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# lecture1-7 - METHODS IV SYSTEMS ANALYSIS AND DECISION...

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Unformatted text preview: METHODS IV: SYSTEMS ANALYSIS AND DECISION MAKING Allahviranloo, Winter,2012 4 CEE111: METHODS IV: SYSTEMS ANALYSIS AND DECISION MAKING Lab sessions instructor: Mahdieh Allahviranloo, Winter 2011. 1 Session 1:Linear problem optimization and examples Linear programming models: 1- Formulating the problem a. Decision variable b. Constraints formulation c. Objective function formulation 2- Data gathering 3- Sensitivity analysis 4- Validation and application In every lecture, I will bring 2 examples from the book and 3 examples from other resources. 1.1 Example1: Public transportation A private company plans to purchase some vehicles, (Vans, minibuses, buses).Total assigned budget for vehicles is 1 million dollar. The price of different vehicles are: Van: \$9500 , Minibus: \$12500 , Bus: \$45000 The company has 30 drivers. The monthly benefits of each vehicle for the company are: Van: \$2500/month, Minibus: \$3500/month, Bus: \$10000/month The number of vans should be at least 30 percent of all vehicles. The number of minibuses cannot be more than 10 and the company should have at least 2 buses. Formulate an optimization model that maximizes the company benefits given the constraints. 1) Decision variable X1: vans, X2: minibus, X3: bus 2) Constraints a. 9500g1 + 12500g2 + 45000g3 ≤ 1000000 b. g1 + g2 + g3 ≤ 30 c. g1 ≥ 0.3(g1 + g2 + g3) d. g2 ≤ 10 e. g3 ≥ 2 f. g1,g2, g3 ≥ 0 3) Objective function: Max Z= 2500x1+3500x2+10000x3 METHODS IV: SYSTEMS ANALYSIS AND DECISION MAKING Allahviranloo, Winter,2012 5 1.2 Example 2: Crops problem A farmer wants to plant 3 different corps in three farms. Farm Maximum planting area (Ha) Available water (1000m3) 1 400 3000 2 600 4000 3 300 1800 Crop Maximum area that crop can cover (Ha) Required water (1000m3/Ha) Benefits A 700 10 400 B 800 8 300 C 300 6 100 Formulate the model that maximizes the benefits for the farmer: 1) Decision variable: a. g G¡ : the variable indicating planting crop j in farm i. so we have g ¢£ ,g ¢¤ ,g ¢¥ , g ¦£ ,g ¦¤ ,g ¦¥ ,g §£ ,g §¤ ,g §¥ 2) The objective function is: ¨©g ª = 400(g ¢£ + g ¦£ + g §£ ) + 300(g ¢¤ + g ¦¤ + g §¤ ) + 100(g ¢¥ + g ¦¥ + g §¥ ) 3) Constraints: g ¢£ + g ¢¤ + g ¢¥ ≤ 400 g ¦£ + g ¦¤ + g ¦¥ ≤ 600 g §£ + g §¤ + g §¥ ≤ 300 10g ¢£ + 8g ¢¤ + 6g ¢¥ ≤ 3000 10g ¦£ + 8 g ¦¤ + 6g ¦¥ ≤ 4000 10g §£ + 8 g §¤ + 6g §¥ ≤ 1800 g ¢£ + g ¦£ + g §£ ≤ 700 g ¢¤ + g ¦¤ + g §¤ ≤ 800 g ¢¥ + g ¦¥ + g §¥ ≤ 300 g G¡ ≥ 0,« = 1,2,3 ¬ = ­, ®,¯ METHODS IV: SYSTEMS ANALYSIS AND DECISION MAKING Allahviranloo, Winter,2012 6 1.3 Example 3: example 2.6 of the text book , (Selecting projects for the bidding) A contractor has 8 major construction projects that are to be awarded on the basis of bids....
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## This note was uploaded on 03/30/2012 for the course CIVIL ENGI CEE111 taught by Professor Recker during the Winter '12 term at UC Irvine.

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lecture1-7 - METHODS IV SYSTEMS ANALYSIS AND DECISION...

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