Branch-and-bound methods are commonly used to find a permutation schedule that minimizes maximum completion time in an m-machine flow-shop. In this paper we describe a classification scheme for lower bounds that generates most previously known bounds and leads to a number of promising new ones as well. After a discussion of dominance relations within this scheme and of the implementation of each bound, we report on computational experience that indicates the superiority of one of the new bounds.

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We address the problem of scheduling n identical jobs on m uniform parallel machines to optimize scheduling criteria that are nondecreasing in the job completion times. It is well known that this can be formulated as a linear assignment problem, and subsequently solved in O(n3) time. We give a more concise formulation for minsum criteria, and show that general minmax criteria can be minimized in O(n2) time. We present faster algorithms, requiring only O(n +mlog m) time for minimizing makespan and total completion time, O(nlogn) time for minimizing total weighted completion time, m'aximum lateness, total tardiness and the weighted number of tardy jobs, and O(nlog2n) time for maximum weighted tardiness. In the case of release dates, we propose an O(nlogn) algorithm for minimizing makespan, and an O(mn2m+') time dynamic programming algorithm for minimizing total completion time.

Hierarchical planning systems have become popular for multilevel decision problems. After reviewing the concept of hierarchical planning and citing some examples, we describe a method for analytic evaluation of a hierarchical planning system. We show that multilevel decision problems can be nicely modeled as multistage stochastic programs. Then any hierarchical planning system can be measured against the yardstick of optimality in this stochastic program. We demonstrate this approach on a hierarchical system that can be shown to be asymptotically optimal for a job shop design/scheduling problem.

Suppose we have n jobs that arrive simultaneously to be processed on a continuously available machine that can handle only one job at a time. Each job has a fixed processing time and a cost function that is nondecreasing in its finishing time. We want to find a schedule that minimizes total costs. After reviewing the relevant work on this problem, we present a new algorithm for a general cost function. The algorithm is tested for the well known case of a weighted tardiness criterion.