MinimizeWsubjectto(1)Ci≤Wi=1,2....,NMZYm=1 i=1,2...N(2)m=1N+1Z(3)Xujm≤Yimi=1,2,...,Nj=landi+)ND(4)Xijm≤Yjmj=1,2,**.Ni=land i+j1≥Xijm+Xjm≥Yim+Yjm-1i,j=1,2,...,Nyandij;(5)m=12,.MJanditj;C+ID.P, +T≤K(I-Xijm)+Cji,j=1,2,...,N(6)m=1,2,...M(7)a+T≤Ci=1,2,.....N(8)rm+t..P+T≤Ci=1,2,...,N:m=1,2....,MXijmYime(0,1)i=0,1....,N-I;j=1,2....,N;m=1,2.....M(9)(10)Candw≥0j=l,2....,NwhereKisalargepositivenumber
Theobjectiveof thetruck scheduling problemistominimizethemakespan of theN jobs.Constraints(1)givethemakespan.Constraints(2)ensurethateach jobis processedby onlyonetruck.Constraints(3)-(5)givetherelationshipbetweenXandYforjobsprocessedbythe sametruck.Constraints(3)ensurethat Yim=1 if truck m processes a job after job iConstraints(4)ensurethatYim=1if truckm processes a jobbefore jobi.Constraints(5)ensure that if Yim+Yim=2,truck m processes either jobibefore job jor jobjbeforejobi.Constraints(6)givetherelationshipbetweenthecompletiontimeof a jobandthatofitssuccessor.Constraints(7)statetherelationshipbetweenthecompletiontime,readytime,andduration of a job.Constraints (8)give therelationship between the duration and completiontime of a job,the truck readytime, and the travel time of a truck from its initial location tothepick-up location.Constraints(9)and (10)are simpleconstraints which definetherangeofvaluesforX,Y.CandW
. The truck scheduling problem is equivalent to the problem ofscheduling M identical machines (trucks)tohandle Nnon-preemptive jobs withsequence-dependent processing times anddifferent ready times to minimize makespan
• The truck scheduling problem is equivalent to the problem of scheduling M identical machines (trucks) to handle N non-preemptive jobs with sequence-dependent processing times and different ready times to minimize makespan