Example 4.5: Using an Unconstrained Solution Warm Start
This example examines
the effect of changing some of the arc costs.
The back order penalty costs are increased by twenty percent.
The sales profit of 25-inch TVs sent to the shops in May is
increased by thirty units.
The backorder penalty costs of 25-inch TVs manufactured in May
for April consumption is decreased by thirty units.
The production cost of 19- and 25-inch TVs made in May are
decreased by five units and twenty units, respectively.
How does the optimal solution of the network after these arc cost
alterations
compare with the optimum of the original network?
If you want to use
the warm start facilities of PROC NETFLOW to solve
this undefined problem,
specify the
WARM option.
Notice that the FUTURE1 option was specified in the last
PROC NETFLOW run.
These SAS statements produce the new NODEOUT= and ARCOUT= data sets.
title 'Minimum Cost Flow problem- Unconstrained Warm Start';
title2 'Production Planning/Inventory/Distribution';
data arc2;
set arc1;
oldcost=_cost_;
oldfc=_fcost_;
oldflow=_flow_;
if key_id='backorder'
then _cost_=_cost_*1.2;
else if _tail_='f2_may_2' then _cost_=_cost_-30;
if key_id='production' & mth_made='May' then
if diagonal=19 then _cost_=_cost_-5;
else _cost_=_cost_-20;
proc netflow
warm future1
nodedata=node2
arcdata=arc2
nodeout=node3
arcout=arc3;
proc print data=arc3 (drop = _status_ _rcost_);
var _tail_ _head_ _capac_ _lo_ _supply_ _demand_ _name_
_cost_ _flow_ _fcost_ oldcost oldflow oldfc
diagonal factory key_id mth_made _anumb_ _tnumb_;
/* to get this variable order */
sum oldfc _fcost_;
proc print data=node3;
run;
The following notes appear on the SAS log:
NOTE: Number of nodes= 21 .
NOTE: Number of supply nodes= 4 .
NOTE: Number of demand nodes= 5 .
NOTE: Total supply= 4350 , total demand= 4350 .
NOTE: Number of iterations performed (neglecting any
constraints)= 8 .
NOTE: Of these, 0 were degenerate.
NOTE: Optimum (neglecting any constraints) found.
NOTE: Minimal total cost= -1285086.45 .
NOTE: The data set WORK.ARC3 has 64 observations and
21 variables.
NOTE: The data set WORK.NODE3 has 20 observations and
10 variables.
The solution is displayed in Output 4.5.1.
Output 4.5.1: ARCOUT=ARC3
