# ----------------------------------------

# STOCHASTIC PROGRAMMING PROBLEM 

# USING BENDERS DECOMPOSITION

# ----------------------------------------


### SUBPROBLEM (always feasible) ###



set PROD;    
# products
param 

T > 0;  
# number of weeks


set SCEN;     
# number of scenarios



param rate {PROD} > 0;          
# tons per hour produced


param avail {1..T} >= 0;        
# hours available in week


param market {PROD,1..T} >= 0;  
# limit on tons sold in week



param prodcost {PROD} >= 0;     
# cost per ton produced


param invcost {PROD} >= 0;      
# carrying cost/ton of inventory



param revenue {PROD,1..T,SCEN} >= 0;  
# projected revenue/ton



param prob {SCEN} >= 0, <= 1;
   

check: 0.99999 < sum {s in SCEN} prob[s] < 1.00001;



param inv1 {PROD} >= 0;  
# inventory at end of first period



var Make {PROD,2..T,SCEN} >= 0;        
# tons produced


var Inv {PROD,2..T,SCEN} >= 0;         
# tons inventoried


var Sell {p in PROD, t in 2..T, SCEN}  # tons sold
   >= 0, <= market[p,t];



maximize Stage2_Profit:
   
	sum {s in SCEN} prob[s] * sum {p in PROD, t in 2..T} (revenue[p,t,s]*Sell[p,t,s] -
 prodcost[p]*Make[p,t,s] - invcost[p]*Inv[p,t,s]);



subject to Time {t in 2..T, s in SCEN}:
   
	sum {p in PROD} (1/rate[p]) * Make[p,t,s] <= avail[t];



subject to Balance2 {p in PROD, s in SCEN}:
   Make[p,2,s] + inv1[p] = Sell[p,2,s] + Inv[p,2,s];



subject to Balance {p in PROD, t in 3..T, s in SCEN}:
   Make[p,t,s] + Inv[p,t-1,s] = Sell[p,t,s] + Inv[p,t,s];



### MASTER PROBLEM ###



param inv0 {PROD} >= 0;  
# initial inventory



param nCUT >= 0 integer;



param time_price {2..T,SCEN,1..nCUT} >= -0.000001;


param bal2_price {PROD,SCEN,1..nCUT};


param sell_lim_price {PROD,2..T,SCEN,1..nCUT} >= -0.000001;



var Make1{PROD} >= 0;


var Inv1 {PROD} >= 0;


var Sell1 {p in PROD} >= 0, <= market[p,1];



var Min_Stage2_Profit >= 0;



maximize Expected_Profit:
   
	sum {s in SCEN} prob[s] * sum {p in PROD} (revenue[p,1,s]*Sell1[p] - 
prodcost[p]*Make1[p] - invcost[p]*Inv1[p]) +
   Min_Stage2_Profit;



subj to Cut_Defn {k in 1..nCUT}:
   
	Min_Stage2_Profit <= 
sum {t in 2..T, s in SCEN} time_price[t,s,k] * avail[t] +
 sum {p in PROD, s in SCEN} bal2_price[p,s,k] * (-Inv1[p]) +
 sum {p in PROD, t in 2..T, s in SCEN}
         sell_lim_price[p,t,s,k] * market[p,t];



subject to Time1:
   
	sum {p in PROD} (1/rate[p]) * Make1[p] <= avail[1];



subject to Balance1 {p in PROD}:
   
	Make1[p] + inv0[p] = Sell1[p] + Inv1[p];