Benchmarking in Data Envelopment Analysis: An Approach Based on Genetic Algorithms and Parallel Programming

Algorithm 3

Decrease 𝛽_𝑘.

Require:  𝛽_𝑘, 𝑞∈ℤ, 𝑀𝑎𝑥𝐼𝑡𝑒𝑟∈ℤ.

Ensure: A minimal 𝛽_𝑘 for the chromosome that satisfy constraint 11: ∀𝑡⁻_𝑖𝑘≥0.

  𝑑←0

  while  𝑑≤𝑀𝑎𝑥𝐼𝑡𝑒𝑟  do

    while  ∀𝑡⁻_𝑖𝑘≥0  do

   {Decrease 𝛽_𝑘 while still satisfies (c.11)}

   𝛽_𝑘←𝛽_𝑘−𝑞𝑑

   Generate 𝑡⁻_𝑖𝑘 using expression (2).

    end  while

    {At this point (c.11) is not satisfied because of the decrease of 𝛽_𝑘. Increase 𝛽_𝑘 value

    until it is satisfied again}

    repeat

   𝛽_𝑘←𝛽_𝑘+𝑞𝑑

   Generate 𝑡⁻_𝑖𝑘 using (3).

    until  ∀𝑡⁻_𝑖𝑘≥0

    𝑑←𝑑+1

  end  while