an existing supplier can only remain competitive if it improves its performance in the key criteria set by the decision-makers.

This paper presents a two-stage mathematical model for supplier selection and development, and it evaluates the performance of this model using a case study from Zamiad Company in the Iranian automotive industry. In the first stage, the model assesses the eligibility of existing suppliers to remain in the competition, excluding those who fail to meet the minimum required criteria. In the second stage, the selected suppliers are identified, and production volumes for each supplier in each production period are planned. The model also allows for production scheduling, where suppliers can back-order their production. In addition to production planning, the paper considers the multi-period and multi-product nature of the environment. The multi-period feature enables suppliers to meet demand through backordering, which reduces the overall costs of the supply chain. Furthermore, this feature allows existing suppliers to improve their performance in selected criteria over different production periods. The multi-product aspect ensures that all suppliers have the opportunity to compete for supplying at least one product based on their capabilities, giving manufacturers more freedom in supplier selection. If a supplier can improve its performance in the accepted criteria for a specific product, it can be considered as a candidate for supplying that product.

The model is formulated in a sustainable supply chain framework with performance criteria defined as economic, environmental, and social aspects. After linearizing the model, a single-objective model is obtained by using the weighted sum method. The model is solved using the GAMS optimization software. The results show that the multi-period feature adds two key benefits to the model: firstly, it allows suppliers to back-order production, reducing overall supply chain costs; secondly, it provides an opportunity for existing suppliers to develop over time in various performance criteria. Additionally, the multi-product feature enables all suppliers to have the chance to compete to supply at least one product, offering more flexibility in the supplier selection process. According to the results, development costs have the most significant impact on the objective function compared to other model parameters, emphasizing the importance for manufacturers to define clear and fundamental development criteria for suppliers to enhance their capabilities in these areas.