/* 

  Transportation problem in Picat.

  This is in princple the same model as in 
  Pascal Van Hentenryck "The OPL Optimization Programming Language",
  page 116.

  Data from OPL example transp1.dat


  This Picat model was created by Hakan Kjellerstrand, hakank@gmail.com
  See also my Picat page: http://www.hakank.org/picat/

*/


import mip.


main => go.


go =>
  capacity(Capacity),
  supply(Supply),
  demand(Demand),
  cost(Cost),

  NumProducts = Supply.length,
  NumCities = Supply[1].length,
  
  % decision variables
  Trans = new_array(NumProducts,NumCities,NumCities),
  % Trans.vars() :: 0.0..1000000.0,

  % Z :: 0.0..10000000.0,
  Z #= sum([ Cost[P,O,D] * Trans[P,O,D] : P in 1..NumProducts , O in 1..NumCities, D in 1..NumCities]),


  foreach(P in 1..NumProducts , O in 1..NumCities) 
      sum([Trans[P,O,D] : D in 1..NumCities]) #= Supply[P,O]
  end,

  foreach(P in 1..NumProducts , D in 1..NumCities)
    sum([Trans[P,O,D] : O in 1..NumCities]) #= Demand[P,D]
  end,

  foreach(O in 1..NumCities, D in 1..NumCities)
     sum([Trans[P,O,D] : P in 1..NumProducts]) #<= Capacity
  end,


  solve($[min(Z)],Trans),

  println(z=Z),
  println("Trans:"),
  foreach(T in Trans)
    foreach(R in T)
     foreach(S in R)
       printf("%6.1f ", S)
     end,
     nl
    end
  end,  


  nl.


capacity(Capacity) => Capacity = 625.0.

% 1..NumProducts,1..NumCities
supply(Supply) =>
  Supply = 
  [
   [400.0,  700.0,  800.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
   [800.0, 1600.0, 1800.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0],
   [200.0,  300.0,  300.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
  ].

% 1..NumProducts,1..NumCities
demand(Demand) => 
  Demand = 
  [
    [0, 0, 0,300,300,100, 75,650,225,250], % bands
    [0, 0, 0,500,750,400,250,950,850,500], % coils
    [0, 0, 0,100,100,  0, 50,200,100,250]  % plate
  ].

% 1..NumProducts, 1..NumCities,1..NumCities
cost(Cost) =>
  Cost =
   [
   % bands
      [
       [0,    0,    0,    30,  10,    8,   10,   11,   71,    6],
       [0,    0,    0,    22,   7,   10,    7,   21,   82,   13],
       [0,    0,    0,    19,  11,   12,   10,   25,   83,   15],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0]   
      ]
   ,
    % coils
      [
       [0,    0,    0,   39,   14,   11,   14,   16,   82,    8],
       [0,    0,    0,   27,    9,   12,    9,   26,   95,   17],
       [0,    0,    0,   24,   14,   17,   13,   28,   99,   20],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0]   
     ]
   ,
   % plate
     [
       [0,    0,    0,   41,   15,   12,   16,   17,   86,    8],
       [0,    0,    0,   29,    9,   13,    9,   28,   99,   18],
       [0,    0,    0,   26,   14,   17,   13,   31,  104,   20],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0],
       [0,    0,    0,    0,    0,    0,    0,    0,    0,    0]
     ]
  ].