### Example 6.7 Using a Constrained Solution Warm Start

Suppose the 25-inch screen TVs produced at factory 1 in May can be sold at either shop with an increased profit of 40 dollars each. What is the new optimal solution? Because only arc costs have been changed, information about the present solution in DUALOUT=dual4 and CONOUT=con4 can be used as a warm start in the following PROC NETFLOW run. It is still necessary to specify CONDATA=con3 SPARSECONDATA RHSOBS='CHIP/BO LIMIT', since the CONDATA= data set is always read.

```  title 'Using a Constrained Solution Warm Start';
title2 'Production Planning/Inventory/Distribution';
data new_con4;
set con4;
oldcost=_cost_;
oldflow=_flow_;
oldfc=_fcost_;
if _tail_='f1_may_2'
then _cost_=_cost_-40;
run;
```
```proc netflow
warm
arcdata=new_con4
dualin=dual4
condata=con3
sparsecondata
rhsobs='CHIP/BO LIMIT'
dualout=dual5
conout=con5;
run;
quit;
```
```proc print data=con5 heading=h width=min;
sum _fcost_;
var _tail_ _head_ _capac_ _lo_ _supply_ _demand_ _name_ _cost_ _flow_ _fcost_;
run;
```
```proc print data=con5 heading=h width=min;
sum oldfc;
var oldcost oldflow oldfc diagonal factory key_id mth_made _anumb_ _tnumb_;
run;
```
```proc print data=dual5;
run;
```

The following messages appear on the SAS log:

 Using a Constrained Solution Warm Start Production Planning/Inventory/Distribution

 NOTE: The following 1 variables in NODEDATA do not belong to any SAS variable list. These will be ignored. _VALUE_ NOTE: Number of nodes= 21 . NOTE: Number of supply nodes= 4 . NOTE: Number of demand nodes= 5 . NOTE: The greater of total supply and total demand= 4350 . NOTE: Number of <= side constraints= 5 . NOTE: Number of == side constraints= 0 . NOTE: Number of >= side constraints= 0 . NOTE: Number of arc and nonarc variable side constraint coefficients= 16 . NOTE: Number of iterations, optimizing with constraints= 6 . NOTE: Of these, 0 were degenerate. NOTE: Optimum reached. NOTE: Minimal total cost= -1295661.8 . NOTE: The data set WORK.CON5 has 68 observations and 21 variables. NOTE: The data set WORK.DUAL5 has 25 observations and 14 variables.

Output 6.7.1: CONOUT=CON5

 Using a Constrained Solution Warm Start Production Planning/Inventory/Distribution

