·A multi sub colony artificial bee colony MABC is proposed to minimize makespan and total tardiness simultaneously in which initial population is generated by heuristics s employed bee sub colonies are obtained by division and all these sub colonies except the worst one are learned by s − 1 onlooker bee sub colonies diversified
·In the past years many researchers has been investigated parallel machine scheduling problem by considering various operational constraints However the first study on parallel machine scheduling problem has been conducted by McNaughton 1959 in the late fifties Other researchers such as Horowitz and Sahni 1976 Cheng and Sin 1990
·In this paper an unrelated parallel machine scheduling problem with sequence and machine dependent setup times and makespan minimization is studied A new makespan linearization and several mixed integer formulations are proposed for this problem These formulations outperform the previously published formulations regarding
·Precedence relations between jobs p r e c The complexity of scheduling problems with precedence constraints has been studied since the seventies see Lenstra and Rinnooy Kan 1978 Chudak and Shmoys 1999 introduced approximation algorithms for the PMSP with precedence constraints where each machine has its own speed Hu et
In this paper we consider Parallel Machines Scheduling with nonsimultaneous machine available time We give the exact worst case performance bound of MLPT proposed by Lee Furthermore two other modified LPT algorithms are discussed The paper is ended by numerical experiments of these algorithms
·In this paper we study an important real life scheduling problem that can be formulated as an unrelated parallel machine scheduling problem with sequence dependent setup times due dates and machine eligibility constraints The objective is to minimise total tardiness and makespan We adapt and extend a mathematical model to
·1 Introduction In manufacturing environments it is ordinary to have different machines operating in parallel each of which with different shifts and inactive time intervals such as for preventive maintenance Li Liu Sethi & Xu 2017 The Unrelated Parallel Machine Scheduling Problem with Machine Availability and Eligibility Constraints
·This paper studies the NP hard problem of scheduling jobs on identical parallel machines with machine dependent delivery times to minimize the total weighted tardiness A mixed integer linear programming formulation is presented that does not require machine indexed variables due to a transformation of the problem A variable
· ABSTRACT MODELS OF PARALLEL MACHINES The most popular abstraction of a parallel machine is by far the parallel random access machine or PRAM A PRAM consists of a collection of indepen dent processors and a single shared memory It is as sumed that each processor can read or write to any lo cation in the memory in a
·A bi criteria scheduling problem for parallel identical batch processing machines in semiconductor wafer fabrication facilities is studied Only jobs belonging to the same family can be batched together The performance measures are the total weighted tardiness and the electricity cost where a time of use TOU tariff is assumed Unequal
·A problem of parallel machine scheduling with coordinated job deliveries is handled to minimize the makespan Different jobs call for dissimilar sizes of storing space in the process of transportation tougher to resolve compared with models involving jobs of equal size since the batching decision now involves bin packing which alone is NP
·Before I u k l we find the last sub interval I v l ′ with length p satisfying anyone of the three conditions a there is a machine idle in sub interval I v l ′; b a non full batch is processed on a machine in sub interval I v l ′; c there is a job denoted by J j that completes before J k such that q j − r j ≤ q k − r k
·This paper addresses an unrelated parallel machine scheduling problem with due dates and sequence dependent setup times with the objective to minimize total weighted tardiness TWT Four search heuristics are suggested for the problem which include the earliest weighted due date EWDD rule the shortest weighted processing
·The literature on parallel machine scheduling has developed over multiple decades and contains many useful models and algorithms see for instance [1] [2] [3] One of the most frequently studied objectives in scheduling identical parallel machines is to minimize the makespan the maximum completion time of the jobs
·Qjam is a framework for the rapid prototyping of parallel machine learning algorithms on clusters I Introduction Many machine learning algorithms are easy to parallelize in theory However the xed cost of creating a distributed system that organizes and manages the work is an obstacle to parallelizing existing algorithms and prototyping
· （） 。PRAM PRAM（Parallel Random Access Machine ） SIMD RAM
·This problem can be classified according to Graham et al 1979 as a R − P S M p r e c S i j C m a x where R PSM means that the main machines are Unrelated Parallel Machines R and the Support Machines are Identical Parallel Machine PSM prec the presence of precedences S i j the existence of machine and job dependent setup
·It is well known that with the development of economic globalization and increasing competition in the market enterprises are facing a huge challenge in the unrelated parallel machine scheduling problem with setup time UPMST Determining the processing order of all jobs and assigning machines to production scheduling has
·We consider the problem of scheduling unrelated parallel machines with sequence and machine dependent setup times and ready times to minimise total weighted tardiness TWT We present a mixed integer programming model that can find optimal solutions for the studied problem We also propose a heuristic ATCSR Rm and an
·The classical parallel machine scheduling problem PMSP is a typical scheduling problem in textile industry electronic manufacturing mechanical processing etc Pinedo 2016 In 1959 PMSPs were firstly proposed by McNaughton and have attracted wide attention from scholars since even the two identical parallel
·This paper investigates a parallel machine scheduling problem with uncertain job processing time where the job tardiness and optional machines are considered To address the factor of energy saving only a subset of all available machines are turned on which is referred to as not all machine NAM To depict the uncertain
·European Journal of Operational Research 47 1990 271 292 271 North Holland Invited Review A state of the art review of parallel machine scheduling research CHENG Department of Actuarial and Management Sciences University of Manitoba Winnipe Manitoba Canada R3T 2N2 SIN Department of Management Sciences
·In this paper an unrelated parallel machine scheduling problem with sequence and machine dependent setup times and makespan minimization is studied A new makespan linearization and several mixed integer formulations are proposed for this problem These formulations outperform the previously published formulations regarding
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