Example 7.1 Shortest Path Problem

Whole pineapples are served in a restaurant in London. To ensure freshness, the pineapples are purchased in Hawaii and air freighted from Honolulu to Heathrow in London. The network diagram in Figure 7.39 outlines the different routes that the pineapples could take.

The cost to freight a pineapple is known for each arc. You can use PROC NETFLOW to determine what routes should be used to minimize total shipping cost. The shortest path is the least cost path that all pineapples should use. The SHORTPATH option indicates this type of network problem.

Figure 7.39 Pineapple Routes: Shortest Path Problem

The SINK= option value HEATHROW LONDON is not a valid SAS variable name so it must be enclosed in single quotes. The TAILNODE list variable is FFROM. Because the name of this variable is not _TAIL_ or _FROM_, the TAILNODE list must be specified in the PROC NETFLOW statement. The HEADNODE list must also be explicitly specified because the variable that belongs to this list does not have the name _HEAD_ or _TO_, but is TTO.

  title 'Shortest Path Problem';
  title2 'How to get Hawaiian Pineapples to a London Restaurant';
  data aircost1;
     input   ffrom&$13. tto&$15. _cost_ ;
     datalines;
  Honolulu       Chicago          105
  Honolulu       San Francisco     75
  Honolulu       Los Angeles       68
  Chicago        Boston            45
  Chicago        New York          56
  San Francisco  Boston            71
  San Francisco  New York          48
  San Francisco  Atlanta           63
  Los Angeles    New York          44
  Los Angeles    Atlanta           57
  Boston         Heathrow London   88
  New York       Heathrow London   65
  Atlanta        Heathrow London   76
  ;

proc netflow
   shortpath
   sourcenode=Honolulu 
   sinknode='Heathrow London'   /* Quotes for embedded blank */
   ARCDATA=aircost1
   arcout=spath;
   tail    ffrom;
   head    tto;
run;

proc print data=spath; 
   sum _fcost_;
run;

The length at optimality is written to the SAS log as

The output data set ARCOUT=SPATH in Output 7.1.1 shows that the best route for the pineapples is from Honolulu to Los Angeles to New York to Heathrow London.