The INTPOINT Procedure

Example 4.1 Production, Inventory, Distribution Problem

The following code shows how to save a specific problem’s data in data sets and solve the model with PROC INTPOINT.

title 'Production Planning/Inventory/Distribution';
title2 'Minimum Cost Flow problem';
title3;

data node0;
   input _node_ $ _supdem_ ;
   datalines;
fact1_1   1000
fact2_1    850
fact1_2   1000
fact2_2   1500
shop1_1   -900
shop2_1   -900
shop1_2   -900
shop2_2  -1450
;

data arc0;
   input _tail_ $ _head_ $ _cost_ _capac_ _lo_ diagonal factory
         key_id $10. mth_made $ _name_&$17. ;
   datalines;
fact1_1  f1_mar_1  127.9  500 50 19 1 production March prod f1 19 mar
fact1_1  f1_apr_1   78.6  600 50 19 1 production April prod f1 19 apl
fact1_1  f1_may_1   95.1  400 50 19 1 production May   .
f1_mar_1 f1_apr_1   15     50  . 19 1 storage    March .
f1_apr_1 f1_may_1   12     50  . 19 1 storage    April .
f1_apr_1 f1_mar_1   28     20  . 19 1 backorder  April back f1 19 apl
f1_may_1 f1_apr_1   28     20  . 19 1 backorder  May   back f1 19 may
f1_mar_1 f2_mar_1   11      .  . 19 . f1_to_2    March .
f1_apr_1 f2_apr_1   11      .  . 19 . f1_to_2    April .
f1_may_1 f2_may_1   16      .  . 19 . f1_to_2    May   .
f1_mar_1 shop1_1  -327.65 250  . 19 1 sales      March .
f1_apr_1 shop1_1  -300    250  . 19 1 sales      April .
f1_may_1 shop1_1  -285    250  . 19 1 sales      May   .
f1_mar_1 shop2_1  -362.74 250  . 19 1 sales      March .
f1_apr_1 shop2_1  -300    250  . 19 1 sales      April .
f1_may_1 shop2_1  -245    250  . 19 1 sales      May   .
fact2_1  f2_mar_1   88.0  450 35 19 2 production March prod f2 19 mar
fact2_1  f2_apr_1   62.4  480 35 19 2 production April prod f2 19 apl
fact2_1  f2_may_1  133.8  250 35 19 2 production May   .
f2_mar_1 f2_apr_1   18     30  . 19 2 storage    March .
f2_apr_1 f2_may_1   20     30  . 19 2 storage    April .
f2_apr_1 f2_mar_1   17     15  . 19 2 backorder  April back f2 19 apl
f2_may_1 f2_apr_1   25     15  . 19 2 backorder  May   back f2 19 may
f2_mar_1 f1_mar_1   10     40  . 19 . f2_to_1    March .
f2_apr_1 f1_apr_1   11     40  . 19 . f2_to_1    April .
f2_may_1 f1_may_1   13     40  . 19 . f2_to_1    May   .
f2_mar_1 shop1_1  -297.4  250  . 19 2 sales      March .
f2_apr_1 shop1_1  -290    250  . 19 2 sales      April .
f2_may_1 shop1_1  -292    250  . 19 2 sales      May   .
f2_mar_1 shop2_1  -272.7  250  . 19 2 sales      March .
f2_apr_1 shop2_1  -312    250  . 19 2 sales      April .
f2_may_1 shop2_1  -299    250  . 19 2 sales      May   .
fact1_2  f1_mar_2  217.9  400 40 25 1 production March prod f1 25 mar
fact1_2  f1_apr_2  174.5  550 50 25 1 production April prod f1 25 apl
fact1_2  f1_may_2  133.3  350 40 25 1 production May   .
f1_mar_2 f1_apr_2   20     40  . 25 1 storage    March .
f1_apr_2 f1_may_2   18     40  . 25 1 storage    April .
f1_apr_2 f1_mar_2   32     30  . 25 1 backorder  April back f1 25 apl
f1_may_2 f1_apr_2   41     15  . 25 1 backorder  May   back f1 25 may
f1_mar_2 f2_mar_2   23      .  . 25 . f1_to_2    March .
f1_apr_2 f2_apr_2   23      .  . 25 . f1_to_2    April .
f1_may_2 f2_may_2   26      .  . 25 . f1_to_2    May   .
f1_mar_2 shop1_2  -559.76   .  . 25 1 sales      March .
f1_apr_2 shop1_2  -524.28   .  . 25 1 sales      April .
f1_may_2 shop1_2  -475.02   .  . 25 1 sales      May   .
f1_mar_2 shop2_2  -623.89   .  . 25 1 sales      March .
f1_apr_2 shop2_2  -549.68   .  . 25 1 sales      April .
f1_may_2 shop2_2  -460.00   .  . 25 1 sales      May   .
fact2_2  f2_mar_2  182.0  650 35 25 2 production March prod f2 25 mar
fact2_2  f2_apr_2  196.7  680 35 25 2 production April prod f2 25 apl
fact2_2  f2_may_2  201.4  550 35 25 2 production May   .
f2_mar_2 f2_apr_2   28     50  . 25 2 storage    March .
f2_apr_2 f2_may_2   38     50  . 25 2 storage    April .
f2_apr_2 f2_mar_2   31     15  . 25 2 backorder  April back f2 25 apl
f2_may_2 f2_apr_2   54     15  . 25 2 backorder  May   back f2 25 may
f2_mar_2 f1_mar_2   20     25  . 25 . f2_to_1    March .
f2_apr_2 f1_apr_2   21     25  . 25 . f2_to_1    April .
f2_may_2 f1_may_2   43     25  . 25 . f2_to_1    May   .
f2_mar_2 shop1_2  -567.83 500  . 25 2 sales      March .
f2_apr_2 shop1_2  -542.19 500  . 25 2 sales      April .
f2_may_2 shop1_2  -461.56 500  . 25 2 sales      May   .
f2_mar_2 shop2_2  -542.83 500  . 25 2 sales      March .
f2_apr_2 shop2_2  -559.19 500  . 25 2 sales      April .
f2_may_2 shop2_2  -489.06 500  . 25 2 sales      May   .
;

