Improved polynomialalgorithmsforrobustbottleneckproblemswithintervaldata

To modeluncertaintiesinaproblemonecanprovideintervalsofuncertaintyspecifyingarangeforeach uncertain parametervalue.Tohedgeagainst`worst-casescenariosʹ,i.e.,mostunwelcomerealizationsof the uncertainparametersafterasolutionhasbeendetermined,the minmax-regret criterion hasbeen adopted inrobustoptimization.Withinthisfield,weconsiderbottleneckproblemswithoneormore uncertain parameterfunctions. We applyaknownpolynomialtimesolutionschemeforanumberofspecificproblemsofthistypewith one uncertainparameterfunction.Thisleadstoimprovedalgorithmsofreducedcomplexity,e.g.,forthe bottleneck Steinertreeproblemandthebottleneckassignmentproblem. Further, weformulateaframeworktosolvesinglemachineschedulingproblemsinpolynomialtime under themaximumtardinesscriterion,withuptothreeuncertainparameterfunctions.