Possibilistic inventory and supplier selection model for an assembly system

In this paper, the problem of inventory lot-sizing and supplier selection for an assembly system is considered, where the supplier available capacities are assumed as ambiguous dynamic parameters. In this scenario, which is a frequent case in large assembly-based factories such as automobile manufacturers, the final product is assembled from multiple components with different conversion factors, which can be sourced from multi-capacitated suppliers through the multi-period horizon of imprecise demand. Due to high shut-down costs of assembly lines, it is assumed that production never stops even though some components may not be available. Therefore, the unfinished products are transferred to a buffer zone and preserved there until the lacking components become available. In this study, a possibilistic mixed integer mathematical model, with fuzzy objective function and soft constraints, is developed to determine which component in what quantities, from which suppliers, and in which periods should be ordered. The model, inspired by the real case of the Iran Khodro Car Company, aims to maximize the profit while keeping a high customer service level by avoiding shortages. This model also considers the ambiguity of dynamic parameters such as demand, suppliers’ available capacities, prices, and holding and shortage costs. To solve the problem, the possibilistic model is first converted into an auxiliary crisp multi-objective model. Through an interactive fuzzy approach, the suggested multi-objective problem is then transformed into an equivalent single-objective model. Finally, a particle swarm optimization is proposed to achieve the overall satisfactory compromise solution. A numerical sample is used to validate the proposed model.