Example 7.7 Using a Constrained Solution Warm Start :: SAS/OR(R) 12.1 User's Guide: Mathematical Programming Legacy Procedures

Example 7.7 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' 
        & (_head_='shop1_2' | _head_='shop2_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 7.7.1: 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 7.7.2: 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 7.7.3: 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