Showing papers on "Single-machine scheduling published in 1986"
TL;DR: This work gives efficient algorithms to find a feasible schedule, if any, which minimizes the final completion time under the assumption such that for r"i > r"j, d"i >= d"j.
273 citations
TL;DR: In this paper, the authors consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date and present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold.
Abstract: We consider a single machine scheduling problem in which the objective is to minimize the mean absolute deviation of job completion times about a common due date. We present an algorithm for determining multiple optimal schedules under restrictive assumptions about the due date, and an implicit enumeration procedure when the assumptions do not hold. We also establish the similarity of this problem to the two parallel machines mean flow time problem.
165 citations
TL;DR: The approach used in the paper is fully based on the eliminative properties of a block of jobs and in contradiction to the existing algorithms, it does not require any heuristic method to generate a current solution in a search tree.
151 citations
TL;DR: In this paper, the Smith-heuristic is used for the single-machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a predefined maximum allowable tardiness.
Abstract: This paper analyzes the Smith-heuristic for the single-machine scheduling problem where the objective is to minimize the total weighted completion time subject to the constraint that the tradiness for any job does not exceed a prespecified maximum allowable tardiness. We identify several cases of this problem for which the Smith-heuristic is guaranteed to lead to optimal solutions. We also provide a worst-case analysis of the Smith-heuristic; the analysis shows that the fractional increase in the objective function value for the Smith-heuristic from the optimal solution is unbounded in the worst case.
38 citations
01 Jan 1986
12 citations
TL;DR: A number of results are proved, including one to the effect that the optimal schedule must be V shaped when the jobs have identical means or variances or have exponential processing times.
Abstract: We consider the problem of scheduling n jobs with random processing times on a single machine in order to minimize the expected variance of the completion times. We prove a number of results, including one to the effect that the optimal schedule must be V shaped when the jobs have identical means or variances or have exponential processing times.
7 citations
TL;DR: In this paper, a mixed-integer programming model of the bicriterion single machine scheduling problem where early shipments are forbidden is presented, where the objective function is a combination of total tardiness and earliness.
5 citations