Assignment 2.docx - Assignment 2 Data Envelopment Analysis Q1(a Outputs q1 Cars(‘000 q2 Trucks(‘000 Inputs x1 Capital(quantity index x2

Assignment 2.docx - Assignment 2 Data Envelopment Analysis...

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Assignment 2 Data Envelopment Analysis Q1: (a) Outputs: q 1 : Cars (‘000), q 2 : Trucks (‘000) Inputs: x 1 : Capital (quantity index), x 2 : Labour (‘000 hours), x 3 : Energy (Mwh), x 4 = Materials (quantity index). The VRS DEA model envelopment form of the OTE problem is: Max s.t. 2.5 – 2.5 1 – 2.8 2 – 3.2 3 – 2.1 4 ≤ 0 (Cars) 1 – 1.3 2 – 1.8 3 4 ≤ 0 (Trucks) 1 1 + 0.8 2 +1.3 3 +1.1 4 ≤ 1 (Capital) 3.1 1 + 2.2 2 +2.8 3 +3.2 4 ≤ 3.1 (Labour) 1.5 1 + 1.7 2 +1.1 3 +1.5 4 ≤ 1.5 (Energy) 2 1 + 2.3 2 +1 3 +1.5 4 ≤ 2 (Materials) 1 + 2 + 3 + 4 = 1 all variables ≥ 0 Solve the problem using Excel QM: From the above table, 1 = 4 = 0, 2 = 0.6, 3 = 0.4 and = 1.184. The OTE = 1/1.184 = 0.8446. Thus, we estimate that Plant 1 is only 84.46% technically efficient, not fully efficient. (b) The plant 1 should look at most closely in plant 2 and plant 3 efforts to become technically 1
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efficient. The set of input and output targets for Plant 1: Output targets: Cars: q 11 * = 1 q 11 + 2 q 12 + 3 q 13 + 4 q 14 = 0.6*2.8 + 0.4*3.2 = 2.96 Trucks: q 21 * = 1 q 21 + 2 q 22 + 3 q 23 + 4 q 24 = 0.6*1.3 +0.4*1.8 = 1.5 Input targets: Capital: x 11 * = 1 x 11 +
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