The INTPOINT Procedure

Example 4.4 Using Constraints and More Alteration to Arc Data

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?

title2 'Using Constraints and Altering arc data';
data new_arc4;
   set arc4;
   oldcost=_cost_;
   oldflow=_flow_;
   oldfc=_fcost_;
   if _tail_='f1_may_2' & (_head_='shop1_2' | _head_='shop2_2')
      then _cost_=_cost_-40;
   run;

proc intpoint
bytes=1000000
printlevel2=2
arcdata=new_arc4 nodedata=node0
condata=con3 sparsecondata rhsobs='CHIP/BO LIMIT'
conout=arc5;
run;

title2 'Using Constraints and Altering Arc Data';
proc print data=arc5;
   var _tail_ _head_ _cost_ _capac_ _lo_ 
       _supply_ _demand_ _name_ _flow_ _fcost_ oldflow oldfc;
          /* to get this variable order */
   sum oldfc _fcost_;
run;

The following messages appear on the SAS log:

NOTE: Number of nodes= 20 .

NOTE: Number of supply nodes= 4 .

NOTE: Number of demand nodes= 4 .

NOTE: Total supply= 4350 , total demand= 4150 .

NOTE: Number of arcs= 64 .

NOTE: Number of <= side constraints= 5 .

NOTE: Number of == side constraints= 0 .

NOTE: Number of >= side constraints= 0 .

NOTE: Number of side constraint coefficients= 16 .

NOTE: The following messages relate to the equivalent Linear Programming problem

solved by the Interior Point algorithm.

NOTE: Number of <= constraints= 5 .

NOTE: Number of == constraints= 21 .

NOTE: Number of >= constraints= 0 .

NOTE: Number of constraint coefficients= 152 .

NOTE: Number of variables= 68 .

NOTE: After preprocessing, number of <= constraints= 5.

NOTE: After preprocessing, number of == constraints= 20.

NOTE: After preprocessing, number of >= constraints= 0.

NOTE: The preprocessor eliminated 1 constraints from the problem.

NOTE: The preprocessor eliminated 9 constraint coefficients from the problem.

NOTE: 5 columns, 0 rows and 5 coefficients were added to the problem to handle

unrestricted variables, variables that are split, and constraint slack or

surplus variables.

NOTE: There are 74 sub-diagonal nonzeroes in the unfactored A Atranspose matrix.

NOTE: The 25 factor nodes make up 17 supernodes

NOTE: There are 88 nonzero sub-rows or sub-columns outside the supernodal

triangular regions along the factors leading diagonal.

Iter Complem_aff Complem-ity Duality_gap Tot_infeasb Tot_infeasc Tot_infeasd

0 -1.000000 201073760 0.894528 65408 35351 10995

1 39022799 25967436 0.919693 4741.966761 2562.885742 256.192394

2 5186078 1844990 0.589523 0 0 6.174556

3 371920 320310 0.197224 0 0 1.074616

4 151369 87643 0.060906 0 0 0.267952

5 35115 25158 0.018017 0 0 0.072961

6 14667 6194.354873 0.004475 0 0 0.005048

7 2723.955063 2472.352937 0.001789 0 0 0.001714

8 1028.390365 280.346187 0.000203 0 0 0.000235

9 39.957867 5.611483 0.000004063 0 0 0

10 0.014117 0.000291 9.492733E-11 0 0 0

NOTE: The Primal-Dual Predictor-Corrector Interior Point algorithm performed 10

iterations.

NOTE: Optimum reached.

NOTE: Objective= -1295661.8.

NOTE: The data set WORK.ARC5 has 64 observations and 17 variables.

NOTE: There were 64 observations read from the data set WORK.NEW_ARC4.

NOTE: There were 8 observations read from the data set WORK.NODE0.

NOTE: There were 21 observations read from the data set WORK.CON3.

