Ranking and selection with two-stage decision

Ranking & selection (R&S) is concerned with the selection of the best decision from a finite set of alternative decisions when the outcome of the decision has to be estimated using stochastic simulation. In this paper, we extend the R&S problem to a two-stage setting where after a first-stage decision has been made, some information may be observed and a second-stage decision then needs to be made based on the observed information to achieve the best outcome. We then extend two popular single-stage R&S algorithms, expected value of information (EVI) and optimal computing budget allocation (OCBA), to efficiently solve the new two-stage R&S problem. We prove the consistency of the new two-stage EVI (2S-EVI) and OCBA (2S-OCBA) algorithms. Experiment results on benchmark test problems and a two-stage multi-product assortment problem show that both algorithms outperform applying single-stage EVI and OCBA in the two-stage setting. Between 2S-EVI and 2S-OCBA, numerical results suggest that 2S-EVI tends to perform better with smaller number of decisions at first and second stage while 2S-OCBA has better performance for larger problems.