Trucking Scheduling inContainer Terminals
Trucking Scheduling in Container Terminals
.Typicalactivities involved in a transportation job performed by a truck areasfollows:(i)whenatransportationjobisdispatchedtoanidletruck,ittravelsfromthecontainerdrop-offlocationofitslastjobtothecontainerpick-uplocationofthedispatchedjobandwaitsfora crane (quay/yardcrane)toserveit;(ii)afterbeingloadedwithacontainerbythecrane,thetruck travelsto the container drop-off location and waits fora crane(yard/quay crane)to unload the container; (ii)once thecontainerisunloaded,thetruckisavailabletoperformanothertransportationjob.Thetimetoprocessatransportationjobdependsonthetimetakenbythecranetoload a container onto andoffthe truck and thetime spent bythetrucktravellingfromthecontainerdrop-offlocationofitslastjobtothepick-uplocationofthenextjob.Hence,theprocessingtimeofajobdependsonthejobprocessing sequence of thetruck dispatchedtoit
• Typical activities involved in a transportation job performed by a truck are as follows: (i) when a transportation job is dispatched to an idle truck, it travels from the container drop-off location of its last job to the container pick-up location of the dispatched job and waits for a crane (quay/yard crane) to serve it; (ii) after being loaded with a container by the crane, the truck travels to the container drop-off location and waits for a crane (yard/quay crane) to unload the container; (iii) once the container is unloaded, the truck is available to perform another transportation job. The time to process a transportation job depends on the time taken by the crane to load a container onto and off the truck and the time spent by the truck travelling from the container drop-off location of its last job to the pick-up location of the next job. Hence, the processing time of a job depends on the job processing sequence of the truck dispatched to it
.Transportinga container fromits pick-up locationto its drop-offlocationisreferredto asajobforthetrucks.· An efficient truck operation can speed up container handlingprocesses, smooth containerflows, and thus improve terminalperformance..Schedulingafleetoftruckstoperforma setoftransportationjobswith sequence-dependent processing timesand different readytimesto minimize makespan is formulated as an integer program
• Transporting a container from its pick-up location to its drop-off location is referred to as a job for the trucks. • An efficient truck operation can speed up container handling processes, smooth container flows, and thus improve terminal performance. • Scheduling a fleet of trucks to perform a set of transportation jobs with sequence-dependent processing times and different ready times to minimize makespan is formulated as an integer program
NotationsM-thenumberofidenticaltruckswithunitcarryingcapacity.N-numberofcontainerstobetransportedbytheMtrucksinthecurrentperiod:Lm-Initiallocationoftruckm.rm-Initialavailabletime of truckmP,-Pickuplocationofjobi.D,-Dropofflocationofjobitr-Truck (loadedorempty)traveltimebetween locationl'e(LmP,D)and locationle(P,D)alongtheshortestpathThe travelling time between two locations is equal to the rectilinear distance between the two locations divided by the truck travelling speed..a-ReadytimeofjobiT,-Durationof jobi(fromthemomentthatthetruckdispatchedforjobiarrivesatP(pick-uplocationforjobi)tothemomentthatitstartstoleaveD,(thedrop-offlocationofjobi).).Processingtimeofjobi=truckstartsmovingfromitscurrentlocationtoP,+T.Theprocessingtimeofeachjobissequencedependent
Notations • M - the number of identical trucks with unit carrying capacity • N - number of containers to be transported by the M trucks in the current period • Lm – Initial location of truck m • rm – Initial available time of truck m • Pi – Pickup location of job i • Di – Dropoff location of job i • tl’l – Truck (loaded or empty) travel time between location l’{Lm Pi Di } and location l {Pi Di } along the shortest path • The travelling time between two locations is equal to the rectilinear distance between the two locations divided by the truck travelling speed. • ai – Ready time of job i • Ti – Duration of job i (from the moment that the truck dispatched for job i arrives at Pi (pick-up location for job i) to the moment that it starts to leave Di (the drop-off location of job i).) • Processing time of job i = truck starts moving from its current location to Pi + Ti • The processing time of each job is sequence dependent
Xiim a binaryvariable which takesavalue of 1 iftruck m (m=1,2,..,M)processes jobjj=1,2,...,N+)after jobi(i=1,2,...,N),wherejobN+1isadummyjobusedtofacilitatetherepresentation of the case when job i isthelast job processedbytruckm.Yima binaryvariablewhich takes a value of 1 if truck m (m =l,2,...,M)processes jobi(i =1, 2,..., N).Cithecompletiontimeofjobi(i=l2,...,N).Wthe makespan of the N jobs.DenotethesetofXiimbyX,thesetof YimbyY,and thesetof CbyC