Obs _tail_ _head_ _capac_ _lo_ _SUPPLY_ _DEMAND_ _name_ _cost_ _FLOW_ _FCOST_
1 fact1_1 _EXCESS_ 99999999 0 1000 200   0.00 5.000 0.00
2 fact2_1 _EXCESS_ 99999999 0 850 200   0.00 45.000 0.00
3 fact1_2 _EXCESS_ 99999999 0 1000 200   0.00 0.000 0.00
4 fact2_2 _EXCESS_ 99999999 0 1500 200   0.00 150.000 0.00
5 fact1_1 f1_apr_1 600 50 1000 . prod f1 19 apl 78.60 533.333 41920.00
6 f1_mar_1 f1_apr_1 50 0 . .   15.00 0.000 0.00
7 f1_may_1 f1_apr_1 20 0 . . back f1 19 may 33.60 0.000 0.00
8 f2_apr_1 f1_apr_1 40 0 . .   11.00 0.000 0.00
9 fact1_2 f1_apr_2 550 50 1000 . prod f1 25 apl 174.50 250.000 43625.00
10 f1_mar_2 f1_apr_2 40 0 . .   20.00 0.000 0.00
11 f1_may_2 f1_apr_2 15 0 . . back f1 25 may 49.20 0.000 0.00
12 f2_apr_2 f1_apr_2 25 0 . .   21.00 0.000 0.00
13 fact1_1 f1_mar_1 500 50 1000 . prod f1 19 mar 127.90 333.333 42633.33
14 f1_apr_1 f1_mar_1 20 0 . . back f1 19 apl 33.60 20.000 672.00
15 f2_mar_1 f1_mar_1 40 0 . .   10.00 40.000 400.00
16 fact1_2 f1_mar_2 400 40 1000 . prod f1 25 mar 217.90 400.000 87160.00
17 f1_apr_2 f1_mar_2 30 0 . . back f1 25 apl 38.40 30.000 1152.00
18 f2_mar_2 f1_mar_2 25 0 . .   20.00 25.000 500.00
19 fact1_1 f1_may_1 400 50 1000 .   90.10 128.333 11562.83
20 f1_apr_1 f1_may_1 50 0 . .   12.00 0.000 0.00
21 f2_may_1 f1_may_1 40 0 . .   13.00 0.000 0.00
22 fact1_2 f1_may_2 350 40 1000 .   113.30 350.000 39655.00
23 f1_apr_2 f1_may_2 40 0 . .   18.00 0.000 0.00
24 f2_may_2 f1_may_2 25 0 . .   13.00 0.000 0.00
25 f1_apr_1 f2_apr_1 99999999 0 . .   11.00 13.333 146.67
26 fact2_1 f2_apr_1 480 35 850 . prod f2 19 apl 62.40 480.000 29952.00
27 f2_mar_1 f2_apr_1 30 0 . .   18.00 0.000 0.00
28 f2_may_1 f2_apr_1 15 0 . . back f2 19 may 30.00 0.000 0.00
29 f1_apr_2 f2_apr_2 99999999 0 . .   23.00 0.000 0.00
30 fact2_2 f2_apr_2 680 35 1500 . prod f2 25 apl 196.70 550.000 108185.00
31 f2_mar_2 f2_apr_2 50 0 . .   28.00 0.000 0.00
32 f2_may_2 f2_apr_2 15 0 . . back f2 25 may 64.80 0.000 0.00
33 f1_mar_1 f2_mar_1 99999999 0 . .   11.00 0.000 0.00
34 fact2_1 f2_mar_1 450 35 850 . prod f2 19 mar 88.00 290.000 25520.00
35 f2_apr_1 f2_mar_1 15 0 . . back f2 19 apl 20.40 0.000 0.00
36 f1_mar_2 f2_mar_2 99999999 0 . .   23.00 0.000 0.00
37 fact2_2 f2_mar_2 650 35 1500 . prod f2 25 mar 182.00 650.000 118300.00
38 f2_apr_2 f2_mar_2 15 0 . . back f2 25 apl 37.20 0.000 0.00
39 f1_may_1 f2_may_1 99999999 0 . .   16.00 115.000 1840.00
40 fact2_1 f2_may_1 250 35 850 .   128.80 35.000 4508.00
41 f2_apr_1 f2_may_1 30 0 . .   20.00 0.000 0.00
42 f1_may_2 f2_may_2 99999999 0 . .   26.00 0.000 0.00
43 fact2_2 f2_may_2 550 35 1500 .   181.40 150.000 27210.00
44 f2_apr_2 f2_may_2 50 0 . .   38.00 0.000 0.00
45 f1_mar_1 shop1_1 250 0 . 900   -327.65 143.333 -46963.17
46 f1_apr_1 shop1_1 250 0 . 900   -300.00 250.000 -75000.00
47 f1_may_1 shop1_1 250 0 . 900   -285.00 13.333 -3800.00
48 f2_mar_1 shop1_1 250 0 . 900   -297.40 250.000 -74350.00
49 f2_apr_1 shop1_1 250 0 . 900   -290.00 243.333 -70566.67
50 f2_may_1 shop1_1 250 0 . 900   -292.00 0.000 0.00
51 f1_mar_2 shop1_2 99999999 0 . 900   -559.76 0.000 0.00
52 f1_apr_2 shop1_2 99999999 0 . 900   -524.28 0.000 0.00
53 f1_may_2 shop1_2 99999999 0 . 900   -515.02 350.000 -180257.00
54 f2_mar_2 shop1_2 500 0 . 900   -567.83 500.000 -283915.00
55 f2_apr_2 shop1_2 500 0 . 900   -542.19 50.000 -27109.50
56 f2_may_2 shop1_2 500 0 . 900   -491.56 0.000 0.00
57 f1_mar_1 shop2_1 250 0 . 900   -362.74 250.000 -90685.00
58 f1_apr_1 shop2_1 250 0 . 900   -300.00 250.000 -75000.00
59 f1_may_1 shop2_1 250 0 . 900   -245.00 0.000 0.00
60 f2_mar_1 shop2_1 250 0 . 900   -272.70 0.000 0.00
61 f2_apr_1 shop2_1 250 0 . 900   -312.00 250.000 -78000.00
62 f2_may_1 shop2_1 250 0 . 900   -299.00 150.000 -44850.00
63 f1_mar_2 shop2_2 99999999 0 . 1450   -623.89 455.000 -283869.95
64 f1_apr_2 shop2_2 99999999 0 . 1450   -549.68 220.000 -120929.60
65 f1_may_2 shop2_2 99999999 0 . 1450   -500.00 0.000 0.00
66 f2_mar_2 shop2_2 500 0 . 1450   -542.83 125.000 -67853.75
67 f2_apr_2 shop2_2 500 0 . 1450   -559.19 500.000 -279595.00
68 f2_may_2 shop2_2 500 0 . 1450   -519.06 150.000 -77859.00
-1295661.80

