简介:Thispaperconsiderssingle-machineschedulingproblemsingrouptechnologywiththejobs'processingtimesbeingsimplelinearfunctionsoftheirstarttimes.Theobjectivefunctionsaretheminimizingofmakespanandtotalweightedcompletiontime.SomeoptimalconditionsandalgorithmsaregivenandthefactthattheproblemoftotalweightedcompletiontimesisNP-hardisproved.
简介:Thispaperstudiesonlineschedulingofjobswithkindreleasetimesonasinglemachine.Here“kindreleasetime”meansthatinonlinesetting,nojobscanbereleasedwhenthemachineisbusy.EachjobJhasakindreleasetimer(J)≥0,aprocessingtimep(J)>0andadeadlined(J)>0.Thegoalistodetermineaschedulewhichmaximizestotalprocessingtime(∑p(J)E(J))ortotalnumber(∑E(J))oftheacceptedjobs.Forthefirstobjectivefunction∑p(J)E(J),wefirstpresentalowerbound√2,andthenprovideanonlinealgorithmLEJwithacompetitiveratioof3.Thisisthefirstdeterministicalgorithmfortheproblemwithaconstantcompetitiveratio.Whenp(J)∈{1,k},k>1isarealnumber,wefirstpresentalowerboundminf(1+k)/k,2k/(1+k)g,andthenweshowthatLEJhasacompetitiveratioof1+┌k┐=k.Inparticular,whenalltheklengthjobshavetightdeadlines,wefirstpresentalowerboundmax{4=(2+k),1}(for∑p(J)E(J))and4/3(for∑E(J)).ThenweprovethatLEJis┌k┐/k-competitivefor∑p(J)E(J)andweprovideanonlinealgorithmHwithacompetitiveratioof2┌k┐/(┌k┐+1)forthesecondobjectivefunction∑E(J).
简介:为无线特定的网络的大量应用程序是时间批评的并且在通讯潜伏上强加紧要求。关键通讯操作之一是从一个来源节点广播一条消息。这篇论文学习在没有碰撞的传播模型下面在无线特定的网络安排问题的最小的潜伏广播。为这个NP难的问题的以前最好的已知的算法生产其潜伏是至少648的一张广播时间表(r最大/rmin)2时间最佳的时间表,在哪儿r最大和rmin分别地是在一个网络的节点的最大、最小的传播范围。我们显著地由至多建议表演比率是其近似的一个新安排算法改进这结果(1+2r最大/rmin)2+32。而且,在建议安排下面,每个节点就需要至多提交一条消息一次。
简介:Thispaperconsidersaschedulingproblemintwo-stagehybridflowshop,wherethefirststageconsistsoftwomachinesformedanopenshopandtheotherstagehasonlyonemachine.Theobjectiveistominimizethemakespan,i.e.,themaximumcompletiontimeofalljobs.WefirstshowtheproblemisNP-hardinthestrongsense,thenwepresenttwoheuristicstosolvetheproblem.Computationalexperimentsshowthatthecombinedalgorithmofthetwoheuristicsperformswellonrandomlygeneratedprobleminstances.