Simultaneous lot sizing and loading of product families on parallel facilities of different classes

Hierarchical production planning is a structured approach which reduces the size of the decision-making model dealt with in production planning. The first level in the hierarchy is aggregate and decisions are made in terms of the product type. The next two levels consist of planning models for product families and end items. The problem considered here is involved with determining simultaneously feasible family lot sizes as well as a feasible loading of families on facilities. The problem is relevant in manufacturing systems where obtaining a feasible schedule for product families at the bottleneck department or major cost centre is essential in minimizing production costs and the capacity within the department is not homogeneous, i.e. facilities are of multiple classes and at the aggregate planning level capacity cannot be represented in such detail. Since the lot sizing and loading decisions are inseparable, the resulting mathematical model becomes nonlinear and integer. The objective function consists ...