#
# Aggregate Planning Model Example solve on NEOS server (who does not like end;)
#

set PROD;       # Set of products
param T > 0;    # Time horizon (number of months)

param InitWrk >=0; # Initial work force
param OTLimit >=0; # Over-time limit in relation to regular time of the labor

param Demand{PROD, 1..T}  >= 0; # Demand for each product in each period

param InvCost{PROD} >= 0; # Inventory cost for each product
param StCost{PROD}  >= 0; # Stock out cost for each product
param PrCost{PROD}  >= 0; # Production cost for each product
param SubCost{PROD} >= 0; # Subcontracting cost for each product
param ProdRate{PROD}>= 0; # Production rate per period for each product
param ProdTime{PROD}>= 0; # Time required to produce a unit of a product

param InitInv{PROD} >= 0; # Initial Inventory for each product
param InitOut{PROD} >= 0; # Initial stock out/backlog for each product

param FinInv{PROD} >= 0; # Final Inventory for each product
param FinOut{PROD} >= 0; # Final stock out/backlog for each product

param FTCost{1..T} >= 0; # Full-time workers cost per period
param OTCost{1..T} >= 0; # Over-time cost per period
param HCost{1..T}  >= 0; # Hiring cost of new labor per period
param LCost{1..T}  >= 0; # Layoff cost per period


var w{0..T} >= 0; # Total numbers of emploees working in each period
var h{1..T} >= 0; # Workesrs hired at the beginning of a period 
var l{1..T} >= 0; # Workers laid off at the beginning of a period
var o{1..T} >= 0; # Overtime hours worked in period t

var W{p in PROD, t in 1..T} >= 0; # Labor working on product p in month t
var P{p in PROD, t in 1..T} >= 0; # Units of product p produced at the end of period t
var I{p in PROD, t in 0..T} >= 0; # Inventory of product p at the end of perio t
var S{p in PROD, t in 0..T} >= 0; # Units of product p stocked out/backlogged at the end of period t
var C{p in PROD, t in 1..T} >= 0; # Units of product p subcontracted for period t
var O{p in PROD, t in 1..T} >= 0; # Overtime hours on product p in period t

minimize total_cost:
     sum{t in 1..T} ( FTCost[t]*w[t] + OTCost[t]*o[t] + HCost[t]*h[t] + LCost[t] *l[t] ) +
     sum{p in PROD, t in 1..T} ( InvCost[p]*I[p,t] + StCost[p]*S[p,t] + PrCost[p]*P[p,t] + SubCost[p]*C[p,t]);

subject to workforce{t in 1..T}:
      w[t] = w[t-1] + h[t] -l[t];

subject to total_workforce{t in 1..T}:
      w[t] = sum{p in PROD} W[p,t];

subject to capacity{p in PROD, t in 1..T}:
      P[p,t] <= ProdRate[p]*W[p,t] + O[p,t]/ProdTime[p];

subject to overtime{p in PROD, t in 1..T}:
      O[p,t] <= OTLimit * W[p,t];

subject to total_overtime{t in 1..T}:
      o[t] = sum{p in PROD} O[p,t];

subject to inventory_balance{p in PROD, t in 1..T}:
	I[p,t-1] + P[p,t] + C[p,t] = Demand[p,t] + S[p,t-1] + I[p,t] - S[p,t];

subject to initial_workforce:
        w[0] = InitWrk;

subject to initial_inventory{p in PROD}:
	I[p,0] = InitInv[p];

subject to initial_stock_out{p in PROD}:
        S[p,0] = InitOut[p];
        
subject to final_inventory{p in PROD}:
        I[p,T] = FinInv[p];

subject to final_stock_out{p in PROD}:
        S[p,T] = FinOut[p];

# end;

data;

set PROD := A B;

param T := 6;

param OTLimit := 48;

param InvCost := A 2 B 3;

param StCost := A 6 B 8;

param PrCost := A 10 B 15;

param SubCost := A 35 B 50;

param ProdRate := A 480 B 320;

param ProdTime := A 0.33 B 0.50;

param FTCost := 1 2560 2 2560 3 2560 4 2560 5 2560 6 2560;

param OTCost := 1 24 2 24 3 24 4 24 5 24 6 24;

param HCost := 1 200 2 200 3 200 4 200 5 200 6 200;

param LCost := 1 300  2 300  3 300  4 300  5 300 6 300;

param Demand :   1    2    3    4    5    6 :=
		A       1300 1500 2000 1400 2000 1800   
		B       1000 3000 4000 2000 2000 2200 ;

param InitInv := A 50 B 50;

param FinInv := A 50 B 50;

param InitOut := A 0 B 0;

param FinOut := A 0 B 0;

param InitWrk = 15;


# end;

solve;

display total_cost;

display w;

dispaly o;

display P;

display I;

display S;

display C;