Hierarchical Production Planning in Flexible Automated Workshops with Delay Interaction

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This paper addresses the hierarchical production planning (HPP) problem for flexible automated workshops (FAWs) with delay interaction, each with a number of flexible manufacturing systems (FMSs). The delay interaction aspect arises from taking into consideration the transfer of parts between FMSs. Any job which requires processing on more than one FMS cannot be transferred directly from one FMS to the next. Instead a semi-finished-product completed in one period must be put into shop storage until the next period at which it can be transferred to the next FMS for further processing. The objective is to decompose medium-term plans (assigned to an FAW by ERP/MRP II) into short-term plans (to be executed by FMSs in the FAW) so as to obtain the lowest production cost. The HPP problem is formulated in this paper by a nonlinear programming model whose constraints are linear but whose objective function is piecewise linear. For the convenience of solving the nonlinear programming model, it is transformed into a linear programming model. Because the model for a general workshop is too large to be solved by the simplex method on a personal computer within acceptable time, Karmarkar's algorithm and an interaction/prediction algorithm, respectively, are used to solve the model, the former for medium- or small-scale problems and the latter for large-scale problems. With the implementations of these algorithms and with many HPP examples, Karmarkar's algorithm, the interaction/prediction algorithm and the linear programming method in Matlab 5.0 are compared, showing that the proposed approaches are very effective.