Output 6.7.2: CONOUT=CON5 (continued)

 Using a Constrained Solution Warm Start Production Planning/Inventory/Distribution

Obs oldcost oldflow oldfc diagonal factory key_id mth_made _ANUMB_ _TNUMB_
1 0.00 5.000 0.00 . .     65 1
2 0.00 45.000 0.00 . .     66 10
3 0.00 0.000 0.00 . .     67 11
4 0.00 150.000 0.00 . .     68 20
5 78.60 533.333 41920.00 19 1 production April 4 1
6 15.00 0.000 0.00 19 1 storage March 5 2
7 33.60 0.000 0.00 19 1 backorder May 6 4
8 11.00 0.000 0.00 19 . f2_to_1 April 7 6
9 174.50 250.000 43625.00 25 1 production April 36 11
10 20.00 0.000 0.00 25 1 storage March 37 12
11 49.20 0.000 0.00 25 1 backorder May 38 14
12 21.00 0.000 0.00 25 . f2_to_1 April 39 16
13 127.90 333.333 42633.33 19 1 production March 1 1
14 33.60 20.000 672.00 19 1 backorder April 2 3
15 10.00 40.000 400.00 19 . f2_to_1 March 3 5
16 217.90 400.000 87160.00 25 1 production March 33 11
17 38.40 30.000 1152.00 25 1 backorder April 34 13
18 20.00 25.000 500.00 25 . f2_to_1 March 35 15
19 90.10 128.333 11562.83 19 1 production May 8 1
20 12.00 0.000 0.00 19 1 storage April 9 3
21 13.00 0.000 0.00 19 . f2_to_1 May 10 7
22 113.30 350.000 39655.00 25 1 production May 40 11
23 18.00 0.000 0.00 25 1 storage April 41 13
24 13.00 0.000 0.00 25 . f2_to_1 May 42 17
25 11.00 13.333 146.67 19 . f1_to_2 April 14 3
26 62.40 480.000 29952.00 19 2 production April 15 10
27 18.00 0.000 0.00 19 2 storage March 16 5
28 30.00 0.000 0.00 19 2 backorder May 17 7
29 23.00 0.000 0.00 25 . f1_to_2 April 46 13
30 196.70 577.500 113594.25 25 2 production April 47 20
31 28.00 0.000 0.00 25 2 storage March 48 15
32 64.80 0.000 0.00 25 2 backorder May 49 17
33 11.00 0.000 0.00 19 . f1_to_2 March 11 2
34 88.00 290.000 25520.00 19 2 production March 12 10
35 20.40 0.000 0.00 19 2 backorder April 13 6
36 23.00 0.000 0.00 25 . f1_to_2 March 43 12
37 182.00 650.000 118300.00 25 2 production March 44 20
38 37.20 0.000 0.00 25 2 backorder April 45 16
39 16.00 115.000 1840.00 19 . f1_to_2 May 18 4
40 128.80 35.000 4508.00 19 2 production May 19 10
41 20.00 0.000 0.00 19 2 storage April 20 6
42 26.00 350.000 9100.00 25 . f1_to_2 May 50 14
43 181.40 122.500 22221.50 25 2 production May 51 20
44 38.00 0.000 0.00 25 2 storage April 52 16
45 -327.65 143.333 -46963.17 19 1 sales March 21 2
46 -300.00 250.000 -75000.00 19 1 sales April 22 3
47 -285.00 13.333 -3800.00 19 1 sales May 23 4
48 -297.40 250.000 -74350.00 19 2 sales March 24 5
49 -290.00 243.333 -70566.67 19 2 sales April 25 6
50 -292.00 0.000 0.00 19 2 sales May 26 7
51 -559.76 0.000 0.00 25 1 sales March 53 12
52 -524.28 0.000 0.00 25 1 sales April 54 13
53 -475.02 0.000 0.00 25 1 sales May 55 14
54 -567.83 500.000 -283915.00 25 2 sales March 56 15
55 -542.19 400.000 -216876.00 25 2 sales April 57 16
56 -491.56 0.000 0.00 25 2 sales May 58 17
57 -362.74 250.000 -90685.00 19 1 sales March 27 2
58 -300.00 250.000 -75000.00 19 1 sales April 28 3
59 -245.00 0.000 0.00 19 1 sales May 29 4
60 -272.70 0.000 0.00 19 2 sales March 30 5
61 -312.00 250.000 -78000.00 19 2 sales April 31 6
62 -299.00 150.000 -44850.00 19 2 sales May 32 7
63 -623.89 455.000 -283869.95 25 1 sales March 59 12
64 -549.68 220.000 -120929.60 25 1 sales April 60 13
65 -460.00 0.000 0.00 25 1 sales May 61 14
66 -542.83 125.000 -67853.75 25 2 sales March 62 15
67 -559.19 177.500 -99256.23 25 2 sales April 63 16
68 -519.06 472.500 -245255.85 25 2 sales May 64 17
-1282708.63

