(1)maxChhSubject to:(2)VI<h≤HCh-Ph≥0KX从=1VI<h<H(3)kl(4)Ch-(Ch-Pu)+YhRM>0VI≤h,h≤H(5)Ch-(CH-PH)-(1-YhR)M≤0VI≤h,h≤HKKM(YHH+YRA)≥EKXhK-iX+1(6)VI≤h<h≤Hk=1(7)X,Y=oorIVl≤h,H≤H,VI<k≤K
The objective function (l)minimizes the makespan of handling one single container vessel, which is the latestcompletion timeamongall holds.Constraints (2)definetheproperty of thedecision variable Ch.Constraints(3)ensurethat everyholdmustbeperformedonlybyonequaycrane.Constraints(4)and(5)definetheproperties ofdecisionvariables Yh.w:Constraints (4)indicate thatYh,= if C,≤Cw-pw,whichmeans Yh=1when hold h finishes no later than hold h'starts; Constraints (5)indicate that Yh=0 if Ch>Cw-Pw,whichmeans Yh=O when hold h finishes after hold h'starts.Finally,the interference between quay cranes can beavoided by imposing Constraints(6).Suppose thatholds hand h'areperformed simultaneouslyand h<h',then this means that Yhu + Yw',h = o. Note that both quay cranes and holds are arranged in an increasing or-der from the front to the tail of the container vessel.Thus, if quay crane k handles hold h and quay crane!handlesholdh,thenk+I≤l