Minimum Cost Flow problem- Unconstrained Warm Start |
Production Planning/Inventory/Distribution |
Obs |
_tail_ |
_head_ |
_capac_ |
_lo_ |
_SUPPLY_ |
_DEMAND_ |
_name_ |
_cost_ |
_FLOW_ |
_FCOST_ |
oldcost |
oldflow |
oldfc |
diagonal |
factory |
key_id |
mth_made |
_ANUMB_ |
_TNUMB_ |
1 |
fact1_1 |
_EXCESS_ |
99999999 |
0 |
1000 |
200 |
|
0.00 |
5 |
0.00 |
0.00 |
5 |
0.00 |
. |
. |
|
|
65 |
1 |
2 |
fact2_1 |
_EXCESS_ |
99999999 |
0 |
850 |
200 |
|
0.00 |
45 |
0.00 |
0.00 |
45 |
0.00 |
. |
. |
|
|
66 |
10 |
3 |
fact1_2 |
_EXCESS_ |
99999999 |
0 |
1000 |
200 |
|
0.00 |
0 |
0.00 |
0.00 |
10 |
0.00 |
. |
. |
|
|
67 |
11 |
4 |
fact2_2 |
_EXCESS_ |
99999999 |
0 |
1500 |
200 |
|
0.00 |
150 |
0.00 |
0.00 |
140 |
0.00 |
. |
. |
|
|
68 |
20 |
5 |
fact1_1 |
f1_apr_1 |
600 |
50 |
1000 |
. |
prod f1 19 apl |
78.60 |
540 |
42444.00 |
78.60 |
600 |
47160.00 |
19 |
1 |
production |
April |
4 |
1 |
6 |
f1_mar_1 |
f1_apr_1 |
50 |
0 |
. |
. |
|
15.00 |
0 |
0.00 |
15.00 |
0 |
0.00 |
19 |
1 |
storage |
March |
5 |
2 |
7 |
f1_may_1 |
f1_apr_1 |
20 |
0 |
. |
. |
back f1 19 may |
33.60 |
0 |
0.00 |
28.00 |
0 |
0.00 |
19 |
1 |
backorder |
May |
6 |
4 |
8 |
f2_apr_1 |
f1_apr_1 |
40 |
0 |
. |
. |
|
11.00 |
0 |
0.00 |
11.00 |
0 |
0.00 |
19 |
. |
f2_to_1 |
April |
7 |
6 |
9 |
fact1_2 |
f1_apr_2 |
550 |
50 |
1000 |
. |
prod f1 25 apl |
174.50 |
250 |
43625.00 |
174.50 |
550 |
95975.00 |
25 |
1 |
production |
April |
36 |
11 |
10 |
f1_mar_2 |
f1_apr_2 |
40 |
0 |
. |
. |
|
20.00 |
0 |
0.00 |
20.00 |
0 |
0.00 |
25 |
1 |
storage |
March |
37 |
12 |
11 |
f1_may_2 |
f1_apr_2 |
15 |
0 |
. |
. |
back f1 25 may |
49.20 |
15 |
738.00 |
41.00 |
15 |
615.00 |
25 |
1 |
backorder |
May |
38 |
14 |
12 |
f2_apr_2 |
f1_apr_2 |
25 |
0 |
. |
. |
|
21.00 |
0 |
0.00 |
21.00 |
0 |
0.00 |
25 |
. |
f2_to_1 |
April |
39 |
16 |
13 |
fact1_1 |
f1_mar_1 |
500 |
50 |
1000 |
. |
prod f1 19 mar |
127.90 |
340 |
43486.00 |
127.90 |
345 |
44125.50 |
19 |
1 |
production |
March |
1 |
1 |
14 |
f1_apr_1 |
f1_mar_1 |
20 |
0 |
. |
. |
back f1 19 apl |
33.60 |
20 |
672.00 |
28.00 |
20 |
560.00 |
19 |
1 |
backorder |
April |
2 |
3 |
15 |
f2_mar_1 |
f1_mar_1 |
40 |
0 |
. |
. |
|
10.00 |
40 |
400.00 |
10.00 |
40 |
400.00 |
19 |
. |
f2_to_1 |
March |
3 |
5 |
16 |
fact1_2 |
