A general primal bounding framework for large-scale multistage stochastic programs under endogenous uncertainties

Abstract

Multistage stochastic programming is an approach for modeling and solving optimization problems under uncertainty. Such problems are commonly seen in production planning and scheduling in chemical process industry. This paper considers large-scale multistage stochastic programs under a specific type of uncertainty, i.e., endogenous uncertainty, and develops a general primal-bounding framework based on extending the concepts of expected value solution and value of stochastic solution from multistage stochastic programs under exogenous uncertainties. Under traditional decision-making process with uncertainties, decision makers utilize known information to-date along with the expected results for unrealized information to take action, realize some uncertainty, and repeat this process along the planning horizon. The bounding framework introduced here fits this decision-making process. It yields a tight feasible bound and an implementable solution for multistage stochastic programs under endogenous uncertainties, which we call the absolute expected value solution (AEEV). The framework is tested on three planning problems with up to 16,384 scenarios. It yielded primal bounds within 1% of the true solutions for all tested cases, and generated these implementable solutions up to four orders of magnitude faster than solving the original multistage stochastic programs.