proc intpoint
   bytes=1000000
   printlevel2=2
   nodedata=node0
   arcdata=arc0
   conout=arc1;
   run;

proc print data=arc1 width=min;
   var _tail_ _head_ _cost_ _capac_ _lo_ _flow_ _fcost_
       diagonal factory key_id mth_made;
   sum _fcost_;
   run;

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

solved by the Interior Point algorithm.

NOTE: Number of <= constraints= 0 .

NOTE: Number of == constraints= 21 .

NOTE: Number of >= constraints= 0 .

NOTE: Number of constraint coefficients= 136 .

NOTE: Number of variables= 68 .

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

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

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

surplus variables.

NOTE: There are 48 sub-diagonal nonzeroes in the unfactored A Atranspose matrix.

NOTE: The 20 factor nodes make up 8 supernodes

NOTE: There are 27 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 192857968 0.895105 66024 25664 0

1 37620673 24479828 0.919312 4575.155540 1778.391068 0

2 4392127 1833947 0.594993 0 0 0

3 654204 426961 0.249790 0 0 0

4 161214 108340 0.075186 0 0 0

5 50985 43146 0.030894 0 0 0

6 37774 34993 0.025167 0 0 0

7 17695 9774.172272 0.007114 0 0 0

8 2421.777663 1427.435257 0.001042 0 0 0

9 522.394743 240.454270 0.000176 0 0 0

10 57.447587 7.581156 0.000005540 0 0 0

11 0.831035 0.007569 5.5317109E-9 0 0 0

NOTE: The Primal-Dual Predictor-Corrector Interior Point algorithm performed 11

iterations.

NOTE: Optimum reached.

NOTE: Objective= -1281110.338.

NOTE: The data set WORK.ARC1 has 64 observations and 14 variables.

NOTE: There were 64 observations read from the data set WORK.ARC0.

