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dekker.one
1/***
2!Test
3expected:
4- !Result
5 solution: !Solution
6 Total: 383
7 cost: [30, 27, 70, 2, 4, 22, 5, 13, 35, 55]
8 objective: 383
9 open: [true, true, true, false, true]
10 supplier: [5, 2, 5, 1, 5, 2, 2, 3, 2, 3]
11***/
12
13%-----------------------------------------------------------------------------
14% Warehouse allocation
15% (Problem 034 in CSPLib)
16% vim: ft=zinc ts=2 sw=2 et tw=0
17%
18% Guido Tack, tack@gecode.org
19% 2007-02-22
20%
21% Ported from the Gecode example
22%-----------------------------------------------------------------------------
23% A company needs to construct warehouses to supply stores with goods. Each
24% warehouse possibly to be constructed has a certain capacity defining how many
25% stores it can supply. Constructing a warehouse incurs a fixed cost. Costs
26% for transportation from warehouses to stores depend on the locations of
27% warehouses and stores.
28%
29% Determine which warehouses should be constructed and which warehouse should
30% supply which store such that overall cost (transportation cost plus
31% construction cost) is smallest.
32%-----------------------------------------------------------------------------
33
34include "globals.mzn";
35
36%-----------------------------------------------------------------------------
37% Instance
38
39n_suppliers = 5;
40n_stores = 10;
41building_cost = 30;
42
43capacity = [1,4,2,1,3];
44
45cost_matrix =
46 [|20, 24, 11, 25, 30
47 |28, 27, 82, 83, 74
48 |74, 97, 71, 96, 70
49 | 2, 55, 73, 69, 61
50 |46, 96, 59, 83, 4
51 |42, 22, 29, 67, 59
52 | 1, 5, 73, 59, 56
53 |10, 73, 13, 43, 96
54 |93, 35, 63, 85, 46
55 |47, 65, 55, 71, 95|];
56
57%-----------------------------------------------------------------------------
58% Model
59
60int: n_suppliers;
61int: n_stores;
62int: building_cost;
63array[1..n_suppliers] of int: capacity;
64array[1..n_stores,1..n_suppliers] of int: cost_matrix;
65
66int: MaxCost = max(i in 1..n_stores, j in 1..n_suppliers)(cost_matrix[i,j]);
67int: MaxTotal = (n_suppliers * building_cost)
68 + sum(i in 1..n_stores, j in 1..n_suppliers)(cost_matrix[i,j]);
69
70array[1..n_stores] of var 1..n_suppliers: supplier;
71array[1..n_suppliers] of var bool: open;
72array[1..n_stores] of var 1..MaxCost: cost;
73var 1..MaxTotal: Total;
74
75constraint
76 sum (i in 1..n_suppliers) (building_cost * bool2int(open[i])) +
77 sum (i in 1..n_stores) (cost[i])
78 = Total;
79
80constraint
81 forall (i in 1..n_stores) (
82 cost_matrix[i,supplier[i]] = cost[i]
83 );
84
85constraint
86 forall (i in 1..n_suppliers) (
87 let {
88 var int: use
89 } in
90 count(supplier,i,use) /\ use <= capacity[i]
91 );
92
93constraint
94 forall (i in 1..n_suppliers) (
95 (exists (j in 1..n_stores) (supplier[j] == i)) == open[i]
96 );
97
98solve
99 :: int_search(
100 supplier ++ cost ++ [bool2int(open[i]) | i in 1..n_suppliers],
101 first_fail,
102 indomain_split,
103 complete
104 )
105 minimize Total;
106
107output
108 [ "warehouses:" ]
109 ++
110 [ "\nTotal = ", show(Total) ]
111 ++
112 [ "\nsupplier = [\n" ]
113 ++
114 [ "\t" ++ show(supplier[i]) ++
115 if i = n_stores then "\n]"
116 elseif i mod 5 = 0 then ",\n"
117 else ","
118 endif
119 | i in 1..n_stores
120 ]
121 ++
122 [ "\ncost = [\n" ]
123 ++
124 [ "\t" ++ show(cost[i]) ++
125 if i = n_stores then "\n]"
126 elseif i mod 5 = 0 then ",\n"
127 else ","
128 endif
129 | i in 1..n_stores
130 ]
131 ++
132 [ "\nopen = [\n" ]
133 ++
134 [ "\t" ++ show(open[i]) ++
135 if i = n_suppliers then "\n]\n"
136 elseif i mod 5 = 0 then ",\n"
137 else ","
138 endif
139 | i in 1..n_suppliers
140 ]
141
142%-----------------------------------------------------------------------------
143%-----------------------------------------------------------------------------