Nonlinear Blend Scheduling via Inventory Pinch-based Algorithm using Discrete- and Continuous-time Models

Mathematical optimization has become an important supply chain management tool for any contemporary enterprise. Increasing profit margins through better design, planning, and operative decisions across the supply chain represents a huge opportunity in the more than ever competitive economic market, especially in a global scale. Industrial and academic researchers have been working intensively in the process systems engineering area, and several advancements have been made in the optimization field, from new mathematical models, more efficient solution algorithms, use of more powerful computing machines and with parallel capabilities, and the development of different optimization frameworks. A supply chain is composed of the following elements: procurement and storage of raw materials, facilities and processes to transform the raw materials into intermediate and final products, storage of these products and its distribution to warehouses or to the final customers. Operating the complete supply chain structure in the best possible manner (i.e. maximizing profit or minimizing cost) involves making decisions at different levels along the supply chain network. Production planning determines the production targets of each different product along a defined planning horizon (usually ranging from a few months to 2 years), for the entire supply chain, for each different production facility, or for each production line or unit. Production scheduling determines the best operating sequences and the best operating conditions to achieve the inventory and production targets determined by the production plan. Scheduling is done on smaller time horizons (e.g. days or weeks), and includes more operational rules and constraints than planning models. Fig. 1 shows how the length of the time horizon and model accuracy changes, depending on the spatial or time scale, under a hierarchical production planning framework. Nonlinear Blend Scheduling via Inventory Pinch-based Algorithm using Discreteand Continuous-time Models