Output 4.4.1: CONOUT=ARC5

Using Constraints and Altering Arc Data

Obs	_tail_	_head_	_cost_	_capac_	_lo_	_SUPPLY_	_DEMAND_
1	fact1_1	f1_apr_1	78.60	600	50	1000	.
2	f1_mar_1	f1_apr_1	15.00	50	0	.	.
3	f1_may_1	f1_apr_1	33.60	20	0	.	.
4	f2_apr_1	f1_apr_1	11.00	40	0	.	.
5	fact1_2	f1_apr_2	174.50	550	50	1000	.
6	f1_mar_2	f1_apr_2	20.00	40	0	.	.
7	f1_may_2	f1_apr_2	49.20	15	0	.	.
8	f2_apr_2	f1_apr_2	21.00	25	0	.	.
9	fact1_1	f1_mar_1	127.90	500	50	1000	.
10	f1_apr_1	f1_mar_1	33.60	20	0	.	.
11	f2_mar_1	f1_mar_1	10.00	40	0	.	.
12	fact1_2	f1_mar_2	217.90	400	40	1000	.
13	f1_apr_2	f1_mar_2	38.40	30	0	.	.
14	f2_mar_2	f1_mar_2	20.00	25	0	.	.
15	fact1_1	f1_may_1	90.10	400	50	1000	.
16	f1_apr_1	f1_may_1	12.00	50	0	.	.
17	f2_may_1	f1_may_1	13.00	40	0	.	.
18	fact1_2	f1_may_2	113.30	350	40	1000	.
19	f1_apr_2	f1_may_2	18.00	40	0	.	.
20	f2_may_2	f1_may_2	13.00	25	0	.	.
21	f1_apr_1	f2_apr_1	11.00	99999999	0	.	.
22	fact2_1	f2_apr_1	62.40	480	35	850	.
23	f2_mar_1	f2_apr_1	18.00	30	0	.	.
24	f2_may_1	f2_apr_1	30.00	15	0	.	.
25	f1_apr_2	f2_apr_2	23.00	99999999	0	.	.
26	fact2_2	f2_apr_2	196.70	680	35	1500	.
27	f2_mar_2	f2_apr_2	28.00	50	0	.	.
28	f2_may_2	f2_apr_2	64.80	15	0	.	.
29	f1_mar_1	f2_mar_1	11.00	99999999	0	.	.
30	fact2_1	f2_mar_1	88.00	450	35	850	.
31	f2_apr_1	f2_mar_1	20.40	15	0	.	.
32	f1_mar_2	f2_mar_2	23.00	99999999	0	.	.
33	fact2_2	f2_mar_2	182.00	650	35	1500	.
34	f2_apr_2	f2_mar_2	37.20	15	0	.	.
35	f1_may_1	f2_may_1	16.00	99999999	0	.	.
36	fact2_1	f2_may_1	128.80	250	35	850	.
37	f2_apr_1	f2_may_1	20.00	30	0	.	.
38	f1_may_2	f2_may_2	26.00	99999999	0	.	.
39	fact2_2	f2_may_2	181.40	550	35	1500	.
40	f2_apr_2	f2_may_2	38.00	50	0	.	.
41	f1_mar_1	shop1_1	-327.65	250	0	.	900
42	f1_apr_1	shop1_1	-300.00	250	0	.	900
43	f1_may_1	shop1_1	-285.00	250	0	.	900
44	f2_mar_1	shop1_1	-297.40	250	0	.	900
45	f2_apr_1	shop1_1	-290.00	250	0	.	900
46	f2_may_1	shop1_1	-292.00	250	0	.	900
47	f1_mar_2	shop1_2	-559.76	99999999	0	.	900
48	f1_apr_2	shop1_2	-524.28	99999999	0	.	900
49	f1_may_2	shop1_2	-515.02	99999999	0	.	900
50	f2_mar_2	shop1_2	-567.83	500	0	.	900
51	f2_apr_2	shop1_2	-542.19	500	0	.	900
52	f2_may_2	shop1_2	-491.56	500	0	.	900
53	f1_mar_1	shop2_1	-362.74	250	0	.	900
54	f1_apr_1	shop2_1	-300.00	250	0	.	900
55	f1_may_1	shop2_1	-245.00	250	0	.	900
56	f2_mar_1	shop2_1	-272.70	250	0	.	900
57	f2_apr_1	shop2_1	-312.00	250	0	.	900
58	f2_may_1	shop2_1	-299.00	250	0	.	900
59	f1_mar_2	shop2_2	-623.89	99999999	0	.	1450
60	f1_apr_2	shop2_2	-549.68	99999999	0	.	1450
61	f1_may_2	shop2_2	-500.00	99999999	0	.	1450
62	f2_mar_2	shop2_2	-542.83	500	0	.	1450
63	f2_apr_2	shop2_2	-559.19	500	0	.	1450
64	f2_may_2	shop2_2	-519.06	500	0	.	1450

