3D loading problem formulation using mixed integer nonlinear programming

The manufacturing of different types of cylindrical parts requires loading of parts into baskets for heat treatment operation. This loading process is complex and involves issues relating to geometry, and heterogeneity in the parts and in their processing requirements. The parts loaded for heat treatment often do not utilize the available capacity adequately because layer-loading is accomplished by operator ingenuity. Productivity in heat treatment operation can be increased by improving utilization, which is determined by the loading process. This paper describes the development mathematical model using mixed integer nonlinear formulation for loading of cylindrical parts into baskets. The mathematical modeling considers the exact location of parts to be loaded on the layers with the primary objective of minimizing unutilized volume of the baskets.