f1_mar_2 |
400 |
40 |
1000 |
. |
prod f1 25 mar |
217.90 |
400 |
87160.00 |
217.90 |
400 |
87160.00 |
25 |
1 |
production |
March |
33 |
11 |
17 |
f1_apr_2 |
f1_mar_2 |
30 |
0 |
. |
. |
back f1 25 apl |
38.40 |
30 |
1152.00 |
32.00 |
30 |
960.00 |
25 |
1 |
backorder |
April |
34 |
13 |
18 |
f2_mar_2 |
f1_mar_2 |
25 |
0 |
. |
. |
|
20.00 |
25 |
500.00 |
20.00 |
25 |
500.00 |
25 |
. |
f2_to_1 |
March |
35 |
15 |
19 |
fact1_1 |
f1_may_1 |
400 |
50 |
1000 |
. |
|
90.10 |
115 |
10361.50 |
95.10 |
50 |
4755.00 |
19 |
1 |
production |
May |
8 |
1 |
20 |
f1_apr_1 |
f1_may_1 |
50 |
0 |
. |
. |
|
12.00 |
0 |
0.00 |
12.00 |
50 |
600.00 |
19 |
1 |
storage |
April |
9 |
3 |
21 |
f2_may_1 |
f1_may_1 |
40 |
0 |
. |
. |
|
13.00 |
0 |
0.00 |
13.00 |
0 |
0.00 |
19 |
. |
f2_to_1 |
May |
10 |
7 |
22 |
fact1_2 |
f1_may_2 |
350 |
40 |
1000 |
. |
|
113.30 |
350 |
39655.00 |
133.30 |
40 |
5332.00 |
25 |
1 |
production |
May |
40 |
11 |
23 |
f1_apr_2 |
f1_may_2 |
40 |
0 |
. |
. |
|
18.00 |
0 |
0.00 |
18.00 |
0 |
0.00 |
25 |
1 |
storage |
April |
41 |
13 |
24 |
f2_may_2 |
f1_may_2 |
25 |
0 |
. |
. |
|
13.00 |
0 |
0.00 |
43.00 |
0 |
0.00 |
25 |
. |
f2_to_1 |
May |
42 |
17 |
25 |
f1_apr_1 |
f2_apr_1 |
99999999 |
0 |
. |
. |
|
11.00 |
20 |
220.00 |
11.00 |
30 |
330.00 |
19 |
. |
f1_to_2 |
April |
14 |
3 |
26 |
fact2_1 |
f2_apr_1 |
480 |
35 |
850 |
. |
prod f2 19 apl |
62.40 |
480 |
29952.00 |
62.40 |
480 |
29952.00 |
19 |
2 |
production |
April |
15 |
10 |
27 |
f2_mar_1 |
f2_apr_1 |
30 |
0 |
. |
. |
|
18.00 |
0 |
0.00 |
18.00 |
0 |
0.00 |
19 |
2 |
storage |
March |
16 |
5 |
28 |
f2_may_1 |
f2_apr_1 |
15 |
0 |
. |
. |
back f2 19 may |
30.00 |
0 |
0.00 |
25.00 |
0 |
0.00 |
19 |
2 |
backorder |
May |
17 |
7 |
29 |
f1_apr_2 |
f2_apr_2 |
99999999 |
0 |
. |
. |
|
23.00 |
0 |
0.00 |
23.00 |
0 |
0.00 |
25 |
. |
f1_to_2 |
April |
46 |
13 |
30 |
fact2_2 |
f2_apr_2 |
680 |
35 |
1500 |
. |
prod f2 25 apl |
196.70 |
680 |
133756.00 |
196.70 |
680 |
133756.00 |
25 |
2 |
production |
April |
47 |
20 |
31 |
f2_mar_2 |
f2_apr_2 |
50 |
0 |
. |
. |
|
28.00 |
0 |
0.00 |
28.00 |
0 |
0.00 |
25 |
2 |
storage |
March |
48 |
15 |
32 |
f2_may_2 |
f2_apr_2 |
15 |
0 |
. |
. |
back f2 25 may |
64.80 |
0 |
0.00 |
54.00 |
15 |
810.00 |
25 |
2 |
backorder |
