We consider an assembly line with m stations in series having finite capacity buffers. Blocking occurs when buffers are full. There are M different types of products to be assembled, each with its own processing requirements. There is a production target set for each type. The problem is to operate the line to maximize throughput. We propose heuristic approaches to this problem based on an equivalent maximum flow problem and on critical path techniques.

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Consider a network C = ( V , E ) with distinguished vertices s and t , and with k different costs on every edge. We consider the problem of finding k disjoint paths from s to t such that the total cost of the paths is minimized, where thejth edge-cost is associated with thejth path. The problem has several variants: The paths may be vertex-disjoint or arcdisjoint and the network may be directed or undirected. We show that all four versions of the problem are strongly NP-complete even for k = 2. We describe polynomial time heuristics for the problem and a polynomial time algorithm for the acyclic directed case.Q 1992 John Wiley & Sons, Inc.