Hybrid flow-shop scheduling with assembly operations

Hybrid scheduling for the production system including parts machining and assembly operations is studied. Several products of different kinds are ordered to be produced and parts for the products are manufactured in the flow-shop consisting of multiple machines. Each product is produced by hierarchical assembly operations from the parts. Several parts are assembled into the first sub-assembly, and several other parts and the first sub-assembly are assembled into the second sub-assembly. These assembly operations are continued until the last sub-assembly that is the final product is obtained. In this paper, the problem to obtain a schedule having the minimum weighted sum of completion time of each product is considered. The decision variables are the sequence of products to be assembled and the sequence of parts to be processed. A technique to get better lower bounds and a calculation procedure using branch and bound method is developed to obtain an optimum or ϵ-optimum schedule. The meaning of the model is demonstrated by a numerical example and the effectiveness of the proposed calculation procedure is shown by several computational experiments.