Hierarchical stochastic production planning with delay interaction and demand constraints

Abstract

This paper explores the hierarchical stochastic production planning (HSPP) problem of flexible automated workshops, each with a number of flexible manufacturing systems (FMSs), the part transfer between which is delayed by a time period (i.e. delay interaction). The problem not only includes uncertainties in the demand, capacities, material supply, processing times, necessity for rework and scrap but also considers multiple products and multiple time periods. The objective is to devise a production plan which tells each FMS how many parts to produce and when to produce them so as to obtain the lowest cost under the condition of demands being just met. Herein, the HSPP problem is formulated by a stochastic non-linear programming model whose constraints (including demand constraints) are linear but whose objective function is piecewise linear. For the convenience of solving the stochastic non-linear programming model above, it is approximately transformed into a deterministic non-linear programming model and further into a linear programming model. Then, Karmarkar's algorithm and an interaction/prediction algorithm are used to solve the model, the former for the medium- or small-scale problems and the latter for the large-scale problems. With the help of the implementations of the above-mentioned algorithms and through many HSPP examples, Karmarkar's algorithm, the interaction/prediction algorithm and the linear programming method in Matlab 5.0 are compared, the result of which shows that the proposed approaches are very effective and suitable for not only ‘push’ production but also ‘pull’ production.