Using Constraints and Altering Arc Data

Obs	_name_	_FLOW_	_FCOST_	oldflow	oldfc
1	prod f1 19 apl	533.333	41920.00	533.333	41920.00
2		0.000	0.00	0.000	0.00
3	back f1 19 may	0.000	0.00	0.000	0.00
4		0.000	0.00	0.000	0.00
5	prod f1 25 apl	250.000	43625.00	250.000	43625.00
6		0.000	0.00	0.000	0.00
7	back f1 25 may	0.000	0.00	0.000	0.00
8		0.000	0.00	0.000	0.00
9	prod f1 19 mar	333.333	42633.33	333.333	42633.33
10	back f1 19 apl	20.000	672.00	20.000	672.00
11		40.000	400.00	40.000	400.00
12	prod f1 25 mar	400.000	87160.00	400.000	87160.00
13	back f1 25 apl	30.000	1152.00	30.000	1152.00
14		25.000	500.00	25.000	500.00
15		128.333	11562.83	128.333	11562.83
16		0.000	0.00	0.000	0.00
17		0.000	0.00	0.000	0.00
18		350.000	39655.00	350.000	39655.00
19		0.000	0.00	0.000	0.00
20		0.000	0.00	0.000	0.00
21		13.333	146.67	13.333	146.67
22	prod f2 19 apl	480.000	29952.00	480.000	29952.00
23		0.000	0.00	0.000	0.00
24	back f2 19 may	0.000	0.00	0.000	0.00
25		0.000	0.00	0.000	0.00
26	prod f2 25 apl	550.000	108185.00	577.500	113594.25
27		0.000	0.00	0.000	0.00
28	back f2 25 may	0.000	0.00	0.000	0.00
29		0.000	0.00	0.000	0.00
30	prod f2 19 mar	290.000	25520.00	290.000	25520.00
31	back f2 19 apl	0.000	0.00	0.000	0.00
32		0.000	0.00	0.000	0.00
33	prod f2 25 mar	650.000	118300.00	650.000	118300.00
34	back f2 25 apl	0.000	0.00	0.000	0.00
35		115.000	1840.00	115.000	1840.00
36		35.000	4508.00	35.000	4508.00
37		0.000	0.00	0.000	0.00
38		0.000	0.00	350.000	9100.00
39		150.000	27210.00	122.500	22221.50
40		0.000	0.00	0.000	0.00
41		143.333	-46963.17	143.333	-46963.16
42		250.000	-75000.00	250.000	-75000.00
43		13.333	-3800.00	13.333	-3800.00
44		250.000	-74350.00	250.000	-74350.00
45		243.333	-70566.67	243.333	-70566.67
46		0.000	0.00	0.000	0.00
47		0.000	0.00	0.000	0.00
48		0.000	0.00	0.000	0.00
49		350.000	-180257.00	0.000	0.00
50		500.000	-283915.00	500.000	-283915.00
51		50.000	-27109.50	400.000	-216876.00
52		0.000	0.00	0.000	0.00
53		250.000	-90685.00	250.000	-90685.00
54		250.000	-75000.00	250.000	-75000.00
55		0.000	0.00	0.000	0.00
56		0.000	0.00	0.000	0.00
57		250.000	-78000.00	250.000	-78000.00
58		150.000	-44850.00	150.000	-44850.00
59		455.000	-283869.95	455.000	-283869.95
60		220.000	-120929.60	220.000	-120929.60
61		0.000	0.00	0.000	0.00
62		125.000	-67853.75	125.000	-67853.75
63		500.000	-279595.00	177.500	-99256.23
64		150.000	-77859.00	472.500	-245255.85
			-1295661.80		-1282708.62