Reference no: EM131018807
Super-efficiency
During our first residency, we talked about how to rank or distinguish the performance of best-practice DMUs. I mentioned a model called "super-efficiency".
What is a super-efficiency model?
DEA model discussed in Chapter 1 looks like the following (suppose DMU1 is under evaluation and we have 20 DMUs)
Max weighted outputs for DMU1
subject to (constraints)
Weighted outputs < weighted inputs for DMU1
Weighted outputs < weighted inputs for DMU2
Weighted outputs < weighted inputs for DMU3
...
Weighted outputs < weighted inputs for DMU20
Weighted inputs = 1 (for DMU1)
The super-efficiency model for DMU1 is as follows
Max weighted outputs for DMU1
subject to (constraints)
Weighted outputs < weighted inputs for DMU1(remove this constraint in Solver)
Weighted outputs < weighted inputs for DMU2
Weighted outputs < weighted inputs for DMU3
...
Weighted outputs < weighted inputs for DMU20
Weighted inputs = 1 (for DMU1)
As you can see, the super efficiency model removes the DMU under consideration from the constraints. If DMU2 is under evaluation, we will have the following super efficiency model
Max weighted outputs for DMU2
subject to (constraints)
Weighted outputs < weighted inputs for DMU1
Weighted outputs < weighted inputs for DMU2(remove this constraint in Solver)
Weighted outputs < weighted inputs for DMU3
...
Weighted outputs < weighted inputs for DMU20
Weighted inputs = 1 (for DMU2)
Now, for the model discussed in Chapter 6, the super efficiency model is different. Let us present the model in chapter 6 in the following manner.
Suppose the (unknown) benchmarking shares are (j = 1, 2, ...,17 as in 17 airlines). These represent cells J2:J18. Now, let the score (or efficiency score) in cell E22 be . Then the excel version of the model in chapter 6 can be expressed in an algebraic form
Minimize (objective cell)
subject to (constraints)
*input1 (for DMU1) + *input1 (for DMU2) +...+ *input1 (for DMU17) < *input 1 (for DMU1)
*input2 (for DMU1) + *input2 (for DMU2) +...+ *input2 (for DMU17) < *input 2 (for DMU1)
*input3 (for DMU1) + *input3 (for DMU2) +...+ *input3 (for DMU17) < *input 3 (for DMU1)
*input4 (for DMU1) + *input4 (for DMU2) +...+ *input4 (for DMU17) < *input 4 (for DMU1)
*output1 (for DMU1) + *output1 (for DMU2) +...+ *output1 (for DMU17) > output1 (for DMU1)
*output2 (for DMU1) + *output2 (for DMU2) +...+ *output2 (for DMU17) > output2 (for DMU1)
+ +...+ = 1
If DMU2 is under evaluation, then we need to replace the data on the right-hand-side of the constraints with DMU2.
The super efficiency model for DMU1 is
Minimize (objective cell)
subject to (constraints)
*input1 (for DMU1) + *input1 (for DMU2) +...+ *input1 (for DMU17) < *input 1 (for DMU1)
*input2 (for DMU1) + *input2 (for DMU2) +...+ *input2 (for DMU17) < *input 2 (for DMU1)
*input3 (for DMU1) + *input3 (for DMU2) +...+ *input3 (for DMU17) < *input 3 (for DMU1)
*input4 (for DMU1) + *input4 (for DMU2) +...+ *input4 (for DMU17) < *input 4 (for DMU1)
*output1 (for DMU1) + *output1 (for DMU2) +...+ *output1 (for DMU17) > output1 (for DMU1)
*output2 (for DMU1) + *output2 (for DMU2) +...+ *output2 (for DMU17) > output2 (for DMU1)
+ +...+ = 1
That is, we obtain a super efficiency model, by removing the DMU under evaluation, or setting the benchmarking share = 0
For the homework, please use the your data set for Chapter 1 Homework and solve for the super efficiency scores in Excel. You need to solve for the two models described above.
For the model in chapter 6, it is relatively easy to automate the solving procedure using VBA. For the model in chapter 1, it may be difficult to use VBA - if so, please change one DMU to another manually.
Attachment:- VBA.rar
|
Scientific management and strategic management
: Explain the similarities and differences between Scientific Management and Strategic Management. Explain whether Strategic Management could have been developed without Scientific Management as its predecessor.
|
|
What is the length of the prism
: Samir knows that the volume of a prism is 40 cubic units . He also knows that the width of the prism is 2 units and the height is 5 units. What is the length of the prism?
|
|
How the global business environment is bringing change
: How the global mindset of a manager affects the outcome of change management.
|
|
Find the three poles and estimate the 3-db frequency fh
: Associated with each stage is a parasitic input capacitance (to ground) of 10 pF and a arasitic output capacitance (to ground) of 2 pF. Parasitic capacitances of 10 pF and 7 pF also are associated with the signal-source and load connections, respe..
|
|
What is a super-efficiency model
: What is a super-efficiency model - distinguish the performance of best-practice DMUs
|
|
Find corresponding midband voltage gain
: For a particular amplifier modeled by the circuit of Fig. 10.18(a), gm = 5 mA/V, Rsig = 150 KΩ, RG = 0.65 MΩ,R1 L = 10 kΩ, Cgs = 2 pF, and Cgd = 0.5 pF. There is also a load capacitance of 30 pF. Find the corresponding midband voltage gain, the op..
|
|
Identify what techniques you can implement to improve
: In a 250-300 word response, identify what techniques you can implement to improve the likelihood that your communications will be received and understood as you intended. Can you identify and reduce the likelihood of barriers interfering with t..
|
|
Four primary service outputs of spatial convenience
: Why are the four primary service outputs of spatial convenience, lot size, waitingtime, and product variety important to logistics management? Provide examples ofcompeting firms that differ in the level of each service output provided tocustomers.
|
|
What does the transfer function become
: The high-frequency response of a direct-coupled amplifier having a dc gain of -1000 V/V incorporates zeros at ∞and 104 rad/s (one at each frequency) and poles at 103 rad/s and 105 rad/s (one at each frequency). Write an expression for the amplifier..
|