Scheduling flexible manufacturing systems for apparel production

In mid to high volume apparel production, garments are typically grouped into production lots, and each lot is processed in its own manufacturing cell. A flexible manufacturing system used in this environment enables quick cell configuration, and the efficient operation of cells. The scheduling problem is to decide when to set up a cell and consequently begin garment production in the cell, and to decide the quantity of machines to allocate to each cell, under the constraints of limited machines. The time to process a production lot depends on the quantity of machines allocated to the cell in which the lot will be processed, and thus scheduling and resource allocation are highly coupled. In this paper, an accurate and low-order integer programming model is developed which integrates scheduling and resource allocation. Insight is provided into how the model relates to the operation of a real factory. The model is solved using the Lagrangian relaxation methodology, and a new bundle method is used for optimizing the Lagrangian dual function. The combination of an accurate low-order model, Lagrangian relaxation, and the bundle method is shown to be very practical.