Hierarchical production planning with demand constraints

This paper explores the hierarchical production planning (HPP) problem of flexible automated workshops (FAWs), each of which has a number of flexible manufacturing systems (FMSs). The objective is to decompose medium-term production plans (assigned to an FAW by ERP/MRP II) into short-term production plans (to be executed by FMSs in the FAW) so as to minimize cost on the condition that demands have just been met. Herein, the HPP problem is formulated by a linear programming model with the overload penalty different from the underload penalty and with demand constraints. Since the scale of the model for a general workshop is too large to be solved in the simplex method on a personal computer within acceptable time, Karmarkarʹs algorithm and an interaction/prediction algorithm, respectively, are used to solve the model, the former for the large scale problems and the latter for the very large scale. With the help of the above-mentioned algorithms and HPP examples, Karmarkarʹs algorithm and the interaction/prediction algorithm are compared and analyzed, the results of which show that the proposed approaches are quite effective and suitable for both ‘push’ and ‘pull’ production.