Page - 12 - in Algorithms for Scheduling Problems

Algorithms 2018,11, 18 Table1.TheTOUtariffsusedforall instances. PeriodType ElectricityPrice (CNY/kwh) TimePeriods On-peak 1.2473 8:00–11:30 18:30–23:00 Mid-peak 0.8451 7:00–8:00 11:30–18:30 Off-peak 0.4430 23:00–7:00 CmaxandCBdenote thegivenmakespanandthetotalprocessingtimesofall the jobs, respectively. Theparameter e=Cmax/CB (e≥1) isusedtomeasure thedegreeof timetightness. In these instances, Cmax can be obtained by the formulaCmax = e×CB as long as the parameter e is set. Obviously, as e increases,Cmax increases.Note that bm+1 is calculated by bm+1 = Cmax/24) ×24. LetTECF andTECHbethe totalelectricitycostcalculatedbyouralgorithm(GIH-F)andCheetal.’salgorithm (GIH), respectively. Theruntimesof the twoalgorithmsarerepresentedbyCTF andCTH, respectively. ThegapsbetweenTECFandTECHarerepresentedbyG,G=(TECF−TECH)/TECH×100%.Theratio ofCTH/CTF is representedbyR. 4.1.ARealCaseStudy TheMILPmodelandtheproposedalgorithmareapplied toaverticalmachiningcenter (SMTCL VMC1600P) fromamachinerymanufacturingcompanyshowninFigure8. In this real-life instance, the company receives someorders of processing rectangular partswith threeproductmodels for continuouscastingmachinesof thesteelplants. Figure9 is thepictureof the rectangularpart, and thecomplexcavitysurfaces including theplanes, cambersurfaces, andspherical surfacesare tobe processed on theVMC. Thepower consumptionper hour required by theVMC is related to the materialof the job, cuttingdepth, feedspeed,andsoon. Toobtain theaveragepowerconsumption rateof themachine,apowermeasurement isperformedusingapowermeter (UNI-TUT232), andthe measurementdata ispresentedbyTable2. Inaddition, theorderquantityof the threemodels is15,35, and10parts, respectively. Figure8.Verticalmachiningcenter. Figure9.Thegeometryof therectangularpart. 12