Showing papers on "Single-machine scheduling published in 1981"
TL;DR: Certain order-constrained stochastic scheduling problems are shown to have optimal strategies which are nonpreemptive and results for the deterministic case may be utilized to obtain these optimal strategies.
Abstract: Some results of Sidney (Sidney, J. B. 1975. Decomposition algorithms for single machine sequencing with precedence relations and deferral costs. Opns. Res. 23 283–298.) concerning order-constrained...
49 citations
TL;DR: The algorithm is based on the earlier known dynamic programming approach and its main new achievement is the use of a compact labeling scheme for series-parallel graphs which is the best possible in a certain sense.
Abstract: This paper considers a set of tasks to be sequenced for processing on a single machine. The possible sequences may be restricted by given precedence constraints. For each feasible sequence we have an additive cost function (e.g., tardiness or weighted tardiness) and the objective is to find a feasible sequence with minimal total cost. An efficient algorithm is presented for the case when the set of precedence constraints can be represented by a series-parallel graph. The algorithm is based on the earlier known dynamic programming approach, its main new achievement is the use of a compact labeling scheme for series-parallel graphs which is the best possible in a certain sense.
9 citations
TL;DR: This paper suggests in this paper how to determine for which problems heuristics should be developed and, for a class of these problems, how to develop these procedures naturally.
Abstract: For many years difficult combinatorial problems, such as scheduling problems, have been solved by the practitioner with heuristics. We suggest in this paper how to determine for which problems heuristics should be developed and, for a class of these problems, how to develop these procedures naturally. These results are motivated by theoretical results in computer science. The suggestion is numerically tested on a particular single machine scheduling problem.
8 citations