An ILS and VND-Based Approach to an Integrated Supplier Selection and Batch Sizing Problem with Quantity Discounts

Supplier selection and lot sizing are central decisions in supply planning, directly influencing acquisition costs, inventory levels, physical space occupation and the ability to meet demand. In retail contexts, especially in small and medium-sized companies, these decisions are often made empirically, although they involve operational trade-offs. Purchasing larger quantities can allow volume discounts, but also increases inventory held, fixed capital and storage needs. On the other hand, more frequent purchases in smaller batches reduce storage, but can increase unit acquisition costs. In this context, this work addresses an integrated problem of supplier selection and multi-period lot sizing, applied to a retailer of agricultural products in Campina Grande/PB. The problem considers multiple items and suppliers, known demand over the planning horizon, quantity discounts, acquisition and inventory holding costs, and storage capacity constraints. The objective is to determine, for each item and period, which suppliers to buy from and in what quantities, in order to meet demand and minimize the total cost associated with purchasing and inventory planning. To solve the problem, a heuristic approach based on the integration between Variable Neighborhood Descent (VND) and Iterated Local Search (ILS) is proposed