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

The solution is given in the CONOUT=arc1 data sets. In the CONOUT= data set, shown in Output 4.1.1, the variables diagonal, factory, key_id, and mth_made form an implicit ID list. The diagonal variable has one of two values, 19 or 25. factory also has one of two values, 1 or 2, to denote the factory where either production or storage occurs, from where TVs are either sold to shops or used to satisfy backorders. production, storage, sales, and backorder are values of the key_id variable.

Other values of this variable, f1_to_2 and f2_to_1, are used when flow through arcs represents the transportation of TVs between factories. The mth_made variable has values March, April, and May, the months when TVs that are modeled as flow through an arc were made (assuming that no televisions are stored for more than one month and none manufactured in May are used to fill March backorders).

These ID variables can be used after the PROC INTPOINT run to produce reports and perform analysis on particular parts of the company’s operation. For example, reports can be generated for production numbers for each factory; optimal sales figures for each shop; and how many TVs should be stored, used to fill backorders, sent to the other factory, or any combination of these, for TVs with a particular screen, those produced in a particular month, or both.

Output 4.1.1: CONOUT=ARC1

Obs	_tail_	_head_	_cost_	_capac_	_lo_	_FLOW_	_FCOST_	diagonal	factory	key_id	mth_made
1	fact1_1	f1_apr_1	78.60	600	50	600.000	47160.00	19	1	production	April
2	f1_mar_1	f1_apr_1	15.00	50	0	0.000	0.00	19	1	storage	March
3	f1_may_1	f1_apr_1	28.00	20	0	0.000	0.00	19	1	backorder	May
4	f2_apr_1	f1_apr_1	11.00	40	0	0.000	0.00	19	.	f2_to_1	April
5	fact1_2	f1_apr_2	174.50	550	50	550.000	95975.00	25	1	production	April
6	f1_mar_2	f1_apr_2	20.00	40	0	0.000	0.00	25	1	storage	March
7	f1_may_2	f1_apr_2	41.00	15	0	15.000	615.00	25	1	backorder	May
8	f2_apr_2	f1_apr_2	21.00	25	0	0.000	0.00	25	.	f2_to_1	April
9	fact1_1	f1_mar_1	127.90	500	50	344.999	44125.43	19	1	production	March
10	f1_apr_1	f1_mar_1	28.00	20	0	20.000	560.00	19	1	backorder	April
11	f2_mar_1	f1_mar_1	10.00	40	0	40.000	400.00	19	.	f2_to_1	March
12	fact1_2	f1_mar_2	217.90	400	40	400.000	87160.00	25	1	production	March
13	f1_apr_2	f1_mar_2	32.00	30	0	30.000	960.00	25	1	backorder	April
14	f2_mar_2	f1_mar_2	20.00	25	0	25.000	500.00	25	.	f2_to_1	March
15	fact1_1	f1_may_1	95.10	400	50	50.001	4755.06	19	1	production	May
16	f1_apr_1	f1_may_1	12.00	50	0	50.000	600.00	19	1	storage	April
17	f2_may_1	f1_may_1	13.00	40	0	0.000	0.00	19	.	f2_to_1	May
18	fact1_2	f1_may_2	133.30	350	40	40.000	5332.04	25	1	production	May
19	f1_apr_2	f1_may_2	18.00	40	0	0.000	0.00	25	1	storage	April
20	f2_may_2	f1_may_2	43.00	25	0	0.000	0.00	25	.	f2_to_1	May
21	f1_apr_1	f2_apr_1	11.00	99999999	0	30.000	330.00	19	.	f1_to_2	April
