MODEL:
! 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 three possible price levels: high(H), medium(M), cheap(C));
! The possible warranty lengths are: Long(L), Intermed(I), and Short(S).
! Here is the customer preference rankings 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.
HI, MED, CHP
Long 7 8 9
Intermed 3 4 6
Short 1 2 5
We want to construct an additive utility function so that
the utility of combination i,j is WWT(i) + PWT(j).
Variables:
WWT_i = utility assigned to warranty i,
PWT_j = utility assigned to price j,
E_i_j_k_m = error in how the utility function
orders combination i,j vs. combination k,m
! 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;
MIN= E_L_H_L_M + E_L_H_L_C + E_L_M_L_C + E_I_H_L_H + E_I_H_L_M
+ E_I_H_L_C + E_I_H_I_M + E_I_H_I_C + E_I_H_S_C + E_I_M_L_H
+ E_I_M_L_M + E_I_M_L_C + E_I_M_I_C + E_I_M_S_C + E_I_C_L_H
+ E_I_C_L_M + E_I_C_L_C + E_S_H_L_H + E_S_H_L_M + E_S_H_L_C
+ E_S_H_I_H + E_S_H_I_M + E_S_H_I_C + E_S_H_S_M + E_S_H_S_C
+ E_S_M_L_H + E_S_M_L_M + E_S_M_L_C + E_S_M_I_H + E_S_M_I_M
+ E_S_M_I_C + E_S_M_S_C + E_S_C_L_H + E_S_C_L_M + E_S_C_L_C
+ E_S_C_I_C ;
! A Constaint for each pair of combinations for which the customer
preferred combination (k,m) to combination (i,j). The constraint
forces Error(i,j,k,m) >= 1 if the utility function nevertheless
implies (i,j) if preferred to (k,m);
[ _2] E_L_H_L_C - PWT_H + PWT_C >= 1 ;
[ _3] E_L_M_L_C - PWT_M + PWT_C >= 1 ;
[ _4] E_I_H_L_H + WWT_L - WWT_I >= 1 ;
[ _5] E_I_H_L_M - PWT_H + PWT_M + WWT_L - WWT_I >= 1 ;
[ _6] E_I_H_L_C - PWT_H + PWT_C + WWT_L - WWT_I >= 1 ;
[ _7] E_I_H_I_M - PWT_H + PWT_M >= 1 ;
[ _8] E_I_H_I_C - PWT_H + PWT_C >= 1 ;
[ _9] E_I_H_S_C - PWT_H + PWT_C - WWT_I + WWT_S >= 1 ;
[_10] E_I_M_L_H + PWT_H - PWT_M + WWT_L - WWT_I >= 1 ;
[_11] E_I_M_L_M + WWT_L - WWT_I >= 1 ;
[_12] E_I_M_L_C - PWT_M + PWT_C + WWT_L - WWT_I >= 1 ;
[_13] E_I_M_I_C - PWT_M + PWT_C >= 1 ;
[_14] E_I_M_S_C - PWT_M + PWT_C - WWT_I + WWT_S >= 1 ;
[_15] E_I_C_L_H + PWT_H - PWT_C + WWT_L - WWT_I >= 1 ;
[_16] E_I_C_L_M + PWT_M - PWT_C + WWT_L - WWT_I >= 1 ;
[_17] E_I_C_L_C + WWT_L - WWT_I >= 1 ;
[_18] E_S_H_L_H + WWT_L - WWT_S >= 1 ;
[_19] E_S_H_L_M - PWT_H + PWT_M + WWT_L - WWT_S >= 1 ;
[_20] E_S_H_L_C - PWT_H + PWT_C + WWT_L - WWT_S >= 1 ;
[_21] E_S_H_I_H + WWT_I - WWT_S >= 1 ;
[_22] E_S_H_I_M - PWT_H + PWT_M + WWT_I - WWT_S >= 1 ;
[_23] E_S_H_I_C - PWT_H + PWT_C + WWT_I - WWT_S >= 1 ;
[_24] E_S_H_S_M - PWT_H + PWT_M >= 1 ;
[_25] E_S_H_S_C - PWT_H + PWT_C >= 1 ;
[_26] E_S_M_L_H + PWT_H - PWT_M + WWT_L - WWT_S >= 1 ;
[_27] E_S_M_L_M + WWT_L - WWT_S >= 1 ;
[_28] E_S_M_L_C - PWT_M + PWT_C + WWT_L - WWT_S >= 1 ;
[_29] E_S_M_I_H + PWT_H - PWT_M + WWT_I - WWT_S >= 1 ;
[_30] E_S_M_I_M + WWT_I - WWT_S >= 1 ;
[_31] E_S_M_I_C - PWT_M + PWT_C + WWT_I - WWT_S >= 1 ;
[_32] E_S_M_S_C - PWT_M + PWT_C >= 1 ;
[_33] E_S_C_L_H + PWT_H - PWT_C + WWT_L - WWT_S >= 1 ;
[_34] E_S_C_L_M + PWT_M - PWT_C + WWT_L - WWT_S >= 1 ;
[_35] E_S_C_L_C + WWT_L - WWT_S >= 1 ;
[_36] E_S_C_I_C + WWT_I - WWT_S >= 1 ;
[_37] E_L_H_L_M - PWT_H + PWT_M >= 1 ;
END
|