May |
49 |
17 |
33 |
f1_mar_1 |
f2_mar_1 |
99999999 |
0 |
. |
. |
|
11.00 |
0 |
0.00 |
11.00 |
0 |
0.00 |
19 |
. |
f1_to_2 |
March |
11 |
2 |
34 |
fact2_1 |
f2_mar_1 |
450 |
35 |
850 |
. |
prod f2 19 mar |
88.00 |
290 |
25520.00 |
88.00 |
290 |
25520.00 |
19 |
2 |
production |
March |
12 |
10 |
35 |
f2_apr_1 |
f2_mar_1 |
15 |
0 |
. |
. |
back f2 19 apl |
20.40 |
0 |
0.00 |
17.00 |
0 |
0.00 |
19 |
2 |
backorder |
April |
13 |
6 |
36 |
f1_mar_2 |
f2_mar_2 |
99999999 |
0 |
. |
. |
|
23.00 |
0 |
0.00 |
23.00 |
0 |
0.00 |
25 |
. |
f1_to_2 |
March |
43 |
12 |
37 |
fact2_2 |
f2_mar_2 |
650 |
35 |
1500 |
. |
prod f2 25 mar |
182.00 |
635 |
115570.00 |
182.00 |
645 |
117390.00 |
25 |
2 |
production |
March |
44 |
20 |
38 |
f2_apr_2 |
f2_mar_2 |
15 |
0 |
. |
. |
back f2 25 apl |
37.20 |
0 |
0.00 |
31.00 |
0 |
0.00 |
25 |
2 |
backorder |
April |
45 |
16 |
39 |
f1_may_1 |
f2_may_1 |
99999999 |
0 |
. |
. |
|
16.00 |
115 |
1840.00 |
16.00 |
100 |
1600.00 |
19 |
. |
f1_to_2 |
May |
18 |
4 |
40 |
fact2_1 |
f2_may_1 |
250 |
35 |
850 |
. |
|
128.80 |
35 |
4508.00 |
133.80 |
35 |
4683.00 |
19 |
2 |
production |
May |
19 |
10 |
41 |
f2_apr_1 |
f2_may_1 |
30 |
0 |
. |
. |
|
20.00 |
0 |
0.00 |
20.00 |
15 |
300.00 |
19 |
2 |
storage |
April |
20 |
6 |
42 |
f1_may_2 |
f2_may_2 |
99999999 |
0 |
. |
. |
|
26.00 |
335 |
8710.00 |
26.00 |
0 |
0.00 |
25 |
. |
f1_to_2 |
May |
50 |
14 |
43 |
fact2_2 |
f2_may_2 |
550 |
35 |
1500 |
. |
|
181.40 |
35 |
6349.00 |
201.40 |
35 |
7049.00 |
25 |
2 |
production |
May |
51 |
20 |
44 |
f2_apr_2 |
f2_may_2 |
50 |
0 |
. |
. |
|
38.00 |
0 |
0.00 |
38.00 |
0 |
0.00 |
25 |
2 |
storage |
April |
52 |
16 |
45 |
f1_mar_1 |
shop1_1 |
250 |
0 |
. |
900 |
|
-327.65 |
150 |
-49147.50 |
-327.65 |
155 |
-50785.75 |
19 |
1 |
sales |
March |
21 |
2 |
46 |
f1_apr_1 |
shop1_1 |
250 |
0 |
. |
900 |
|
-300.00 |
250 |
-75000.00 |
-300.00 |
250 |
-75000.00 |
19 |
1 |
sales |
April |
22 |
3 |
47 |
f1_may_1 |
shop1_1 |
250 |
0 |
. |
900 |
|
-285.00 |
0 |
0.00 |
-285.00 |
0 |
0.00 |
19 |
1 |
sales |
May |
23 |
4 |
48 |
f2_mar_1 |
shop1_1 |
250 |
0 |
. |
900 |
|
-297.40 |
250 |
-74350.00 |
-297.40 |
250 |
-74350.00 |
19 |
2 |
sales |
March |
24 |
5 |
49 |
f2_apr_1 |
shop1_1 |
250 |
0 |
. |
900 |
|
-290.00 |
250 |
