Multi-Population Genetic Algorithm to Solve the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem

This paper introduces an evolutionary algorithm as a procedure to solve the Synchronized and Integrated Two-Level Lot Sizing and Scheduling Problem (SITLSP). This problem can be found in some industrial settings, mainly soft drink companies, where the production process involves two interdependent levels with decisions concerning raw material storage and soft drink bottling. The challenge is to simultaneously determine the lot-sizing and scheduling of raw materials in tanks and soft drinks in bottling lines, where setup costs and times depend on the previous items stored and bottled. A multi-population genetic algorithm approach with a novel representation of solutions for individuals and a hierarchical ternary tree structure for populations is proposed. Computational tests include comparisons with an exact approach for small-tomoderate sized instances and with real-world production plans provided by a manufacturer.