1. Multiattribute utility theory (Excel) 10pts You are thinking of going on a holiday and trying to find the best holiday destination. Basing on three attributes, you will first build the additive multiattribute model u(x1, x2, x3) = wu (xi) i=1 and then use it to systematically evaluate the goodness of each destination. The attributes for your decision problem are The number of possible activities (i = 1), Safety for tourists (i = 2), and Distance from where you live (i = 3). The measurement scales of attributes i = 1,2,3 are [1, 5], {satisfactory, good, very good, excellent}, and [0 km, 3000 km], respectively. The attribute specific utilities are given as follows: Attribute i = 1 has a linear increasing attribute-specific utility function (the more activities the better) Attribute 2 has the utilities u (satisfactory) = 0, u (good) = 0.5, u (very good) = 0.75, u (excellent) = 1 For attribute i = 3 you'll go through the following internal dialogue: To maximise the exoticism of my holiday and follower engagement on social media, I want the destination to be far away rather than near Then if I have two destinations A and B that are equally preferred on attributes 1 and 2, and distance for A is uncertain with 50-50 chance of being either 0 or 3000 km, then what would be a certain distance for B so that A and B are equally preferred? o That would have to be around 1000 km... Nah, this is too hard to think through, let me just use a piecewise linear utility function that is consistent with x3 = 1000 a) Implement the utility functions U1, U2, U3 on the answer template file. Scale the utilities so that most preferred performance level gets attribute-specific utility of one and the least preferred performance level the utility of zero. Check that your model is correct up to this step by inputting an alternative xcheck = (4, good, 2100) that should give attribute-specific utilities of 0.75, 0.5, and 0.775, respectively. Then you start thinking about the relative importance of each attribute, i.e. the attribute weights. You make internally the following two observations about your preferences: If there are two destinations C and D that have outcomes xc = (5,satisfactory, 3000) and x = (x,excellent, 3000), you would think that a level of x = 2 would make C and D equally preferred If there are two destinations E and F with outcomes x = (3,satisfactory, 3000) and xF (3,excellent, 0), then E and F would be equally desirable for you. = b) Estimate attribute weights W, W2, W3 so that they sum to one and implement the overall utility function on the answer template. The alternative x check = (4, good, 21) should give a total utility of 0.6825. c) Compute the expected utilities for the following three alternatives using your model: Alternative Number of activities Reykjavik 4 Prague Tbilisi 3 5 Safety excellent very good satisfactory, 0.4; good, 0.6 Distance (km) 1500 1600 2900 Note: the Safety rating for 'Tbilisi' is random and depending on geopolitical uncertainties. The outcomes are: rating = satisfactory with probability 0.4, otherwise rating = good. Motivation: A practical exercise on constructing the MAUT model. A B C D E F 1 Note: please use only the green coloured cells for your answer input, do not add, merge, or delete cells or rows 123 10 11 12 13 45698020723 Alternative Number of activities Reykjavik 4 3 Tbilisi 5 Safety excellent 1500 SAT Prague very good 1600 Distance (km) (satisfactory,.4; good,.6) 2900 G H J K L M N a) Attribute specific utilities u1(4,good,2100) u2(4,good,2100)| u3(4,good,2100)| b) Attribute weights w1 w2 W3 c) Expected total utilities Reykjavik Prague Tbilisi P