This paper aims to investigate the conditions under which randomized inventory policies outperform deterministic ones when demand follows a multimodal distribution. By analyzing both bimodal and multimodal demand patterns – common in real-world scenarios due to transportation delays – it seeks to demonstrate the advantages and behavioral characteristics of randomized policies. The study contributes to inventory theory by offering both analytical insights and a novel optimization algorithm to identify globally optimal randomized strategies.
The study adopts a single-period inventory optimization framework to compare deterministic and randomized policies under various demand distributions, including unimodal, bimodal and multimodal settings. Analytical intuitions are developed to explain when and why randomized policies yield lower expected inventory levels for a fixed out-of-stock risk. Numerical experiments validate these insights, and a derivative-based algorithm is proposed to efficiently compute global optima for randomized policies under complex demand distributions.
Randomized inventory policies can significantly outperform deterministic ones when demand is multimodal, particularly due to uncertainty in delay-induced demand coverage. The magnitude of the benefit varies non-monotonically with parameters like delay probability and variance. Under multimodal distributions, performance gains exhibit cyclical patterns as demand parameters change. The proposed optimization algorithm effectively identifies globally optimal randomized policies, highlighting their practical potential in realistic supply chain settings.
The current model focuses on a single-period decision framework and assumes demand distributions derived from mixtures of normal components. Extensions to multi-period settings or alternative demand distributions (e.g. skewed or discrete) remain unexplored. Future research may generalize the methodology of dynamic environments and quantify the relationship between multimodality metrics and policy performance. These limitations suggest promising directions for extending the applicability and robustness of randomized inventory policies.
To the best of the authors’ knowledge, this paper is among the first to systematically examine the performance of randomized inventory policies under realistic multimodal demand distributions caused by delay uncertainty. Unlike prior studies that focus on deterministic strategies or use randomization solely for algorithmic approximation, this work highlights the structural advantages of randomization in reducing expected inventory while maintaining service levels. It also introduces a novel, efficient algorithm for identifying globally optimal randomized policies. The study provides both theoretical and practical insights, offering valuable guidance for supply chain decision-makers facing complex, uncertain demand environments.
