Example 4.3: Using a Warm Start

The NETFLOW Procedure

Example 4.3: Using a Warm Start

Suppose that the airlines state that the freight cost per pineapple in flights that leave Chicago has been reduced by 30. How many pineapples should take each route between Hawaii and London? This example illustrates how PROC NETFLOW uses a warm start. In Example 4.2, the RESET statement of PROC NETFLOW is used to specify FUTURE1. A NODEOUT= data set is also specified. The warm start information is saved in the arcout1 and nodeout1 data sets.

In the following DATA step, the costs, reduced costs, and flows in the arcout1 data set are saved in variables called oldcost, oldflow, and oldfc. These variables form an implicit ID list in the following PROC NETFLOW run and will appear in ARCOUT=arcout2. Thus, it is easy to compare the previous optimum and the new optimum.

title 'Minimum Cost Flow Problem - Warm Start';
title2 'How to get Hawaiian Pineapples to a London Restaurant';
data aircost2;
   set arcout1;
      oldcost=_cost_;
      oldflow=_flow_;
      oldfc=_fcost_;
      if ffrom='Chicago' then _cost_=_cost_-30;
proc netflow
   warm
      arcdata=aircost2
      nodedata=nodeout1
      arcout=arcout2;
         tail    ffrom;
         head    tto;
proc print data=arcout2;
   var ffrom tto _cost_ oldcost _capac_ _lo_ 
       _flow_ oldflow _fcost_ oldfc; 
   sum _fcost_ oldfc;
run;

The following notes appear on the SAS log:

NOTE: Number of nodes= 8 .
NOTE: Number of supply nodes= 1 .
NOTE: Number of demand nodes= 1 .
NOTE: Total supply= 500 , total demand= 500 .
NOTE: Number of iterations performed (neglecting any
      constraints)= 3 .
NOTE: Of these, 1 were degenerate.
NOTE: Optimum (neglecting any constraints) found.
NOTE: Minimal total cost= 93150 .

ARCOUT=arcout2 is shown in Output 4.3.1.

Output 4.3.1: ARCOUT=ARCOUT2

Minimum Cost Flow Problem - Warm Start

How to get Hawaiian Pineapples to a London Restaurant

Obs	ffrom	tto	_cost_	oldcost	_CAPAC_	_LO_	_FLOW_	oldflow	_FCOST_	oldfc
1	San Francisco	Atlanta	63	63	350	0	0	0	0	0
2	Los Angeles	Atlanta	57	57	350	0	0	150	0	8550
3	Chicago	Boston	15	45	350	0	150	0	2250	0
4	San Francisco	Boston	71	71	350	0	0	0	0	0
5	Honolulu	Chicago	105	105	350	0	150	0	15750	0
6	Boston	Heathrow London	88	88	350	0	150	0	13200	0
7	New York	Heathrow London	65	65	350	0	350	350	22750	22750
8	Atlanta	Heathrow London	76	76	350	0	0	150	0	11400
9	Honolulu	Los Angeles	68	68	350	0	350	350	23800	23800
10	Chicago	New York	26	56	350	0	0	0	0	0
11	San Francisco	New York	48	48	350	0	0	150	0	7200
12	Los Angeles	New York	44	44	350	0	350	200	15400	8800
13	Honolulu	San Francisco	75	75	350	0	0	150	0	11250
									93150	93750

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