CIVE 646 Homework 3 Solution, Fall 2011

AUB-FEA-CEE CIVE646- Water Resources Systems: Planning and Management Fall 2011-12 Homework # 3 - Solution CIVE 646 - Water Resources Systems: Planning and Management (Fall 2011-12) Topics: 5) Multicriteria Decision Analysis Problems 5.1 The following performance matrix is for a multicriteria decision making problem related to a water resources project: g1 g2 g3 g4 g5 g6 Min/Max Min Max Min Min Min Max a1 80 90 600 54 8 5 a2 65 58 200 97 1 1 a3 83 60 400 72 4 7 a4 40 80 1000 75 7 10 a5 52 72 600 20 3 8 a6 94 96 700 36 5 6 A is the set of alternatives and G is the set of criteria. g1: estimated annual maintenance cost (M US$) g2: technical value (rating score out of 100) g3: construction cost (M US$) g4: annual operation cost (M US$) g5: environmental impact (rating score out of 10) g6: estimated water supply (103 m3/day) Rank the alternatives using Promothee method. Apply the following parameters: Criterion Type Parameters Weight g1 q = 10 1 g2 p = 30 1 g3 q = 50, p = 500 1 g4 q = 10, p = 60 1 g5 - 1 g6 p = 2 1 AUB-FEA-CEE CIVE646- Water Resources Systems: Planning and Management Fall 2011-12 Solution: g1(a): Criterion to be minimized: g1(a1) – g1(a2) = 15 and therefore: c1(a1,a2) = 0 c1(a2,a1) =1 g2(a): Criterion to be maximized: g2(a1) – g2(a2) = 32 and therefore: c2(a1,a2) = 1 c2(a2,a1) =0 g3(a): Criterion to be minimized: g3(a1) – g3(a2) = 32 and therefore: c3(a1,a2) = 1 c3(a2,a1) = 0.778 g4(a): Criterion to be minimized: g4(a1) – g4(a2) = - 43 and therefore: c4(a1,a2) = 0.5 c4(a2,a1) = 0 g5(a): Criterion to be minimized: g5(a1) – g5(a2) = 7 and therefore: c5(a1,a2) = 0 1 - 10 0 + 10 d 1 0 d -30 +30 1 0 d 50 500 - 500 - 50 1 0 d 10 60 - 60 -10 1/2 1 0 d AUB-FEA-CEE CIVE646- Water Resources Systems: Planning and Management Fall 2011-12 c5(a2,a1) = 1 g6(a): Criterion to be maximized: g6(a1) – g6(a2) = 4 and therefore: c6(a1,a2) = 1 c6(a2,a1) = 0 g1 g2 g3 g4 g5 g6 c(a1,a2) 0 1 0 0.5 0 1 c(a1,a3) 0 1 0 0.5 0 0 c(a1,a4) 0 0.33 0.78 0.5 0 0 c(a1,a5) 0 0.6 0 0 0 0 c(a1,a6) 1 0 0.11 0 0 0 c(a2,a1) 1 0 0.78 0 1 0 c(a2,a3) 1 0 0.33 0 1 0 c(a2,a4) 0 0 1 0 1 0 c(a2,a5) 0 0 0.78 0 1 0 c(a2,a6) 1 0 1 0 1 0 c(a3,a1) 0 0 0.33 0 1 1 c(a3,a2) 0 0.067 0 0.5 0 1 c(a3,a4) 0 0 1 0 1 0 c(a3,a5) 0 0 0.33 0 0 0 c(a3,a6) 1 0 0.55 0 1 0.5 c(a4,a1) 1 0 0 0 1 1 c(a4,a2) 1 0.73 0 0.5 0 1 c(a4,a3) 1 0.67 0 0 0 1 c(a4,a5) 1 0.267 0 0 0 1 c(a4,a6) 1 0 0 0 0 1 c(a5,a1) 1 0 0 0.5 1 1 c(a5,a2) 1 0.47 0 1 0 1 c(a5,a3) 1 0.4 0 0.5 1 0.5 c(a5,a4) 0 0 0.78 0.5 1 0 c(a5,a6) 1 0 0.11 0.5 1 1 c(a6,a1) 0 0.2 0 0.5 1 0.5 c(a6,a2) 0 1 0 1 0 1 c(a6,a3) 0 1 0 0.5 0 0 c(a6,a4) 0 0.53 0.55 0.5 1 0 c(a6,a5) 0 0.8 0 0 0 0 S a1 a2 a3 a4 a5 a6 +  = + - - a1 0.417 0.25 0.268 0.1 0.185 1.22 - 1.081 a2 0.463 0.388 0.33 0.297 0.5 1.978 - 0.308 a3 0.388 0.261 0.33 0.055 0.508 1.542 - 0.358 a4 0.5 0.538 0.445 0.378 0.33 2.191 0.453 a5 0.583 0.57 0.567 0.38 0.6 2.71 1.74 a6 0.367 0.5 0.25 0.43 0.133 1.68 - 0.443 - 2.301 2.286 1.9 1.738 0.962 2.123 1 0 d -2 +2 AUB-FEA-CEE CIVE646- Water Resources Systems: Planning and Management Fall 2011-12 Ranking of alternatives: 5.2 The Lebanese government intends to construct a treatment plant for wastewater disposal in the Sour drainage Zone (South Lebanon). Four alternatives were identified as follows: Alternative 1 (A1): Treatment of all wastewater generated in the area at a single WWTP located on the coast. Alternative 2 (A2): Coastal WWTP plus four smaller inland WWTPs Alternative 3 (A3): Coastal WWTP plus a WWTP for each interior village Alternative 4 (A4): Coastal WWTP and upgrading of the existing septic tanks in the interior villages The decision matrix is as follows: Cost (Million $) Technical rating Environmental rating Max/Min Min Min Max A1 124 16 16 A2 140 26 21 A3 142 24 20 A4 122 15 16 Rank the four alternative using Promothee method using the following parameters: Cost (Million $) Technical rating Environmental rating Weight 0.8 0.5 0.5 Preference Q = 2, p = 10 q = 2, p = 5 q = 2, p = 6 Solution: Cost Technical Environment weights 0.8 0.5 0.5 c(A1,A2) 1 1 0 c(A1,A3) 1 1 0 c(A1,A4) 0 0 0 c(A2,A1) 0 0 0.75 c(A2,A3) 0 0 0 c(A2,A4) 0 0 0.75 c(A3,A1) 0 0 0.5 c(A3,A2) 0 0 0 a 4 a 3 a 1 a 5 a 2 a 6 AUB-FEA-CEE