On a methodology for discrete–continuous scheduling

Józefowska, Joanna; Węglarz, Jan

doi:10.1016/s0377-2217(97)00346-9

Cited by 53 publications

(38 citation statements)

References 10 publications

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“…The single continuous renewable resource can be allotted to activities in (arbitrary) amounts from the interval [0, 1], and its total amount available at a time is equal to 1. The amount u i (t) (unknown in advance) of the continuous resource allotted to activity A i at time t determines the processing rate of activity A i , as it is described by the following equation [9]:…”

Section: Problem Formulationmentioning

confidence: 99%

“…The general methodology for discrete-continuous project scheduling [10] uses the idea of a feasible sequence introduced in [9] for machine scheduling. Observe that a feasible schedule (i.e.…”

Section: Problem Formulationmentioning

confidence: 99%

“…It has been proved in [9] that for processing rate functions f i such that f i ≤ c i u i , c i = f i (1), i = 1, 2, . .…”

Section: Processing Rate Functions Not Greater Than Linearmentioning

confidence: 99%

“…Concave processing rates correspond to the realistic hypothesis of parallelizing actual large numerical codes (see, e.g., [1]). Now, it was proved in [9] that for concave processing rate functions f i , i = 1, 2, . .…”

Section: Concave Processing Rate Functionsmentioning

confidence: 99%

“…Discrete-continuous project scheduling problems arise when activities simultaneously require discrete and continuous resources. The methodology for discrete-continuous machine scheduling based on the processing rate vs. resource amount model was described in [9], and a model of the discrete-continuous project scheduling problem was first presented in [10].…”

Section: Introductionmentioning

confidence: 99%

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Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan

Waligóra

2010

Comput Optim Appl

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In this paper some discrete-continuous project scheduling problems to minimize the makespan are considered. These problems are characterized by the fact that activities of a project simultaneously require for their execution discrete and continuous resources. A class of these problems is considered where the number of discrete resources is arbitrary, and one continuous, renewable, limited resource occurs. A methodology for solving the defined problems is presented. The continuous resource allocation problem is analyzed. An exact, as well as a heuristic approach to the problem is discussed. The idea of the continuous resource discretization is described, and a special case of the problem with identical processing rate functions is analyzed. Some computational experiments for evaluating the efficiency of the proposed heuristic approaches are presented. Conclusions and directions for future research are given.

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Section: Problem Formulationmentioning

confidence: 99%

Section: Problem Formulationmentioning

confidence: 99%

“…It has been proved in [9] that for processing rate functions f i such that f i ≤ c i u i , c i = f i (1), i = 1, 2, . .…”

Section: Processing Rate Functions Not Greater Than Linearmentioning

confidence: 99%

Section: Concave Processing Rate Functionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan

Waligóra

2010

Comput Optim Appl

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A heuristic approach to allocating the continuous resource in discrete-continuous scheduling problems to minimize the makespan

et al. 2002

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SUMMARYA problem of scheduling jobs on parallel, identical machines under an additional continuous resource to minimize the makespan is considered. Jobs are non-preemtable and independent and all are available at the start of the process. The total amount of the continuous resource available at a time is limited and the resource is a renewable one. Each job simultaneously requires for its processing a machine and an amount (unknown in advance) of the continuous resource. The processing rate of a job depends on the amount of the resource allotted to this job at a time. The problem is to ÿnd a sequence of jobs on machines and, simultaneously, a continuous resource allocation which minimize the makespan. A heuristic approach to allocating the continuous resource is proposed. A tabu search algorithm to solve the considered problem is presented and the results for the algorithms with exact and heuristic procedures for allocating the continuous resource are compared on the basis of some computational experiments.

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A Performance Analysis of Tabu Search for Discrete-Continuous Scheduling Problems

Józefowska

Waligóra

Węglarz

2003

Applied Optimization

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On a methodology for discrete–continuous scheduling

Cited by 53 publications

References 10 publications

Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan

Heuristic approaches to discrete-continuous project scheduling problems to minimize the makespan

A heuristic approach to allocating the continuous resource in discrete-continuous scheduling problems to minimize the makespan

A Performance Analysis of Tabu Search for Discrete-Continuous Scheduling Problems

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