! Conjoint analysis model to decide how much weight
  to give to the two product attributes of warranty
  length and price.
 Keywords: conjoint analysis, marketing, utility function;

! The possible warranty lengths;
! where WWT( i) = utility assigned to warranty i;

! The possible price levels;
   PRICE  : PWT;
! where PWT( j) = utility assigned to price j;

! We have a customer preference ranking for each
DATA: ! The possible warranty lengths and price levels for today's problem; WARRANTY = LONG, INTERMED, SHORT; PRICE= HI, MED, CHP; ! Here is the customer preference ranking, running from a least preferred score of 1 to the most preferred of 9. Note that long warranty and cheap price are most preferred with a score of 9, while short warranty and high price are least preferred with a score of 1; RANK = 7 8 9 3 4 6 1 2 5; ! We want to construct an additive utility function so that the utility of combination i,j is WWT(i) + PWT(j). A weighting that works for this ranking is: WWT( LONG) 7.00 WWT( INTERMED) 2.00 WWT( SHORT) 0.00 PWT( HI) 0.00 PWT( MED) 1.00 PWT( CHP) 4.00; ENDDATA SETS: ! The next set generates all unique pairs of product configurations such that the second configuration is preferred to the first; WPWP( WP, WP) | RANK( &1, &2) #LT# RANK( &3, &4): ERROR; ! The attribute ERROR computes the error of our estimated preference from the preferences given us by the customer; ENDSETS
! For every pair of rankings, compute the amount by which our computed ranking violates the true ranking. Our computed ranking for the (i,j) combination is given by the sum WWT( i) + PWT( j). (NOTE: This makes the bold assumption that utilities are additive!); @FOR( WPWP( i, j, k, l): ERROR( i, j, k, l) >= 1 + ( WWT( i) + PWT( j)) - ( WWT( k) + PWT( l)) ); ! The 1 is required on the righthand-side of the above equation to force ERROR to be nonzero in the case where our weighting scheme incorrectly predicts that the combination (i,j) is equally preferred to the (k,l) combination. Because variables in LINGO have a default lower bound of 0, ERROR will be driven to zero when we correctly predict that (k,l) is preferred to (i,j). Next, we minimize the sum of all errors in order to make our computed utilities as accurate as possible; MIN = @SUM( WPWP: ERROR); END