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.

中文翻译：

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排名和选择，分两阶段决定


排名与选择（R&S）涉及到当决策结果必须使用随机模拟来估计决策结果时，从有限的替代决策中选择最佳决策。在本文中，我们将 R&S 问题扩展到两个阶段，其中在做出第一阶段决策后，可能会观察到一些信息，然后需要根据观察到的信息做出第二阶段决策以获得最佳结果。然后，我们扩展了两种流行的单阶段 R&S 算法，即信息期望值 （EVI） 和最优计算预算分配 （OCBA），以有效解决新的两阶段 R&S 问题。我们证明了新的两阶段 EVI （2S-EVI） 和 OCBA （2S-OCBA） 算法的一致性。基准测试问题和两阶段多产品分类问题的实验结果表明，在两阶段设置中，这两种算法都优于应用单阶段 EVI 和 OCBA。在 2S-EVI 和 2S-OCBA 之间，数值结果表明，2S-EVI 在第一阶段和第二阶段的决策数量较少时往往表现更好，而 2S-OCBA 在处理较大的问题时表现更好。