Mathematical modeling and hybridized evolutionary LP local search method for lot-sizing with supplier selection, inventory shortage, and quantity discounts

This paper addresses the multi-period inventory lot-sizing problem with supplier selection and inventory shortage, and it considers both all-units and incremental quantity discounts. A unique preprocessing approach is introduced that transforms discount quantity intervals into newer ones, revealing the supplier that has the minimum total ordering, purchasing, and transportation costs. This transformation changes the lot-sizing problem with multiple quantity discount models into a problem of a single quantity discount schedule. The problem is formulated as a Mixed Integer Non-Linear Programming (MINLP) model. Since the problem is intractable, a hybridized search method is developed, where both an Evolutionary Algorithm (EA) and a Linear Programming (LP) driven local search are combined. For initialization, Wagner-Whitin (WW), back-shifting and relaxed LP approaches are used. Finally, for validation and justification purposes, test cases from the industry and literature are used.