Utilizing Multi-vehicle Traveling Purchaser Problem for Multiple-Supplier Selection and Multi-period Lot-Sizing in a Fuzzy Demand Environment

The decision of whether to collaborate with one or multiple sources is a crucial challenge in the supply chain. This decision involves considering various criteria, including price and transportation cost. The traveling purchaser problem (TPP) is an extension of the well-known traveling salesman problem (TSP). While the TSP focuses on product distribution, the TPP addresses the supply of products and raw materials. Previous models did not incorporate vehicle routing in solving the multi-period economic lot-sizing problem. In contrast, this paper presents a novel fuzzy mixed-integer linear programming model for determining the optimal multi-period ordering policy when suppliers offer the lowest price. The model integrates the development of the TPP and the multi-period economic lot-sizing problem. In this model, we simultaneously consider all purchasing, transportation, and inventory holding costs, while also determining the optimal vehicle routing. The model takes into account factors such as the percentage of defective items, vehicle capacity, and storage capacity to provide a more realistic approach. The results indicate that neglecting transportation costs can lead to a potential increase of up to 200% in total costs while ignoring product prices can result in a potential increase of up to 50% in total costs. Therefore, the best ordering strategy involves considering all three parameters of purchasing, transportation, and inventory holding costs simultaneously. Given the high computational complexity of the proposed model, we also present a differential evolution algorithm. The numerical results demonstrate that this algorithm can achieve optimal/near-optimal solutions within significantly shorter computational times compared to exact methods.