Research Article Introducing the MCHF/OVRP/SDMP: Multicapacitated/Heterogeneous Fleet/Open Vehicle Routing Problems with Split Deliveries and Multiproducts Duygu Yilmaz Eroglu, Burcu Caglar Gencosman, Fatih Cavdur, and H. Cenk Ozmutlu Department of Industrial Engineering, Uludag University, Gorukle, 16059 Bursa, Turkey CorrespondenceshouldbeaddressedtoDuyguYilmazEroglu;duygueroglu@uludag.edu.tr Received25February2014;Revised7May2014;Accepted7May2014;Published16June2014 AcademicEditor:Chin-ChiaWu Copyright©2014DuyguYilmazErogluetal. hisisanopenaccessarticledistributedundertheCreativeCommonsAttribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In this paper, we analyze a real-world OVRP problem for a production company. Considering real-world constrains, we classifyourproblemasmulticapacitated/heterogeneous leet/openvehicleroutingproblemwithsplitdeliveriesandmultiproduct (MCHF/OVRP/SDMP)whichisanovelclassiicationofanOVRP.Wehavedevelopedamixedintegerprogramming(MIP)model fortheproblemandgeneratedtestproblemsindiferentsize(10–90customers)consideringreal-worldparameters.AlthoughMIP isableto indoptimalsolutionsofsmallsize(10customers)problems,whenthenumberofcustomersincreases,theproblemgets hardertosolve,andthusMIPcouldnotindoptimalsolutionsforproblemsthatcontainmorethan10customers.Moreover,MIP failsto indanyfeasiblesolutionoflarge-scaleproblems(50–90customers)withintimelimits(7200seconds). herefore,we have developedageneticalgorithm(GA)basedsolutionapproachforlarge-scaleproblems. heexperimentalresultsshowthattheGA basedapproachreachessuccessfulsolutionswith9.66%gapin392.8sonaverageinsteadof7200sfortheproblemsthatcontain 10–50 customers. For large-scale problems (50–90 customers), GA reaches feasible solutions of problems within time limits. In conclusion,forthereal-worldapplications,GAispreferableratherthanMIPtoreachfeasiblesolutionsinshorttimeperiods. 1. Introduction Open vehicle routing problems (OVRPs) have gained much attention recently since they represent a problem type that needstobesolvedbymanyproductioncompanies.Inmost industries, companies choose to use a hired vehicle leet for distributing their goods. In this way, they do not have to endure the extra cost for returning vehicles since they use theresourcesofathird-partylogistics(3PL)providersuchas trucksorTIRs[1].Asconsequencesofsuchbeneits,however, thecompanieshavetoacceptsomerestrictionsdeinedbythe 3PLproviders.Forexample,the3PLprovidercandetermine some particular routes considering the experiences of the drivers or the highway conditions. In addition, the 3PL provider can restrict the number of customers visited by a particular vehicle. Such speciications require some changes intheclassicalOVRPstructuretomakethemmoreapplicable forreal-worldproblems. In this paper, we consider a real-world vehicle routing problem for a production company. he company produces twodiferenttypesofproducts(multipleproducts—MP)with diferent volume and weight properties. he irst product is a lightweight but large product, such as styrofoam, and the second product has opposite volume-weight characteristics, heavyweight but small product, such as tar. Since the com- pany uses a leet of vehicles of a 3PL provider, the vehicles donotneedtoreturntothedepot,andthus,theunderlying problembecomesanopenvehicleroutingproblem(OVRP). he3PLprovider hasaheterogeneousleetofvehicles, such astrucksandTIRs(heterogeneousleet—HF),withdiferent volumeandweightcapacities(multiplecapacitated—MC).In addition,onanyroute,thevehiclescanservetwocustomers atmost,andthedemandofacustomercanbesuppliedbydif- ferentvehicles(splitdelivery—SD).Basedontheseproblem speciications,weclassifyourproblemasamulticapacitated/ heterogeneous leet/open vehicle routing problem with split Hindawi Publishing Corporation e Scientific World Journal Volume 2014, Article ID 515402, 14 pages http://dx.doi.org/10.1155/2014/515402