Efficient Simulation Budget Allocation for Ranking the Top 𝑚 Designs

Algorithm 1

Sequential allocation algorithm.

INPUT: 𝑚,𝑘,𝑛,𝑛₀,Δ (𝑛−𝑘𝑛₀ is a multiple of Δ and 𝑛₀≥5)

INITIALIZE: Perform 𝑛₀ simulation replications for all designs.

     𝑙←0;𝑁^𝑙₁=⋯=𝑁^𝑙_𝑖=⋯=𝑁^𝑙_𝑘

WHILE ∑^𝑘_𝑖=1𝑁^𝑙_𝑖<𝑛 DO

   (1) Increase the computing budget by Δ

   (2) Use (28) to determine the new budget allocation rule, that is, 𝑁_𝑖^𝑙+1,𝑖=1,…,𝑘.

      The population distribution parameters are estimated by the sample statistics.

   (3) Simulate additional max(0,𝑁_𝑖^𝑙+1−𝑁^𝑙_𝑖) for each design 𝑖=1,…,𝑘.

END OF WHILE