The growth in computation complexity of multistage stochastic programs (MSSPs) with problem size often prevents its application to real-world size problems. We present two variants of branch-and-bound algorithm, which reduce the resource requirements for the generation and solution of large-scale MSSPs with endogenous uncertainty. Both variants use Knapsack-problem based Decomposition Algorithm (Christian and Cremaschi, Comput Chem Eng. 2015;74:34–47) to generate feasible solutions and primal bounds. First variant (PH-KDA) uses a progressive hedging dual-bounding approach; the second (OSS-KDA) solves the MSSP removing all nonanticipativity constraints. Both variants were used to solve several instances of the pharmaceutical clinical trial planning problem. The first iteration of both algorithms provides a feasible solution, and a primal bound and a dual bound for the problem. Although the dual-bounds of OSS-KDA were generally weaker than PH-KDA, they are generated considerably faster. For the seven-product case the OSS-KDA generated a solution with a gap of 9.92% in 115 CPU seconds. © 2017 American Institute of Chemical Engineers AIChE J, 2017

中文翻译：

---

一种求解内生不确定性的大规模多阶段随机程序的分支定界算法

具有问题大小的多阶段随机程序（MSSP）的计算复杂性的增长通常会阻止其应用于现实世界中的问题。我们提出了分支定界算法的两个变体，它们减少了具有内生不确定性的大规模MSSP的生成和求解所需的资源。两种变体都使用基于背包问题的分解算法（Christian和Cremaschi，Comput Chem Eng。2015; 74：34–47）来生成可行的解和原始边界。第一种（PH-KDA）使用渐进式对冲双边界方法；第二个（OSS-KDA）解决了MSSP，消除了所有非预期性约束。两种变体均用于解决药物临床试验计划问题的几种情况。两种算法的第一次迭代都提供了可行的解决方案，以及该问题的原始边界和双重边界。尽管OSS-KDA的双界通常比PH-KDA弱，但它们的生成速度却相当快。对于七个产品的案例，OSS-KDA在115个CPU秒内生成了9.92％的差距的解决方案。©2017美国化学工程师学会AIChE的Ĵ，2017年