Duality and Data Envelopment Analysis - Statistics Assignment Help

Assignment Task

Assessment Task: Problems

Question 1

An analyst is interested in comparing performance across an airline’s four call centres. Inputs are the average talk time (seconds per call), average computer time per call (seconds per call), a measure of unpleasantness (index between 0 and 1) and the percentage of time fare rules are not explained. The outputs are number of electronic tickets issued (% of calls with ticket sale) and the number of paper tickets issued (% of calls with ticket sale). The inputs and outputs in a particular 3 month period are:

Complete the following tasks:

(a) Use the above information and focus on Centre A to formulate the DEA problem as a linear program model in ratio form.

(b) Explain why you would not use the ratio form to solve the problem.

(c) Formulate the DEA problem as a linear program model in envelope form, explaining the steps taken to complete this task.

(d) Solve the problem using Excel QM, report the relative efficiency score of Call Centre A and its peers and target(s).

Question 2

Sharkies Savings and Loans operate six banking facilities across Sydney. The data set in the table below has been selected to represent the appropriate annual input and output measures of each banking facility. Labour Hours and Operating Costs are considered inputs; Customer Satisfaction, New Loans and Return on Assets are considered outputs.

Complete the following tasks:

(a) Develop and present a dual LP model in envelope form that can be used to determine the relative efficiency of the Bankstown branch. Present the model algebraically.

(b) Solve the problem using Excel QM and present the results.

(c) Is the Bankstown branch relatively efficient? Explain.

(d) Develop a set of input and output targets that could be used by the Bankstown branch in its effort to become fully efficient.

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