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A one-machine deterministic job-shop sequencing problem is considered. Associated with each job is its processing time and linear deferral cost. In addition, the jobs are related by a general precedence relation. The objective is to order the jobs so as to minimize the sum of the deferral costs, subject to the constraint that the ordering must be consistent with the precedence relation. A decomposition algorithm is presented, and it is proved that a permutation is optimal if and only if it can be generated by this algorithm. Four special network structures are then considered, and specializations of the general algorithm are presented.

One of the most important ideas in the theory of sequencing and scheduling is the method of adjacent pairwise job interchange. This method compares the costs of two sequences which differ only by interchanging a pair of adjacent jobs. In 1956, W. E. Smith defined a class of problems for which a total preference ordering of the jobs exists with the property that in any sequence, whenever two adjacentjobs are not in preference order, they may be interchanged with no resultant cost increase. In such a case the unconstrained sequencing problem is easily solved by sequencing thejobs in preference order. In this paper, a natural subclass of these problems is considered for which such a total. preference ordering exists for all subsequences ofjobs. The main result is an efficient general algorirhm for these sequencing problems with series-parallel precedence constraints. These probleris include the least cost fault detcction problem, the one-machine total weighted complction time problem; the two-machine maximum completion time flow-shop problem and the maldmum cumulativi cost problem.

We consider a single-machine job shop scheduling problem in which penalties occur for jobs that either commence before their target start times or are completed after their due dates. The objective is to minimize the maximum penalty, subject to restrictive assumptions on the target start times, the due dates, and the penalty functions. We present an algorithm for solving this problem, along with a method for generating alternative optima. The algorithm is generalized to cover the case in which the machine is available for only a limited time span.

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