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Manufacturingprocessesareresponsibleforaconsiderableamountofglobalenergyconsumption andworldCO 2 emissions.Reducingenergyconsumptionduringmanufacturingisconsideredoneof themostimportantstrategiesincontributingtothegreensupplychain.Inthiscontext,theauthors proposeanewpredictive-reactiveapproachtocontrolenergyconsumptionduringmanufacturing processes.Inadditiontoforecastingtheenergyneeds,theproposedapproachcontrolstheuncertainty ofenergyvolatilityandlimitsenergywasteduringmanufacturingprocesses.Withtheintegrationof thiseconomic-environmentalmanufacturingefficiencyinsupplychains,andcontrollinguncertainty, this approach positively contributes to green and agile supply chains. A multi-objective genetic algorithm(NSGA-2)isproposedasapredictivemethod,andanewreactivemethodisdevelopedto dynamicallycontroltheenergyconsumptionthroughoutthepeakenergyconsumptioninrealtime. TheapproachwastestedontheAIP-PRIMECAbenchmark,whichreflectsarealproductioncell.

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The aim of this paper is to give sufficient conditions on two normal and hyponormal operators (bounded or not), defined on a Hilbert space, which make their algebraic sum hyponormal (only in bounded case). The results are accompanied by some interesting examples and counter examples.