Hello, dear friend, you can consult us at any time if you have any questions, add WeChat: THEend8_
Homework 3
ISE 562
A multi-attribute decision problem is shown below for a decision to select an apartment. The
following six attributes were defined as important to choosing the apartment.
Rental cost per month per tenant, R, dollars
Deposit required, D, dollars
Distance to university, M, miles
Noise level, 6pm-6am, N, subjective scale (0-10)
Length of lease required, L, months
Media (internet/cable) service, I, indicator scale (0= none; 1= internet or cable; 2= both)
The data table for the alternatives and attributes is:
______________________Attributes_________________________________________
Apt Rent, R Deposit, D Distance, M Noise, N Lease, L Media
A $450 $1100 5 5 12 1
B 380 850 4 3 12 0
C 550 1000 0.8 8 9 1
D 640 900 0.5 9 9 2____
After some reflection you and your roommates come up with the following attribute utility functions.
YÐ Ñ œ Ð '%!Ñ $)! Ÿ V Ÿ '%!V "260 R for
YÐHÑ œ ÐH ""!!Ñ )&! Ÿ H Ÿ ""!!"#&! for
YÐQÑ œ ÐQ &Ñ !Þ& Ÿ Q Ÿ &#* for
YÐRÑ œ ÐR *Ñ $ Ÿ R Ÿ *"$' # for
YÐPÑ œ Ð"# PÑ * Ÿ P Ÿ "#"* # for
YÐMÑ œ M ! Ÿ M Ÿ #"% # for
You determine that your own tradeoff scaling constants (you are decision maker 1) are:
k =0.40 k =0.40 k =0.10 k =0.20 k =0.60 k =0.60R D Mà à à à àR P M
1. Using the data in the table, find the master scaling constant for the attributes to 6 decimal'
places. Plot the master scaling constant function over the appropriate range.
2. Compute the multiattribute utility and rankings for the four alternative apartments using the
data for decision maker 1. What is your recommended choice? Why is it in first place (don't
say “because it has the largest utility.”)
3. Compute the additive model equivalent of question 2 by normalizing the attribute tradeoff
scaling constants to 1.0. Does it make a difference?
24. Now suppose your friends who will share the apartment with you want to input their own
attribute scaling constants to the problem. The value data for decision makers 2, 3, and 4 are
shown in the following table. Using the utility functions above, compute the rankings for
decision makers 2, 3, and 4.