-72500.00 |
-290.00 |
245 |
-71050.00 |
19 |
2 |
sales |
April |
25 |
6 |
50 |
f2_may_1 |
shop1_1 |
250 |
0 |
. |
900 |
|
-292.00 |
0 |
0.00 |
-292.00 |
0 |
0.00 |
19 |
2 |
sales |
May |
26 |
7 |
51 |
f1_mar_2 |
shop1_2 |
99999999 |
0 |
. |
900 |
|
-559.76 |
0 |
0.00 |
-559.76 |
0 |
0.00 |
25 |
1 |
sales |
March |
53 |
12 |
52 |
f1_apr_2 |
shop1_2 |
99999999 |
0 |
. |
900 |
|
-524.28 |
0 |
0.00 |
-524.28 |
0 |
0.00 |
25 |
1 |
sales |
April |
54 |
13 |
53 |
f1_may_2 |
shop1_2 |
99999999 |
0 |
. |
900 |
|
-475.02 |
0 |
0.00 |
-475.02 |
25 |
-11875.50 |
25 |
1 |
sales |
May |
55 |
14 |
54 |
f2_mar_2 |
shop1_2 |
500 |
0 |
. |
900 |
|
-567.83 |
500 |
-283915.00 |
-567.83 |
500 |
-283915.00 |
25 |
2 |
sales |
March |
56 |
15 |
55 |
f2_apr_2 |
shop1_2 |
500 |
0 |
. |
900 |
|
-542.19 |
400 |
-216876.00 |
-542.19 |
375 |
-203321.25 |
25 |
2 |
sales |
April |
57 |
16 |
56 |
f2_may_2 |
shop1_2 |
500 |
0 |
. |
900 |
|
-491.56 |
0 |
0.00 |
-461.56 |
0 |
0.00 |
25 |
2 |
sales |
May |
58 |
17 |
57 |
f1_mar_1 |
shop2_1 |
250 |
0 |
. |
900 |
|
-362.74 |
250 |
-90685.00 |
-362.74 |
250 |
-90685.00 |
19 |
1 |
sales |
March |
27 |
2 |
58 |
f1_apr_1 |
shop2_1 |
250 |
0 |
. |
900 |
|
-300.00 |
250 |
-75000.00 |
-300.00 |
250 |
-75000.00 |
19 |
1 |
sales |
April |
28 |
3 |
59 |
f1_may_1 |
shop2_1 |
250 |
0 |
. |
900 |
|
-245.00 |
0 |
0.00 |
-245.00 |
0 |
0.00 |
19 |
1 |
sales |
May |
29 |
4 |
60 |
f2_mar_1 |
shop2_1 |
250 |
0 |
. |
900 |
|
-272.70 |
0 |
0.00 |
-272.70 |
0 |
0.00 |
19 |
2 |
sales |
March |
30 |
5 |
61 |
f2_apr_1 |
shop2_1 |
250 |
0 |
. |
900 |
|
-312.00 |
250 |
-78000.00 |
-312.00 |
250 |
-78000.00 |
19 |
2 |
sales |
April |
31 |
6 |
62 |
f2_may_1 |
shop2_1 |
250 |
0 |
. |
900 |
|
-299.00 |
150 |
-44850.00 |
-299.00 |
150 |
-44850.00 |
19 |
2 |
sales |
May |
32 |
7 |
63 |
f1_mar_2 |
shop2_2 |
99999999 |
0 |
. |
1450 |
|
-623.89 |
455 |
-283869.95 |
-623.89 |
455 |
-283869.95 |
25 |
1 |
sales |
March |
59 |
12 |
64 |
f1_apr_2 |
shop2_2 |
99999999 |
0 |
. |
1450 |
|
-549.68 |
235 |
-129174.80 |
-549.68 |
535 |
-294078.80 |
25 |
1 |
sales |
April |
60 |
13 |
65 |
f1_may_2 |
shop2_2 |
99999999 |
0 |
. |
1450 |
|
-460.00 |
0 |
0.00 |
-460.00 |
0 |
0.00 |
25 |
1 |
sales |
May |
61 |
14 |
66 |
f2_mar_2 |
shop2_2 |
