proc optmodel;

set Period = {1,2,3,4,5,6,7,8,9,10,11,12};
set Period_with_Zero = {0,1,2,3,4,5,6,7,8,9,10,11,12};

number Capacity = 99999;
number Demand{Period} = [200 150 100 50 50 100 150 200 200 250 300 250];
number HoldingCost = 1;
number SetupCost = 500;
number M = sum{t in Period}Demand[t];

var QuantityProduced{Period} >= 0;
var Inventory{Period_with_Zero} >= 0;
var Production{Period} binary;

minimize TotalCost = 
/*Setup Cost*/
sum{t in Period}(SetupCost*Production[t])
+
/*Inventory Holding Cost*/
sum{t in Period}(HoldingCost*Inventory[t])
;

con StartingInventory: Inventory[0]=0;
con ManufacturingCapacity{t in Period}: QuantityProduced[t]<=Capacity;
con FlowConservation{t in Period}: QuantityProduced[t]-Demand[t]+Inventory[t-1]-Inventory[t]=0;
con LinkingConstraint{t in Period}:QuantityProduced[t]-M*Production[t]<=0;

solve;
print TotalCost Production QuantityProduced;
quit;