I think I understand now. I have added now the travel time between the nodes and a new variable which is arrivaltime B{i,j}. Before I add the time constraints I Guess there should be a constraint which tells the value of the arrival time. I have written it like this: X[i,j,k]*runtime[i,j] = B[i]; => Desicion variables * runetime between the nodes = arrival time. After this I would constrain the arrival time to a upper and a lower time window. Is this the correct way to do it? If this is correct, what should come before: X[i,j,k]*runtime[i,j] = B[i];? It should be sum of all trucks. proc optmodel; /*DATA*/ set trucks = {1,2}; set customers = {0,1,2,3}; number distance{customers, customers}=[ 0 2 4 5 2 0 0.8 1.5 4 0.8 0 0.6 5 1.5 0.6 0 ]; number demand{customers} =[0 10 5 10]; number truckCapacity{trucks} = [20 20]; /*NEW DATA*/ /*Time windows Customer 0 (depot) => 07:00-07:00 Customer 1 => 07:00-07:30 Customer 2 => 07:00-07:50 Customer 3 => 08:00-08:30 */ number lowertimeWindows{customers}=[0 0 0 60]; number uppertimeWindows{customers}=[0 30 50 90]; number runtime{customers, customers}=[ 0 10 20 25 10 0 15 22 20 15 0 18 25 22 18 0]; /*VARIABLER*/ var X{customers,customers,trucks} binary; var Y{trucks, customers} binary; var Q{trucks,customers}; /*NEW VARIABLE*/ var B{customers}; /*The number of minutes it takes for the trucks to meet the demand*/ /*Objective function*/ minimize C = sum{i in customers, j in customers, k in trucks} distance[i,j]*X[i,j,k]; /*CONSTRAINTS*/ /*Each truck must start from depot*/ con startDepot{k in trucks} : sum{j in customers : j>0} X[0,j,k] = 1; /*Each truck must return to depot*/ con endDepot{k in trucks} : sum{i in customers : i>0} X[i,0,k] = 1; /*Flow conservation - what comes in - must come out*/ con flowConst{i in customers, k in trucks}: sum{j in customers : j ne i} (X[j,i,k] - X[i,j,k]) =0; /*Demand must be fulfilled*/ con demandFulfill{i in customers: i>0}: sum{k in trucks}Q[k,i] = demand[i]; /*Logical constraint: X -> Y*/ con xyConst{j in customers , k in trucks: j>0}: sum{i in customers : i ne j} X[i,j,k] = Y[k,j]; /*Logical constraint: Q -> Y*/ con qyConst{i in customers , k in trucks: i>0}: Q[k,i] <= demand[i]*Y[k,i]; /*Truck capacity in m^3*/ con truckCapacityConst{k in trucks}: sum{i in customers : i>0}Q[k,i] <= truckCapacity[k]; /*NEW CONSTRAINTS*/ con sum{} X[i,j,k]*runtime[i,j] = B[i]; solve with milp / maxtime=600; print X Y Q C B; quit;
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