1 Process Benchmarking with Data Envelopment Analysis Chapter 11 Business Process Modeling, Simulation and Design

2 Overview DEA: Tool for Benchmarking Relative Efficiency – Important Concepts –Black-box model Graphical Analysis –Efficiency calculations Linear Programming –Formulation –Using the Excel Add-in

3 DEA: Tool for Benchmarking Successfully applied to assess the efficiency of various organizations and/or processes. –Process = Decision Making Unit (DMU) –The efficiency of a process is only relative to the performance of other processes in the set Considers process as a black box and analyzes the relationships between its inputs and outputs

4 Figure 11.1 Black box model of a process Process as Black Box Output Efficiency = Input However, with multiple inputs and outputs, it becomes more difficult to evaluate the process efficiency.

5 Calculating Efficiency Clearly, process A is more efficient than process B, but... A new assessment based on office space shows that process B is more efficient than process A, so…

6 Calculating Efficiency DEA offers a variety of models that use multiple inputs and outputs to compare the efficiency of two or more processes. The ratio model is based on the following definition of efficiency: Weighted Sum of Outputs Efficiency = Weighted Sum of Inputs

7 Graphical Analysis Suppose we have the following input and output data: We label the independent efficiency ratios x and y:

8 Efficient frontier Graphical Analysis Then, we plot the relative position of each process:

9 P1 ( x 1, y 1 ) (xv,yv)(xv,yv) P2 ( x 2, y 2 ) P0 ( x 0, y 0 ) y = output2/input x = output1/input Projection of a relatively inefficient process Efficiency Calculations Relatively efficient processes are those on the efficient frontier: –Considered to have 100% efficiency. –What is the efficiency of the relatively inefficient processes?

10 P1 ( x 1, y 1 ) (xv,yv)(xv,yv) P2 ( x 2, y 2 ) P0 ( x 0, y 0 ) y = output2/input x = output1/input Projection of a relatively inefficient process Efficiency Calculations P1 and P2 are relatively efficient  P0’s peer group. Define a and b such that: Then, we get the efficient virtual process corresponding to x v and y v : The efficiency of process P0 is:

11 Linear Programming The ratio model measures the efficiency of a process by comparing to a hypothetical process that is a weighted linear combination of other processes. Individual processes might value inputs and outputs differently. Therefore, each process is allowed to adopt a set of weights to show it in the most favorable light. Formulated as a sequence of linear programs (one for each process) to: -Maximize the efficiency of one process -Subject to the efficiency of all processes  100%

12 Linear Programming The variables are the weights assigned to each input and output: wout(j), win(i) An LP formulation for a given process p is:

13 Using the Excel Add-in We recommend presenting/explaining the DEA Add-in, available on the CD that comes with the textbook, by running it directly in Excel. However, for your convenience, we have attached a selection of the figures/screenshots from Chapter 11 of the book as the basis for an in class presentation without access to a computer with the Excel Add-in installed. NOTE:

14 Creating a new DEA model Using the Excel Add-in

15 New model dialog window Using the Excel Add-in

16 Completed Example.Output worksheet Using the Excel Add-in

17 Efficiency worksheet Using the Excel Add-in

18 Best Practice worksheet Using the Excel Add-in

19 Targets worksheet Using the Excel Add-in

20 Virtual Output worksheet Using the Excel Add-in

21 Virtual Output chart Using the Excel Add-in