(!******************************************************
   Xpress-SP Example
   ======================
   ``````````````````
   FILE: CapacityExpansionExhaustive.mos
   
   DESCRIPTION: Stochastic multi-stage linear model
   
   TYPE: Energy
   
      In a power-generating plant, we consider three modes 
   of operations; namely low, average, and high. Clearly, 
   the trend of power demanded in each year may vary depending 
   on various factors such as rainfall, weather conditions, 
   etc. We also consider three technologies (old, current, 
   and new). Capacity expansion plans and the operational 
   decisions need to be laid out for next three years. The 
   objective is to minimize the expected total investment 
   and production cost.
   
   MODEL: 
   • Sets
   	o Stages=1..4 :indexed by t 
   	o Technology={old,curr,new} :indexed by i 
   	o Modes={low,avg,high} :indexed by j 
   • Data 
   	o g(i,t): existing capacity of technology i added at time t 
   	o r(i,t):investment cost per unit of capacity of technology i added at time t 
   	o q(i,t):production cost per unit of capacity of technology i added at time t 
   • Decision variables
   	o x(i,t): capacity of technology i added at time t 
   	o y(i,j,t):capacity of type i dedicated in mode j at time t 
   • Constraints 
   	o Accumulated Capacity balance 
   	o Demand balance 
   • Objective 
   	o minimize the expected total investment and production cost
   	
   	
   The capacities are added in the first two years and hence the total available 
   capacities are realized in the second and the third year. In the years second 
   through fourth, the available capacities are distributed among different modes.
  
   The scenarios are created by discretizing the load-duration curve. For simplicity,
   the duration in each mode is considered one-third of a year. We present following way 
   of generating scenarios: 
    Exhaustive: The demand (low, average, and high) has an independent distribution 
   in each year.  
  
   FURTHER INFO: 
   	see section II.4.6: Capacity Expansion of Electric Power Generation Systems, 
   	'Stochastic Modeling in Economics and Finance' - Jitka Dipacova, Jan Hurt, and Joseph Stepan,
   	Kluwer Academic Publishers
   
   	see Xpress-SP guide
      	
   DATE: Oct 2006			
   
   (c) 2006 Dash Associates
       Author: Nitin Verma
       Dash Optimization Inc, NJ  
       
*******************************************************!)
model CapacityExpansion
uses 'mmsp'
parameters
	T=4			!years
	DIR="Data/"
end-parameters
forward procedure generateExhaustiveTree
declarations
	Stages=1..T
	Technology={"old","curr","new"}
	Modes={"low","avg","high"}
	
	r:array(Technology,1..T-2) of real
		!investment cost in $1000/MW capacity added
	g:array(Technology,1..T-1) of real !existing capacity in MW
	q:array(Technology,2..T) of real
		!unit production cost in $1000/MWh
	tau:real !time in hour spent in each mode
	Budget:real !maximum additional capacity that can be added in MW
	Penalty:real !for not meeting demand in $1000/MW
end-declarations

declarations
	d:array(Modes,2..T) of sprand !total demand in MW
	umd:array(Modes,1..T-1) of spvar !total unmet demand in MW
	x:array(Technology,1..T-2) of spvar !additional capacity in MW
	w:array(Technology,2..T-1) of spvar
		!total available capacity in MW
	y:array(Technology,Modes,2..T) of spvar
		!capacity used in production in MW
	Cost:splinctr
	BudgetSpent:splinctr
	AccumulatedCapacity:array(Technology,2..T-1) of splinctr
	Demand:array(Modes,1..T-1) of splinctr
	Capacity:dynamic array(Technology,1..T-1) of splinctr
end-declarations

! Read in data from external file
initializations from DIR+'CapacityExpansion.dat'
	r q g tau Budget Penalty
end-initializations

setparam('xsp_implicit_stage',true)
spsetstages(Stages)
generateExhaustiveTree

Cost:=sum(t in 1..T-2,i in Technology) r(i,t)*x(i,t) +
		sum(t in 2..T,i in Technology,j in Modes) q(i,t)*tau*y(i,j,t) +
		sum(j in Modes,t in 1..T-1) Penalty*umd(j,t)
BudgetSpent:=sum(i in Technology,t in 1..T-2) x(i,t)<=Budget
forall(i in Technology,t in 2..T-1)
    if(t-1>=2) then AccumulatedCapacity(i,t):=w(i,t)=x(i,t-1)+w(i,t-1);
	else AccumulatedCapacity(i,t):=w(i,t)=x(i,t-1)
	end-if
forall(j in Modes,t in 1..T-1) Demand(j,t):=umd(j,t)+
sum(i in Technology) y(i,j,t+1)>=d(j,t+1)
forall(i in Technology,t in 1..T-1)
	if(t>=2) then Capacity(i,t):=sum(j in Modes) 
								y(i,j,t+1)<=(g(i,t)+w(i,t));
	else Capacity(i,t):=sum(j in Modes) y(i,j,t+1)<=g(i,t)
	end-if

forall(t in 2..T) OperatingCost(t):=sum(i in Technology,j in Modes) 
									q(i,t)*tau*y(i,j,t)
minimize(Cost)
writeln(getobjval)

procedure generateExhaustiveTree
	declarations
		E=3 !max # values, each demand can assume
		val,prob:array(Modes,2..T,1..E) of real
	end-declarations
	initializations from DIR+'CapacityExpansionExhaustive.dat'
		val prob
	end-initializations
	declarations
		vals,probs:array(1..E) of real
	end-declarations                     
	forall(j in Modes,t in 2..T) do
		forall(e in 1..E) do
			vals(e):=val(j,t,e)
			probs(e):=prob(j,t,e)
		end-do
		spsetdist(d(j,t),vals,probs)
	end-do
	spgenexhtree
end-procedure

end-model