The OPTNET Procedure

A swimming coach needs to assign male and female swimmers to each stroke of a medley relay team. The swimmers’ best times for each stroke are stored in a SAS data set. The LINEAR_ASSIGNMENT statement evaluates the times and matches strokes and swimmers to minimize the total relay swim time.

The data are stored in matrix format, where the row identifier is the swimmer’s name (variable name) and each event is a column (variables: back, breast, fly, and free). In the following DATA step, the relay times are split into two categories, male and female:

data RelayTimes; 
   input name $ sex $ back breast fly free; 
   datalines; 
Sue     F 35.1 36.7 28.3 36.1 
Karen   F 34.6 32.6 26.9 26.2 
Jan     F 31.3 33.9 27.1 31.2 
Andrea  F 28.6 34.1 29.1 30.3 
Carol   F 32.9 32.2 26.6 24.0 
Ellen   F 27.8 32.5 27.8 27.0 
Jim     M 26.3 27.6 23.5 22.4 
Mike    M 29.0 24.0 27.9 25.4 
Sam     M 27.2 33.8 25.2 24.1 
Clayton M 27.0 29.2 23.0 21.9 
; 

data RelayTimesF RelayTimesM;
   set RelayTimes;
   if      sex='F' then output RelayTimesF;
   else if sex='M' then output RelayTimesM;
run;

The following statements solve the linear assignment problem for both male and female relay teams:

proc optnet
   data_matrix = RelayTimesF;
   linear_assignment
      out      = LinearAssignF
      id       = (name sex);
run;
%put &_OROPTNET_;
%put &_OROPTNET_LAP_;

proc optnet
   data_matrix = RelayTimesM;
   linear_assignment
      out      = LinearAssignM
      id       = (name sex);
run;
%put &_OROPTNET_;
%put &_OROPTNET_LAP_;

The progress of the two PROC OPTNET calls is shown in Output 2.3.1 and Output 2.3.2.

The data sets LinearAssignF and LinearAssignM contain the optimal assignments. Note that in the case of the female data, there are more people (set ) than there are strokes (set ). Therefore, the solver allows for some members of to remain unassigned.