model "Balanced Transportation"
uses "mmxprs"; !gain access to the Xpress-Optimizer solver

parameters
	NUMPLANTS= 3
	NUMCITIES= 4
end-parameters

!sample declarations section
declarations
	!declare sets
	PLANTS= 1..NUMPLANTS
	CITIES=1..NUMCITIES
	
	!declare parameters
	Cost: array(PLANTS,CITIES) of real
	Supply: array(PLANTS) of real
	Demand: array(CITIES) of real
	
	!declare variables
	transport: array(PLANTS,CITIES) of mpvar
	
	TotalCost: linctr
	SupplyConstraint: array(PLANTS) of linctr
end-declarations

!initialisations
Cost::[8,6,10,9,9,12,13,7,14,9,16,5]
Supply::[35,50,40]
Demand::[45,20,30,30]

!constraints
forall(i in PLANTS) do
	SupplyConstraint(i):=
	sum(j in CITIES) transport(i,j) = Supply(i)
end-do

forall(j in CITIES) do
	sum(i in PLANTS) transport(i,j) = Demand(j)
end-do

TotalCost:= sum(i in PLANTS, j in CITIES) Cost(i,j) * transport(i,j)

minimise(TotalCost)

writeln("Total cost is: $", getobjval)

end-model