QUESTION 1:

An analyst is interested in evaluating the performance of a group of four motor vehicle as- sembly plants. In order to measure the performance of these plants, the analyst collects data on the quantities of two outputs (cars and trucks) and four inputs (capital, labour, energy and materials). The data are presented in Table 1.

(a) (4 marks) Formulate a variable-returns-to-scale (VRS) DEA model in envelopment form that can be used to determine the output-oriented technical efficiency of Plant 1. Solve the problem using Excel QM. Is Plant 1 technically efficient?

(b) (6 marks) Suppose inputs and outputs are worth something and can be chosen freely. Develop a set of input and output targets for Plant 1. What plants should Plant 1 look at most closely in its efforts to become technically efficient?

(c) (4 marks) Formulate a constant-returns-to-scale (CRS) DEA model in envelopment form that can be used to determine the technical efficiency of Plant 1. Use the model to determine the output-oriented scale efficiency (OSE) of the plant. Is Plant 1 scale efficient?

QUESTION 2:

The outputs and inputs of five water utilities are reported in Table 2. Assume the production frontier exhibits VRS.

(a) (6 marks) Determine the input-oriented technical efficiency (ITE), cost-allocative effi- ciency (CAE) and cost efficiency (CE) of Utility C. Is Utility C technically efficient?

(b) (3 marks) Use the ITE score to find a set of inputs that Utility C could use if it is to produce the same output and be regarded as technically efficient.

(c) (6marks)UsepeerweightstofindasetofinputsandoutputsthatUtilityCcouldtarget if it wants to be regarded as fully technically efficient but not necessarily cost efficient. What other firms should Utility C study in its efforts to reach those targets?

(d) (3 marks) Identify the input quantities that minimise the cost of producing the outputs currently produced by Utility C.

Table 1: Data for Motor Vehicle Assembly Plants Plant 1 Plant 4 Plant 2 Plant 3 Cars '000) Trucks '000) 3.2 2.5 2.8 2.1 1.3 1.0 1.8 1.0 Capital (quantity index) Labour ('000 hours) 1.0 0.8 1.3 1.1 3.1 2.2 3.2 2.8 Energy (Mwh) Materials (quantity index) 1.5 1.7 1.1 1.5 1.5 2.0 2.3 1.0 Table 2: Data for Water Utilities Quantities Prices Utility Output (GI) Labour Capital (hours) Index) Materials Labour Capital (Index) Materials (S/hour) (Index) (Index) 3.4 21 A 400 11.3 5.2 171 35 400 1.9 1.5 1.0 18 166 32 300 2.4 174 C 6.7 2.5 21 35 500 0.3 2.7 D 2.1 21 233 27 183 E 200 1.2 0.2 1.1 21 18 Table 1: Data for Motor Vehicle Assembly Plants Plant 1 Plant 4 Plant 2 Plant 3 Cars '000) Trucks '000) 3.2 2.5 2.8 2.1 1.3 1.0 1.8 1.0 Capital (quantity index) Labour ('000 hours) 1.0 0.8 1.3 1.1 3.1 2.2 3.2 2.8 Energy (Mwh) Materials (quantity index) 1.5 1.7 1.1 1.5 1.5 2.0 2.3 1.0 Table 2: Data for Water Utilities Quantities Prices Utility Output (GI) Labour Capital (hours) Index) Materials Labour Capital (Index) Materials (S/hour) (Index) (Index) 3.4 21 A 400 11.3 5.2 171 35 400 1.9 1.5 1.0 18 166 32 300 2.4 174 C 6.7 2.5 21 35 500 0.3 2.7 D 2.1 21 233 27 183 E 200 1.2 0.2 1.1 21 18