QUESTION 1: Multi Attribute Utility Theory The infrastructure manager of a road maintenance company needs to prioritize maintenance for 22 bridges that are in need of repair based on four criteria. He is confronted with the constraints of limited budget, network availability and safety, among many others. Moreover, the infrastructure manager wants to perform maintenance only where he can minimise the owner costs and maximise the object's reliability level. Such a decision-making problem requires the assessment and selection of alternatives (i.e. bridges), where a trade-off among the objectives can be made and most of the constraints can be met. The data provided from the road transport agency included description of the twenty-two bridges in terms of bridges' age, geometry, condition index on the element level, traffic intensity, planned maintenance activity on the element level, unit cost of chosen maintenance option, and maintenance duration. For this illustrative application of MAUT, the twenty-two bridges are required to be ranked based on the following 4 criteria's: (a) Condition Index (CI) (b) Owner Cost (OC) (c) User Delay Cost (UDC); and (d) Environmental Impact (EI) The score obtained for each bridge using the available data for each criteria is presented in the Table 1. Table 1: Score of each alternative for each criteria No. Bridges Name Attributes UDC EC 1 Bridge A 2.77 139.35 39.70 0.86 2 Bridge B 1.89 126.41 27.50 0.21 3 Bridge C 2.15 115.67 25.57 0.57 4 Bridge D 2.73 42.94 3.41 0.02 5 Bridge E 2.00 68.16 12.40 0.53 6 Bridge F 2.12 149.21 47.89 0.23 7 Bridge G 2.10 169.56 57.79 0.48 8 Bridge H 2.42 88.60 13.11 1.25 9 Bridge I 2.22 45.82 35.89 1.26 10 Bridge J 2.34 115.93 30.80 0.43 11 Bridge K 2.42 39.42 12.69 0.23 12 Bridge L 2.46 69.61 12.12 0.03 13 Bridge M 1.92 38.14 7.99 0.03 14 Bridge N 2.18 84.89 14.42 1.05 15 Bridge O 2.43 46.89 4.59 0.00 16 Bridge P 1.67 175.33 28.51 0.68 17 Bridge Q 2.08 161.48 55.25 0.37 18 Bridge R 2.30 158.89 51.04 0.22 19 Bridge S 2.58 65.90 8.79 0.10 20 Bridge T 1.96 62.22 22.83 0.42 21 Bridge U 2.02 84.82 25.70 0.28 22 Bridge V 2.34 152.60 42.91 0.27 The manager has also analysed the raw data and established the following utility function for each criteria: Utility function for Cl: U(xi) = 1.26 13.72* e-xi/0.7 Utility function for OC: U(xi) = 1.00 -4.13 * e-xi/27 Utility function for UDC: Ui(*) = 1.00 -1.34* e-xi/14 Utility function for EC: U(xi) = 1.08-1.09 * e-xi/0.5 Additionally, the infrastructure manager has assigned the following weights to each criterion to reflect their relative importance: CI = 0.29; OC = 0.32; UDC = 0.14; and EC = 0.25. By using the information provided in Table 1 and the utility function, rank the bridges using MAUT approach.