Open Access
On a scheduling problem
Toji Makino
- 01 Jan 1965
- pp 32-44
TL;DR: An optimal processing order is obtained in the case where the handling time is treated as random variables to minimize the time required to complete all the operations.
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Abstract: In this paper we consider the problem of deciding the order of the two items which should be processed by n machines in order to minimize the time required to complete all the operations. Up to the present, many studies on the scheduling problem have been published. However, those studies only attempted to provide some results concerning the system with constant handling time, -the time re quired for processing. So, in this paper we are going to obtain an optimal processing order in the case where the handling time is treated as random variables.
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Citations
SimILS: a simulation-based extension of the iterated local search metaheuristic for stochastic combinatorial optimization
TL;DR: The SimILS framework is presented, that extends ILS by integrating simulation to be able to cope with Stochastic COPs in a natural way and give rise to a new brand of ILS-based algorithms.
Scheduling on a two-machine flowshop subject to random breakdowns with a makespan objective function
Ali Allahverdi,John Mittenthal +1 more
TL;DR: It is shown that under appropriate conditions Johnson's algorithm stochastically minimizes makespan in a two-machine flowshop when the machines are subject to random breakdowns.
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A review of flowshop scheduling research
Jatinder N. D. Gupta
- 01 Jan 1979
TL;DR: This paper reviews the flowshop scheduling problem formulation, solution approaches, and analyzes the contributions of each approach to solve practical problems.
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On heuristic solutions for the stochastic flowshop scheduling problem
TL;DR: This paper proposes a procedure with a variable number of iterations that ensures that the error in the estimation of the expected makespan is bounded within a small percentage with a very high probability, and test the main heuristics proposed in the literature and find significant differences in their performance, in contrast with existing studies.
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Determining the optimal sequences and the distributional properties of their completion times in stochastic flow shops
TL;DR: It is shown in this paper that the minimum makespan (MM) in the stochastic case is a random variable (r.v.) not always connected to a particular sequence, which means that a new concept for the optimal sequence is introduced.
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References
Optimal two- and three-stage production schedules with setup times included
TL;DR: A simple decision rule is obtained in this paper for the optimal scheduling of the production so that the total elapsed time is a minimum.