Parallel machine scheduling problems with a single server

Kravchenko, Svetlana A.; Werner, Frank

doi:10.1016/s0895-7177(97)00236-7

Cited by 83 publications

(41 citation statements)

References 2 publications

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“…Papers dealing with resource-based objective functions are infrequent. Koulamas (1996) as well as Kravchenko and Werner (1997) analysed the problem of two parallel machines with a single server minimizing their idle times.…”

Section: Problem Descriptionmentioning

confidence: 99%

Mixed integer programming formulations for the Biomass Truck Scheduling problem

Torjai

Kruzslicz

2015

Cent Eur J Oper Res

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In this paper, we introduce the Biomass Truck Scheduling (BTS) problem that originated in a real-life herbaceous biomass supply chain (HBSC) around Pécs, Hungary. BTS can be considered as a Parallel Machine Scheduling with a Single Server problem, where identical trucks (parallel machines) deliver biomass from satellite storage locations to a central biorefinery operating a single unloader (single server). We make two particular assumptions regarding the server: the server operation has a unit time length for each trip and idle periods are not allowed for it (server no idle time constraint). We consider two objective functions associated with the revealed HBSC logistic cost structure. First, the number of trucks is minimized (resource availability cost) following which the total truck idle time is minimized. Three mixed integer programming formulations are constructed to solve BTS, and their efficiency is evaluated using a number of test cases. We found that, even if the number of trucks is locked at its minimum value, there is always a schedule with zero truck idle time-that is, there is no trade-off between these two objective functions.

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Section: Problem Descriptionmentioning

confidence: 99%

Mixed integer programming formulations for the Biomass Truck Scheduling problem

Torjai

Kruzslicz

2015

Cent Eur J Oper Res

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“…A variation that may be closely related to this work involves machines which are not available at the same time, as opposed to job ready times, under the minimization of makespan objective (Lee 1991). The case of setups that must be performed by a single server has been examined with the makespan criterion (Kravchenko 1997). Uniform (as opposed to identical) parallel machines with sequence dependent setup times have been studied with the goal of minimizing deviations from due dates (Balakrishnan et al 1999).…”

Section: Parallel Machinesmentioning

confidence: 99%

Scheduling flexible flow lines with sequence-dependent setup times

Kurz

Askin

2004

European Journal of Operational Research

212

102

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“…The routing constraints and the no-wait constraint are formulated in (3). Constraints (4) and (5) (respectively (6) and (7)) are the disjunctive constraints at the ÿrst stage (respectively at the second stage).…”

Section: Integer Linear Programming Modelmentioning

confidence: 99%

“…Koulamas [2] proposes a beam search heuristic algorithm for a static environment with two parallel processors and a single server where the aim is to ÿnd a feasible schedule which minimizes the machine idle time resulting from the unavailability of the server. Kravchenko and Werner [3], Hall et al [4] and Brucker et al [5] present a lot of complexity results for these problems. Glass et al [6] consider related models with parallel machines for which jobs are dedicated and provide algorithmic, complexity and heuristic analysis results.…”

Section: Introductionmentioning

confidence: 99%