Mass Transportation Problems(Rachev)

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1、Tomywife,Zoja,Zvetlozar(Zari)RachevandtomyparentsNadezdaandTodorRachevi.Tomywife,Gabi.LudgerR¨uschendorfPrefacetoVolumeIThesubjectofthisbook,masstransportationproblems(MTPs),concernstheoptimaltransferofmassesfromonelocationtoanother,wheretheoptimalitydependsuponthecontextoftheproblem.Masstr

2、ansportationproblemsappearinvariousformsandinvariousareasofmathematicsandhavebeenformulatedatdifferentlevelsofgenerality.Whereasthecontin-uouscaseofthetransportationproblemmaybecastinmeasure-theoreticterms,thediscretecasedealswithoptimizationovergeneralizedtrans-portationpolyhedra.Accordingl

3、y,workontheseproblemshasdevelopedinseveralseparateandindependentdirections.Theaimofthismonographistoinvestigateandtodevelop,inasystem-aticfashion,theMonge–Kantorovichmasstransportationproblem(MKP)andtheKantorovich–Rubinsteintransshipmentproblem(KRP).Wecon-siderseveralmodificationsoftheseprob

4、lemsknownastheMTPwithpar-tialknowledgeofthemarginalsandtheMTPwithadditionalconstraints(MTPA).Wealsodiscussextensivelyavarietyofstochasticapplications.InthefirstvolumeofMassTransportationProblemsweconcentrateonthegeneralmathematicaltheoryofmasstransportation.InVolumeIIweexpandthescopeofapplic

5、ationsofmasstransportationproblems.In1781GaspardMongeproposedinsimpleproseaseeminglystraightfor-wardproblemofoptimization.Itwasdestinedtohavewideramifications.Hebeganhispaperonthetheoryof“clearingsandfillings”asfollows:Whenonemusttransportsoilfromonelocationtoanother,thecustomistogivethenamec

6、learingtothevolumeofthesoilthatoneviiiPrefacetoVolumeImusttransportandthenamefilling(“remblai”)tothespacethatitmustoccupyaftertransfer.Sincethecostoftransportationofonemoleculeis,allotherthingsbeingequal,proportionaltoitsweightandtheintervalthatitmusttravel,andconsequentlythetotalcostoftrans

7、portationbe-ingproportionaltothesumoftheproductsofthemoleculeseachmultipliedbytheintervaltraversed;giventheshapeandposition,theclearingandthefilling,itisnotthesameforonemoleculeoftheclearingtobemovedtooneoranotherspotofthefilling.Rather,thereisacertaindist