CIVE646- Water Resources Systems: Planning and Management Fall 2011-12 c(A3,A4) 0 0 0.5 c(A4,A1) 0 0 0 c(A4,A2) 1 1 0 c(A4,A3) 1 1 0 S A1 A2 A3 A4 +  = + - - A1 0.722 0.722 0 1.444 1.097 A2 0.208 0 0.208 0.416 - 1.028 A3 0.139 0 0.139 0.278 - 1.166 A4 0 0.722 0.722 1.444 1.097 - 0.347 1.444 1.444 0.347 Ranking of alternatives: 5.3 Reformulate and solve the problem 5.2 by introducing the following environmental concerns: - Minimize discharge into Mediterranean - Minimize discharge to surface waters - Minimize discharge into groundwater - Highest potential source of irrigation water for interior areas - Minimize sludge production - Minimize space requirement - Minimize impact to areas of high protection value because of rareness of environment - Minimize impairment of historical or cultural monuments - Not creating mosquito breeding areas - Not causing diseases by use of effluent for irrigation Use a Maximization rating scale between 1 and 4 to evaluate the above mentioned environmental concerns. Solution: A1 A2 A3 A4 Minimize discharge into Mediterranean 4 2 1 1 Minimize discharge to surface waters 1 4 4 2 Minimize discharge into groundwater 1 2 2 4 Highest potential source of irrigation water for interior areas 3 2 2 3 Minimize sludge production 2 2 2 1 Minimize space requirement 1 1 1 1 Minimize impact to areas of high protection value because of rareness of environment 1 1 1 1 Minimize impairment of historical or cultural monuments 1 1 1 1 Not creating mosquito breeding areas 1 3 3 1 Not causing diseases by use of effluent for irrigation 1 3 3 1 Total Environmental rating 16 21 20 16 A1 A4 A2 A3 AUB-FEA-CEE CIVE646- Water Resources Systems: Planning and Management Fall 2011-12 The total Environmental rating of each alternative is the same as problem 5.2 Ranking of alternatives: same as problem 5.2 5.4 A water supply project consists of identifying the most suitable development scenario for water supply in the Sour region. Of necessity the choice of alternatives must consider various criteria; cost (investment, operation and maintenance costs), water quality, water quantity, … Present water sources: The existing water supply in Sour area is provided from: Source Capacity (m3/day) Ras el Ain source 15,000 Er Rachidiye spring 10,000 Ouadi Jilo artesian wells 10,000 Total 45,000 The water demand for the area in the year 2015 is estimated to 90,000 m3/day. Two alternatives were identified: Alternative 1: The concept of alternative 1 is to concentrate the majority of the official water supply at Ras el Ain in order to make maximum use of the good quality water which comes naturally from these springs. The total development for this alternative consists of: - Extension of WTP for Ras el Ain source to provide an additional capacity of 50,000 m3/day - Construction of new pumping station at Ras el Ain - Construction of new transmission pipelines from Ras el Ain to Hanaouay and Saddiqine regional reservoirs - Construction of new distribution pipelines The detailed construction cost of this alternative is as follows: Construction Works Cost Million $ Extension of WTP & pumping station 4,1 Transmission networks 8,9 Distribution networks 4,6 Alternative 2: The concept of this alternative is to provide more dispersed sources of supply rather than concentrating on the major source of Ras el Ain. It consists of: - Extension of WTP for Ras el Ain source to provide an additional capacity of 20,000 m3/day - Drilling new artesian wells in different locations in the region of a capacity of 20,000 m3/day - Construction of new transmission pipelines - Construction of new distribution pipelines The detailed construction cost of this alternative is as follows: Construction Works Cost Million $ Extension of WTP & drilling new wells 3,6 Transmission networks 9,9 AUB-FEA-CEE CIVE646- Water Resources Systems: Planning and Management Fall 2011-12 Distribution networks 4,6 Land 0,2 1- Propose criteria to perform multicriteria decision analysis. 2- Propose methods to evaluate the identified criteria. 3- Construct the performance matrix. 4- Rank the alternatives using Promothee method. Solution: Solution depends on criteria and methods of evaluation selected by students