Computation Section
Subunit Data Envelopment Analysis (DEA)
 - Changing a Model

The model can be changed in several features by the add-in. Reliable changes are best accomplished by clicking buttons on the worksheets.


The LP Model


The most useful change is to add constraints to the LP models. In this example, the managers at the other branches argue that Croydon won the competition with positive weight for personal transactions and zero weight for business transactions. They argue that business transactions are more important and profitable than the personal transactions. The CFU agrees that the weight of business transactions must be at least 12 times the weight of personal transactions. The current solution does not satisfy the requirement as shown for the Croydon solution below.

before the change

The new constraint is reflected by the inequalities below. The second form is necessary for the LP model.

new constraint

This kind of linear constraint is easily incorporated into the model by clicking the Change button on the LP worksheet. The button presents the LP model dialog. In the entry for number of constraints simply change the number from 5 to 6. The LP model is modified by adding an additional row with default coefficients.

lp constraint added
  Changing the coefficients and clicking on the Solve button finds the new solution for Croydon as below. The DEA efficiency has been reduced from 1 to 0.9253.
lp with new row
  Clicking the Solve for Efficiencies button on the Data worksheet finds the solutions for all DMU's. Redhill now has the highest DEA efficiency and Croydon is second. The other branches still lag behind.
data after change

The LP model can be changed in a variety of ways. Any of the enabled fields and check boxes on the LP dialog are candidates. After adding rows and columns to the model, be sure to solve DEA problems with the Solve for Efficiencies button on the data worksheet. If you press the Build DEA LP Model button, the LP model is rebuilt, losing any changes. After any change in the numbers of outputs, inputs and DMU's, the add-in replaces the LP model because its dimensions are different. Parameter value changes on the data worksheet do not require rebuilding the LP model. They are reflected by equations on the LP model worksheet without rebuilding it.

The Excel Solver can be used instead of the Jensen LP/IP by clicking the appropriate dialog on the dialog. Be sure to establish a connection with the Excel Solver by opening and closing its dialog. This must be done before the change, although it can be done after the change after the program issues a warning.

Sensitivity analysis is available from both the solvers.


Change Numbers of Factors


The number of outputs, inputs and DMU's can be changed using the Change button on the DEA Data page. Click the button and get a dialog with the current values of the parameters. Change the values to add or delete factors from the problem. The figure below adds three DMU's for a total of seven.


The data tables are adjusted to accommodate the changes. In the table below we have added input and output data for the new DMU's and solved the model for the DMU efficiencies. DMU 5 and 6 have 100% DEA efficiency while Reigate is dropped from a top spot.
changed dmu
  The LP model is replaced with the change, so any constraints or variables added to the LP model before the change are lost.


Include or Exclude Factors

  The data table includes a column for including or excluding DMU's and a row for including or excluding input and output factors. This might be useful for additional analysis. In the example we have removed Croydon by placing a 0 in the first entry of the Include DMU vector, cell H12. As expected, the Croydon branch is removed but the other DEA's have almost the same DEA efficiency.
  The removal is accomplished on the LP worksheet by placing a large value on the right-hand side of the Croydon constraint (constraint 2). Unrestricted, the Croydon branch loses its effect on the other solutions.
dmu remove lp
  One might ask, what is the effect of removing the personal output measure from the analysis. This is implemented by placing a 0 in the first cell of the Inclde Factor row, cell E19. The DEA results are significantly changed.
remove output
  The change in the LP is reflected by placing an upper bound of zero on the weight for the Personal transactions factor.
remove output lp
  Including or excluding a factor or DMU does not change the LP model by adding or removing rows and columns. Changed cells in the LP model are linked by formulas to the Include row and column. Only 0 and 1 are relevant in the Include row and column.
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tree roots

Operations Management / Industrial Engineering
by Paul A. Jensen
Copyright 2004 - All rights reserved