Question 1

A bank is planning to perform efficiency analysis to learn which branch offices are efficient and how to operation of inefficient units can be improved. All the six units performed 10000 transactions in a given period. Two inputs are considered in the analysis: working hours of employees used for the transactions and the operating expenses. An input oriented constant return to scale model is used for the analysis. The B, D and E branch offices were found efficient. The input and output data of the branch offices are the following:

a ) Prepare a figure which shows the efficiency frontier and the position of the branch offices relative to the efficiency frontier!

b ) How can the efficiency of unit C can be improved? How many working hours and how much operating expenses should be used for the efficient operation of unit C. Answer these questions using the graphical representation of the input - oriented CRS model.

c ) Calculate the efficiency score of unit C?

d ) Formulate the primal and dual linear programming model which calculates the efficiency of unit C.

DMU Branch office Input 1 Working hours of employees Input 2 Operating expenses (Euro) Output No. of transactions A C D E F 200 400 300 200 100 450 3000 1000 2000 2000 4000 2500 10000 10000 10000 10000 10000 10000 B DMU Branch office Input 1 Working hours of employees Input 2 Operating expenses (Euro) Output No. of transactions A C D E F 200 400 300 200 100 450 3000 1000 2000 2000 4000 2500 10000 10000 10000 10000 10000 10000 B