Surrogate-Assisted Scenario-Generation Method for Simulation-Based Stochastic Programming Problems

Abstract

Simulation is required in real-world industrial decision-making to model the complexity, such as supply chain management with uncertain future demand. Scenario generation is critical for handling inherent uncertainties as deterministic scenarios to solve stochastic programming problems (SPPs). Generating a minimal yet representative scenario set is important to solve simulation-based SPPs (SBSPPs) since SBSPPs require thousands of simulation iterations proportional to the number of scenarios, leading to significant computational time. However, conventional methods, such as Monte Carlo method and recent problem-driven approaches, are ineffective in solving SBSPPs due to time-consuming simulation evaluation. This paper proposes a surrogate-assisted scenario-generation method called Inferred Cost-Space Scenario Clustering (ICSSC) that is applicable to various SPPs including SBSPPs. ICSSC employs a scenario clustering based on a new cost-space scenario distance evaluated by the surrogate model trained with offline simulation data to quickly approximate simulation evaluations. We conducted three types of numerical experiments to validate the effectiveness: Markowitz portfolio optimization, stochastic server location, and inventory placement optimization. Empirical results revealed that ICSSC could generate an effective scenario set based on the impact of uncertainties on decision outcomes for broader SPPs, and yields better solutions with 7.2 times shorter runtime than Monte Carlo methods. Note to Practitioners—This paper introduces a scenario-generation method to reduce the computational time of simulation-based optimization under uncertainty. Such optimization problems are common in practical decision-making contexts like production planning and supply chain management, which often require highly optimized and resilient solutions. Conventional methods, such as Monte Carlo method, demand extensive computational resources due to evaluating numerous randomly sampled scenarios. This study addresses scenarios in which similar problems are solved iteratively, a common occurrence in practical applications. Our method uses a surrogate model to approximate simulation evaluations quickly and selects a set of representative scenarios on the basis of the impact of uncertainties on decision outcomes. Numerical experiments demonstrated that our method could generate representative scenarios that obtain more robust and optimal solutions with shorter calculation times than conventional methods.