500 |
0 |
. |
1450 |
|
-542.83 |
110 |
-59711.30 |
-542.83 |
120 |
-65139.60 |
25 |
2 |
sales |
March |
62 |
15 |
67 |
f2_apr_2 |
shop2_2 |
500 |
0 |
. |
1450 |
|
-559.19 |
280 |
-156573.20 |
-559.19 |
320 |
-178940.80 |
25 |
2 |
sales |
April |
63 |
16 |
68 |
f2_may_2 |
shop2_2 |
500 |
0 |
. |
1450 |
|
-519.06 |
370 |
-192052.20 |
-489.06 |
20 |
-9781.20 |
25 |
2 |
sales |
May |
64 |
17 |
|
|
|
|
|
|
|
|
|
|
-1285086.45 |
|
|
-1281110.35 |
|
|
|
|
|
|
|
The associated NODEOUT data set is in Output 4.5.1
Output 4.5.2: NODEOUT=NODE3
Obs |
_node_ |
_supdem_ |
_DUAL_ |
_NNUMB_ |
_PRED_ |
_TRAV_ |
_SCESS_ |
_ARCID_ |
_FLOW_ |
_FBQ_ |
1 |
_ROOT_ |
238 |
0.00 |
22 |
0 |
8 |
0 |
3 |
166 |
-69 |
2 |
_EXCESS_ |
-200 |
-100000198.75 |
21 |
1 |
20 |
13 |
65 |
5 |
65 |
3 |
f1_apr_1 |
. |
-100000277.35 |
3 |
1 |
6 |
2 |
4 |
490 |
4 |
4 |
f1_apr_2 |
. |
-100000387.60 |
13 |
19 |
11 |
2 |
-60 |
235 |
36 |
5 |
f1_mar_1 |
. |
-100000326.65 |
2 |
8 |
1 |
20 |
-21 |
150 |
1 |
6 |
f1_mar_2 |
. |
-100000461.81 |
12 |
19 |
13 |
1 |
-59 |
455 |
33 |
7 |
f1_may_1 |
. |
-100000288.85 |
4 |
1 |
7 |
3 |
8 |
65 |
8 |
8 |
f1_may_2 |
. |
-100000330.98 |
14 |
17 |
10 |
1 |
-50 |
335 |
40 |
9 |
f2_apr_1 |
. |
-100000288.35 |
6 |
3 |
4 |
1 |
14 |
20 |
14 |
10 |
f2_apr_2 |
. |
-100000397.11 |
16 |
19 |
18 |
2 |
-63 |
280 |
46 |
11 |
f2_mar_1 |
. |
-100000286.75 |
5 |
10 |
22 |
1 |
12 |
255 |
11 |
12 |
f2_mar_2 |
. |
-100000380.75 |
15 |
20 |
19 |
9 |
44 |
600 |
43 |
13 |
f2_may_1 |
. |
-100000304.85 |
7 |
4 |
9 |
2 |
18 |
115 |
18 |
14 |
f2_may_2 |
. |
-100000356.98 |
17 |
19 |
14 |
2 |
-64 |
370 |
50 |
15 |
fact1_1 |
1000 |
-100000198.75 |
1 |
2 |
3 |
19 |
-1 |
290 |
-1 |
16 |
fact1_2 |
1000 |
-100000213.10 |
11 |
13 |
17 |
1 |
-36 |
200 |
-33 |
17 |
fact2_1 |
850 |
-100000198.75 |
10 |
21 |
5 |
2 |
-66 |
45 |
-33 |
18 |
fact2_2 |
1500 |
-100000198.75 |
20 |
21 |
15 |
10 |
-68 |
150 |
-65 |
19 |
shop1_1 |
-900 |
-99999999.00 |
8 |
22 |
2 |
21 |
0 |
0 |
21 |
20 |
shop1_2 |
-900 |
-99999854.92 |
18 |
16 |
12 |
1 |
57 |
400 |
53 |
21 |
shop2_1 |
-900 |
-100000005.85 |
9 |
7 |
21 |
1 |
32 |
150 |
27 |
22 |
shop2_2 |
-1450 |
-99999837.92 |
19 |
15 |
16 |
8 |
62 |
110 |
59 |
|
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.