Showing papers on "Single-machine scheduling published in 1990"
TL;DR: Several examples of one‐machine problems in which the minimization of expected cost subject to stochastic breakdowns of the machine can be successfully attacked analytically are provided.
Abstract: We provide several examples of one-machine problems in which the minimization of expected cost subject to stochastic breakdowns of the machine can be successfully attacked analytically. In particular for the weighted flow-time model, we derive strong bounds on the difference between the optimal static policy and the WSPT policy and discuss an example in which the WSPT policy is not optimal.
104 citations
TL;DR: This paper presents two extensions to the joint sequencing/resource allocation scheduling model for single-stage production initially proposed by Van Wassenhove and Baker, and the existence of multiple resources available for processing time control is considered.
44 citations
TL;DR: This work develops algorithms that arc polynomial in the number of nondominatcd schedules to generate all nondominated schedules and shows that the methods can easily be extended to handle more than two criteria, as well as nonzero release dales.
42 citations
TL;DR: The article compares six available lower bounds in the literature and shows that the lower bound based on the optimal solution to the preemptive version of the problem is the dominant lower bound.
Abstract: This article addresses deterministic, nonpreemptive scheduling of n jobs with unequal release times on a single machine to minimize the sum of job completion times. This problem is known to be NP-hard. The article compares six available lower bounds in the literature and shows that the lower bound based on the optimal solution to the preemptive version of the problem is the dominant lower bound.
25 citations
TL;DR: The heuristic solution is compared to the optimal solution for 192 randomly generated problems to investigate the effects of problem size, due date coefficient of variation, and due date lightness on the quality of the heuristic.
25 citations
TL;DR: The paper provides a theoretical background to solve a variety of single machine scheduling problems with quadratic separable functions of completion times including waiting time and due date models using a parametric ordering as well as an adjacent precedence matrix concept.
21 citations
TL;DR: A criterion for optimality of two jobs to be scheduled next to each other is given, and based on this criterion a heuristic algorithm is proposed to solve the static single-facility scheduling problem.
Abstract: We consider the static single-facility scheduling problem where the processing times of jobs are a nondecreasing and differentiable function of their starting (waiting) times and the objective is to minimize the total elapsed time (makespan) in which all jobs complete their processing. We give a criterion for optimality of two jobs to be scheduled next to each other, and based on this criterion we propose a heuristic algorithm to solve the problem. The effectiveness of the algorithm is empirically evaluated for quadratic and exponential cost functions. In the quadratic case it is compared with the static heuristic algorithm proposed by Gupta and Gupta.
21 citations
Proceedings Article•
28 May 1990
TL;DR: It is shown that upon termination of such an ascent direction algorithm for the Lagrangian dual problem of the single-machine scheduling problem of minimizing total weighted completion time subject to precedence constraints, the original problem gets a dual decomposition.
16 citations
Metz1
TL;DR: The one-machine scheduling problem of minimizing total flow time with different release dates is addressed and a necessary and sufficient condition is proved for local optimality and can be considered as a priority rule.
Abstract: The one-machine scheduling problem of minimizing total flow time with different release dates is addressed. This problem is equivalent to the problems of minimizing total completion time, total job lateness, and mean number of jobs in the shop, and it is NP-hard. A necessary and sufficient condition is proved for local optimality and can be considered as a priority rule. Based on this condition, a subset containing all the optimal schedules is defined. Any schedule in this subset verifies some dominance properties proved by other researchers. The author also proposes some efficient heuristic algorithms using the proven condition to build a schedule belonging to this subset. The algorithm performances are provided. >
5 citations
01 Jan 1990
TL;DR: This work presents some properties or conditions for two regular criteria, total tardiness and total flow time, which lead to an optimal schedule in some specificic cases.
Abstract: The single machine scheduling problems have been extensively studied with various criteria to be optimized and under various assumptions. In this work, we review some results obtained recently in the case of different release dates. Most problems with different release dates are NP-hard. Some researchers have proved some dominance properties or sufficient conditions for local optimality which lead to an optimal schedule in some specificic cases. We present some properties or conditions for two regular criteria, total tardiness and total flow time.
3 citations
01 Jan 1990
TL;DR: The min-max problem with unit-time activities, maximum expected completion time of the so-called operations as objective function, and precedence constraints given by an acyclic OR network is shown to be NP-hard.
Abstract: Stochastic min-sum and min-max single-machine scheduling problems are considered where the precedence constraints are given by a so-called OR network. An OR network is a special stochastic activity network (GERT network) which may contain cycles and has some tree-structure property. It turns out that min-max problems are harder than min-sum problems in contrast to deterministic scheduling. If the objective function is the expected weighted flow time, an optimal scheduling policy can be computed in polynomial time. The min-max problem with unit-time activities, maximum expected completion time of the so-called operations as objective function, and precedence constraints given by an acyclic OR network is shown to be NP-hard. However, if we restrict ourselves to priority lists of operations instead of general scheduling policies, there is a polynomial algorithm for the scheduling problem where the activity durations are generally distributed and the objective function is the maximum expected lateness.
20 Aug 1990