How to calculate Malmquist under non-CRS conditions?

One can use the Variable-Benchmark Model (Chapter 7.2) and the Envelopment Model (Chapter 1.2) to calculate the non-CRS Malmquist productivity index.

Suppose we have two periods A and B. We need to run four (4) DEA models to calculate the Malmquist productivity index. They are

Model-1: DEA efficiency in period A

Model-2: DEA efficiency in period B

Model-3: Efficiency of period A with respect to period B; namely, period B is used as a reference set and period A is under evaluation

Model-4: Efficiency of period B with respect to period A; namely, period A is used as a reference set and period B is under evaluation

            For example, if one wants to calculate VRS Malmquist productivity index. One can use the DEA Excel Solver in the following steps:

Step 1: Using the VRS Envelopment Model to calculate Model-1 and Model 2;

Step 2: Using the VRS Variable-Benchmark Model to calculate Model-3 and Model-4.
       
            To calculate Model-3,  put the period B data in sheet "Benchmarks" and put the period A data in sheet "DMUs";

            To calculate Model-4,  put the period A data in sheet "Benchmarks" and put the period B data in sheet "DMUs".

Step 3: Once all the efficiency scores are generated, one can calculate the Malmquist productivity index. Note that you will get "infeasible" for some efficiency scores when Malmquist is calculated under non-CRS conditions.