Output 6.7.3: DUALOUT=DUAL5

 Using a Constrained Solution Warm Start Production Planning/Inventory/Distribution

Obs _node_ _supdem_ _DUAL_ _NNUMB_ _PRED_ _TRAV_ _SCESS_ _ARCID_ _FLOW_ _FBQ_ _VALUE_ _RHS_ _TYPE_ _row_
1 f1_apr_1 . -100000278.00 3 1 6 2 4 483.333 4 . .
2 f1_apr_2 . -100000405.92 13 19 11 2 -60 220.000 36 . .
3 f1_mar_1 . -100000326.65 2 8 1 20 -21 143.333 1 . .
4 f1_mar_2 . -100000480.13 12 19 13 1 -59 455.000 33 . .
5 f1_may_1 . -100000284.00 4 1 7 3 8 78.333 8 . .
6 f1_may_2 . -100000363.43 14 18 10 1 -55 350.000 40 . .
7 f2_apr_1 . -100000289.00 6 3 4 1 14 13.333 14 . .
8 f2_apr_2 . -100000390.60 16 20 18 3 47 515.000 46 . .
9 f2_mar_1 . -100000281.90 5 10 3 1 12 255.000 11 . .
10 f2_mar_2 . -100000399.07 15 19 16 1 -62 125.000 43 . .
11 f2_may_1 . -100000300.00 7 4 9 2 18 115.000 18 . .
12 f2_may_2 . -100000375.30 17 20 19 6 51 115.000 50 . .
13 fact1_1 1000 -100000193.90 1 2 21 19 -1 283.333 -1 . .
14 fact1_2 1000 -100000224.09 11 13 15 1 -36 200.000 -33 . .
15 fact2_1 850 -100000193.90 10 21 5 2 -66 45.000 -33 . .
16 fact2_2 1500 -100000193.90 20 21 17 10 -68 150.000 -65 . .
17 shop1_1 -900 -99999999.00 8 22 2 21 0 0.000 21 . .
18 shop1_2 -900 -99999848.41 18 16 14 2 57 50.000 53 . .
19 shop2_1 -900 -100000001.00 9 7 22 1 32 150.000 27 . .
20 shop2_2 -1450 -99999856.24 19 17 12 5 64 150.000 59 . .
21   . -1.83 2 8 . . 25 243.333 . 2600 2600 LE FACT1 APL GIZMO
22   . -1.62 0 8 . . 23 13.333 . 2600 2600 LE FACT1 MAR GIZMO
23   . 0.00 3 3 . 3 . 110.000 . 3640 3750 LE FACT2 APL GIZMO
24   . 0.00 1 1 . 1 . 280.000 . 3470 3750 LE FACT2 MAR GIZMO
25   . -15.05 4 2 . . 2 20.000 . 50 50 LE TOTAL BACKORDER