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The problem of scheduling a set of jobs on a bank of parallel machines has received consider- able attention. ... also reported on preprocessing techniques (basically primal cut generation) to improve an LP relaxation bound for the same problem. ...doi:10.2307/3010037 fatcat:6qpvgokzlbcqffl5x3mzin27ca
We obtain corresponding bounds on the quality of the LP relaxation. ... We present a new class of randomized approximation algorithms for unrelated parallel machine scheduling problems with the average weighted completion time objective. ... Shmoys for helpful comments on an earlier version of this paper  . ...doi:10.1137/s0895480199357078 fatcat:4ppc6umgefb6td76t4dufhphly
Lecture Notes in Management and Industrial Engineering
Lagrangian Relaxation method has been applied to solve scheduling problem in diverse manufacturing environments like single machine, parallel machine, flow shop, job shop or even in complex real-world ... We highlight two key issues on the application of the method: the first one is about the method to solve the dual problem and second one is the choice of the constraints to relax. ... The resulting subproblems are equivalent to solving a problem of scheduling a single machine or parallel machines. ...doi:10.1007/978-3-319-04705-8_17 fatcat:3pjhavvkfbdgphrg3rzg2e4khy
This research focuses on minimizing the makespan of a set of non-identical parallel batch processing machines. In order to schedule jobs on these machines, two decisions are to be made. ... Lagrangian Relaxation approach has been shown to be very effective in solving scheduling problems. ... If the upper bound Flow Chart of Lagrangian Relaxation Approach For a given set of multipliers, the relaxed problem is solved. ...doi:10.1016/j.cie.2016.09.018 fatcat:pzz5j3zxozasvp2bracq77g4kq
We focus on the two-center hybrid flow shop scheduling problem with identical parallel machines and removal times. ... These procedures are based on the optimal solution of the parallel machine scheduling problem with release dates and delivery times. The heuristic is composed of two phases. ... Acknowledgment The authors would like to extend their sincere appreciation to the Deanship of Scientific Research at King Saud University for its funding of this research through the Research Group Project ...doi:10.1155/2014/605198 pmid:25610911 pmcid:PMC4281465 fatcat:zbt3ajtxd5egphwpdwrfrbzfeq
We consider machine scheduling on unrelated parallel machines with the objective to minimize the schedule makespan. ... On the basis of an integer linear programming formulation for a relaxation of the problem, we use LP rounding techniques to allocate resources to jobs, and to assign jobs to machines. ... Maxim Sviridenko was partially supported by METEOR, the Maastricht Research School of Economics of Technology and Organizations. ...doi:10.1007/s10107-006-0059-3 fatcat:hwkb7qa3frdqrlwd4jvv4rlo7a
The problem of scheduling a set of jobs on a bank of parallel machines has received consider- able attention. ... Key words: scheduling, Lagrangean decomposition, Lagrangean relaxation INTRODUCTION We deal with the problem of allocating workload on parallel unrelated machines with setups (PUMS) in a batch mode. ...doi:10.1057/jors.1996.152 fatcat:lvlgfyr7zjcwjpkv6udp7efnmq
The problem of scheduling a set of jobs on a bank of parallel machines has received consider- able attention. ... Key words: scheduling, Lagrangean decomposition, Lagrangean relaxation INTRODUCTION We deal with the problem of allocating workload on parallel unrelated machines with setups (PUMS) in a batch mode. ...doi:10.1057/palgrave.jors.0471004 fatcat:whwtwn35azdrfaa2uw3buafdjq
Lecture Notes in Computer Science
The same algorithm also is a 2-approximation for the corresponding preemptive scheduling problem on identical parallel machines. ... perform list scheduling on each of them. ... Hence, (LPR) is a relaxation of the scheduling problem under consideration. ...doi:10.1007/3-540-63397-9_32 fatcat:lpmkjeavl5ghvdnbljneml54em
Journal of the ACM
We consider the problem of scheduling unrelated parallel machines subject to release dates so as to minimize the total weighted completion time of jobs. ... We also consider preemptive scheduling problems and derive approximation algorithms and results on the power of preemption which improve upon the best previously known results for these settings. ... We study the following network scheduling problem: A set J of n jobs has to be scheduled on m unrelated parallel processors or machines that are connected by a network. ...doi:10.1145/375827.375840 fatcat:5dbcodih3vdkdddei236hzi2l4
In this paper we address both, and study for the first time a scheduling problem that combines the classical unrelated machine scheduling model with stochastic processing times of jobs. ... Via ∆ = 0, currently best known bounds for deterministic scheduling on unrelated machines are contained as special case. 1 A concrete example may help: Imagine a job j which has processing time either ... Most of the results presented in this paper were obtained during the Dagstuhl Seminar 13111 "Scheduling" in 2013. ...doi:10.1287/moor.2015.0757 fatcat:a72snwo4c5g6vi52vzcj37stiu
In addition, a lower bound of 1.21207 on the competitive ratio of any randomized online algorithm for the considered problem with an arbitrary number of machines is derived which improves a previous result ... The paper presents a deterministic online algorithm for scheduling a set of jobs with given release dates on two parallel machines. ...
For scheduling problems with setup times on unrelated parallel machines, there is limited research on solution methods and to the best of our knowledge, parallel computer architectures have not yet been ... Since many scheduling problems are NP-hard in the strong sense, there is a need for developing solution heuristics. ... In this paper, we focus on a specific problem which occurs in many application domains: the parallel machine scheduling problem on unrelated machines, sequence-and machine-dependent setup times, machine ...arXiv:1605.04682v1 fatcat:pvzpcgq5yzhkhdo5ogti2d4z4m
This research was supported by the project "High performance methods for mathematical optimization" of the Netherlands Organization for Scientific Research (NWO). ... The problem under consideration is the problem of scheduling unrelated parallel machines so as to minimize the total weighted completion time. ... The resulting LP-relaxation is a~-relaxation of the scheduling problem under consideration, Le., the value of an optimal schedule is within a factor~of the optimum LP value. ...doi:10.1287/ijoc.188.8.131.52 fatcat:5zmocep445efnolkjnelbv4kxy
Res. 22 (1997), no. 3, 513-544; MR 98d:90058], and also yields an improved bound on the quality of a well-known linear programming relaxation of the problem.” 2001b:90025 90B35 68M20 Goldman, Sally A. ... Summary: “This paper addresses the problem of finding a feasible schedule of n jobs on m parallel machines, where each job has a deadline and some jobs are preassigned to some machine. ...
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