Practical solution approaches to solve a hierarchical stochastic production planning problem in a flexible automated workshop in China

摘要

This paper deals with a Hierarchical Stochastic Production Planning (HSPP) problem of Flexible Automated Workshops (FAWs), each with a number of Flexible Manufacturing Systems (FMSs). The problem includes not only the standard (demand, capacity and material supply) uncertainties but also uncertainties in processing times, necessity for rework and scrap. In contrast to most work that only considers either single period or infinite horizons, we also considers multiple time periods and multiple products. One objective of this paper is to determine a cost minimizing production plan for each FMS taking into consideration work-in-process inventory, work centers overload and underload, cumulative over- and under-production of finished products over a finite time horizon. The HSPP problem is formulated as a stochastic nonlinear programming model whose constraints are linear but whose objective function is piecewise linear. To facilitate the solution procedure, the model is first transformed into a deterministic nonlinear programming model and then into a linear programming model. For medium- or small-scale problems, Karmarkar's algorithm is applied to obtain the solution. For large-scale problem, an interaction/prediction algorithm is used. The effectiveness of these approaches is benchmarked against the linear programming method in Matlab 5.0 in various HSPP settings.