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dekker.one
1include "fzn_network_flow.mzn";
2include "fzn_network_flow_reif.mzn";
3include "fzn_network_flow_cost.mzn";
4include "fzn_network_flow_cost_reif.mzn";
5
6/** @group globals
7 Defines a network flow constraint.
8
9@param arc: a directed arc of the flow network. Arc \p i connects node \a arc[\p i,1] to node \a arc[\p i,2].
10@param balance: the difference between input and output flow for each node.
11@param flow: the flow going through each arc.
12*/
13
14predicate network_flow(array[int,1..2] of int: arc,
15 array[int] of int: balance,
16 array[int] of var int: flow) =
17
18 let {
19 set of int: ARCS = index_set_1of2(arc);
20 set of int: NODES = index_set(balance);
21 } in
22 assert (
23 ARCS == index_set(flow) /\
24 lb_array(arc) >= min(NODES) /\
25 ub_array(arc) <= max(NODES),
26 "network_flow: wrong sizes of input array parameters",
27 fzn_network_flow(arc, balance, flow)
28 );
29
30/** @group globals
31 Defines a network flow constraint with cost.
32
33@param arc: a directed arc of the flow network. Arc \p i connects node \a arc[\p i,1] to node \a arc[\p i,2].
34@param balance: the difference between input and output flow for each node.
35@param weight: the unit cost of the flow through the arc.
36@param flow: the flow going through each arc.
37@param cost: the overall cost of the flow.
38*/
39predicate network_flow_cost(array[int,1..2] of int: arc,
40 array[int] of int: balance,
41 array[int] of int: weight,
42 array[int] of var int: flow, var int: cost) =
43
44 let {
45 set of int: ARCS = index_set_1of2(arc);
46 set of int: NODES = index_set(balance);
47 } in
48 assert (
49 ARCS == index_set(flow) /\
50 ARCS == index_set(weight) /\
51 lb_array(arc) >= min(NODES) /\
52 ub_array(arc) <= max(NODES),
53 "network_flow: wrong sizes of input array parameters",
54 fzn_network_flow_cost(arc, balance, weight, flow, cost)
55 );