% RUNS ON mzn_mer_fd
% RUNS ON mzn_mer_lp
% RUNS ON zinc_fdic_mznlib
% RUNS ON minizinc_cpx
% RUNS ON minizinc_fd
%-----------------------------------------------------------------------------
% Warehouse allocation
% (Problem 034 in CSPLib)
% vim: ft=zinc ts=2 sw=2 et tw=0
%
% Guido Tack, tack@gecode.org
% 2007-02-22
%
% Ported from the Gecode example
%-----------------------------------------------------------------------------
% A company needs to construct warehouses to supply stores with goods.  Each
% warehouse possibly to be constructed has a certain capacity defining how many
% stores it can supply.  Constructing a warehouse incurs a fixed cost.  Costs
% for transportation from warehouses to stores depend on the locations of
% warehouses and stores.
%
% Determine which warehouses should be constructed and which warehouse should
% supply which store such that overall cost (transportation cost plus
% construction cost) is smallest.
%-----------------------------------------------------------------------------

include "globals.mzn";

%-----------------------------------------------------------------------------
% Instance

n_suppliers = 5;
n_stores = 10;
building_cost = 30;

capacity = [1,4,2,1,3];

cost_matrix =
[|20, 24, 11, 25, 30
|28, 27, 82, 83, 74
|74, 97, 71, 96, 70
| 2, 55, 73, 69, 61
|46, 96, 59, 83,  4
|42, 22, 29, 67, 59
| 1,  5, 73, 59, 56
|10, 73, 13, 43, 96
|93, 35, 63, 85, 46
|47, 65, 55, 71, 95|];

%-----------------------------------------------------------------------------
% Model

int: n_suppliers;
int: n_stores;
int: building_cost;
array[1..n_suppliers] of int: capacity;
array[1..n_stores,1..n_suppliers] of int: cost_matrix;

int: MaxCost = max(i in 1..n_stores, j in 1..n_suppliers)(cost_matrix[i,j]);
int: MaxTotal =   (n_suppliers * building_cost)
+ sum(i in 1..n_stores, j in 1..n_suppliers)(cost_matrix[i,j]);

array[1..n_stores] of var 1..n_suppliers: supplier;
array[1..n_suppliers] of var bool: open;
array[1..n_stores] of var 1..MaxCost: cost;
var 1..MaxTotal: tot;

constraint
sum (i in 1..n_suppliers) (building_cost * bool2int(open[i])) +
sum (i in 1..n_stores) (cost[i])
= tot;

constraint
forall (i in 1..n_stores) (
cost_matrix[i,supplier[i]] = cost[i]
);

constraint
forall (i in 1..n_suppliers) (
let {
var int: use
} in
count(supplier,i,use) /\ use <= capacity[i]
);

constraint
forall (i in 1..n_suppliers) (
(exists (j in 1..n_stores) (supplier[j] == i)) == open[i]
);

solve
:: int_search(
supplier ++ cost ++ [bool2int(open[i]) | i in 1..n_suppliers],
first_fail,
indomain_split,
complete
)
minimize tot;

output
[ "warehouses:" ]
++
[ "\ntot = ", show(tot) ]
++
[ "\nsupplier = [\n" ]
++
[ "\t" ++ show(supplier[i]) ++
if i = n_stores then "\n]"
elseif i mod 5 = 0 then ",\n"
else ","
endif
| i in 1..n_stores
]
++
[ "\ncost = [\n" ]
++
[ "\t" ++ show(cost[i]) ++
if i = n_stores then "\n]"
elseif i mod 5 = 0 then ",\n"
else ","
endif
| i in 1..n_stores
]
++
[ "\nopen = [\n" ]
++
[ "\t" ++ show(open[i]) ++
if i = n_suppliers then "\n]\n"
elseif i mod 5 = 0 then ",\n"
else ","
endif
| i in 1..n_suppliers
]

%-----------------------------------------------------------------------------
%-----------------------------------------------------------------------------