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 of the sum of the number of annual set-ups and the number of facilities/production lines active in the current period. The loading problem considered here can be defined as a bin packing problem with bins of multiple classes. A heuristic solution technique which incorporated different search methods is developed for dealing with this difficult problem. The loading heuristic is a guided local search method integrated with concepts from Tabu Search and Simulated Annealing whereas the lot sizing heuristic is a search method which enhances the related part of the objective function while always remaining in the feasible region.