22	fact2_1	f2_apr_1	62.40	480	35	480.000	29952.00	19	2	production	April
23	f2_mar_1	f2_apr_1	18.00	30	0	0.000	0.00	19	2	storage	March
24	f2_may_1	f2_apr_1	25.00	15	0	0.000	0.00	19	2	backorder	May
25	f1_apr_2	f2_apr_2	23.00	99999999	0	0.000	0.00	25	.	f1_to_2	April
26	fact2_2	f2_apr_2	196.70	680	35	680.000	133755.99	25	2	production	April
27	f2_mar_2	f2_apr_2	28.00	50	0	0.000	0.00	25	2	storage	March
28	f2_may_2	f2_apr_2	54.00	15	0	15.000	810.00	25	2	backorder	May
29	f1_mar_1	f2_mar_1	11.00	99999999	0	0.000	0.00	19	.	f1_to_2	March
30	fact2_1	f2_mar_1	88.00	450	35	290.000	25520.00	19	2	production	March
31	f2_apr_1	f2_mar_1	17.00	15	0	0.000	0.00	19	2	backorder	April
32	f1_mar_2	f2_mar_2	23.00	99999999	0	0.000	0.00	25	.	f1_to_2	March
33	fact2_2	f2_mar_2	182.00	650	35	645.000	117389.96	25	2	production	March
34	f2_apr_2	f2_mar_2	31.00	15	0	0.000	0.00	25	2	backorder	April
35	f1_may_1	f2_may_1	16.00	99999999	0	100.000	1600.01	19	.	f1_to_2	May
36	fact2_1	f2_may_1	133.80	250	35	35.000	4683.00	19	2	production	May
37	f2_apr_1	f2_may_1	20.00	30	0	15.000	299.99	19	2	storage	April
38	f1_may_2	f2_may_2	26.00	99999999	0	0.000	0.00	25	.	f1_to_2	May
39	fact2_2	f2_may_2	201.40	550	35	35.000	7049.00	25	2	production	May
40	f2_apr_2	f2_may_2	38.00	50	0	0.000	0.00	25	2	storage	April
41	f1_mar_1	shop1_1	-327.65	250	0	154.999	-50785.56	19	1	sales	March
42	f1_apr_1	shop1_1	-300.00	250	0	250.000	-75000.00	19	1	sales	April
43	f1_may_1	shop1_1	-285.00	250	0	0.000	0.00	19	1	sales	May
44	f2_mar_1	shop1_1	-297.40	250	0	250.000	-74349.99	19	2	sales	March
45	f2_apr_1	shop1_1	-290.00	250	0	245.001	-71050.17	19	2	sales	April
46	f2_may_1	shop1_1	-292.00	250	0	0.000	0.00	19	2	sales	May
47	f1_mar_2	shop1_2	-559.76	99999999	0	0.000	0.00	25	1	sales	March
48	f1_apr_2	shop1_2	-524.28	99999999	0	0.000	-0.01	25	1	sales	April
49	f1_may_2	shop1_2	-475.02	99999999	0	25.000	-11875.64	25	1	sales	May
50	f2_mar_2	shop1_2	-567.83	500	0	500.000	-283915.00	25	2	sales	March
51	f2_apr_2	shop1_2	-542.19	500	0	375.000	-203321.08	25	2	sales	April
52	f2_may_2	shop1_2	-461.56	500	0	0.000	0.00	25	2	sales	May
53	f1_mar_1	shop2_1	-362.74	250	0	250.000	-90685.00	19	1	sales	March
54	f1_apr_1	shop2_1	-300.00	250	0	250.000	-75000.00	19	1	sales	April
55	f1_may_1	shop2_1	-245.00	250	0	0.000	0.00	19	1	sales	May
56	f2_mar_1	shop2_1	-272.70	250	0	0.000	0.00	19	2	sales	March
57	f2_apr_1	shop2_1	-312.00	250	0	250.000	-78000.00	19	2	sales	April
58	f2_may_1	shop2_1	-299.00	250	0	150.000	-44850.00	19	2	sales	May
59	f1_mar_2	shop2_2	-623.89	99999999	0	455.000	-283869.94	25	1	sales	March
60	f1_apr_2	shop2_2	-549.68	99999999	0	535.000	-294078.78	25	1	sales	April
61	f1_may_2	shop2_2	-460.00	99999999	0	0.000	0.00	25	1	sales	May
62	f2_mar_2	shop2_2	-542.83	500	0	120.000	-65139.47	25	2	sales	March
63	f2_apr_2	shop2_2	-559.19	500	0	320.000	-178940.96	25	2	sales	April
64	f2_may_2	shop2_2	-489.06	500	0	20.000	-9781.20	25	2	sales	May
							-1281110.34