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Dynamic Learning Policy for Multi-Warehouse Multi-Store Systems with Censored Demands
Preprint   Open access

Dynamic Learning Policy for Multi-Warehouse Multi-Store Systems with Censored Demands

Sentao Miao, Yining Wang and Renbo Zhao
SSRN Electronic Journal
2023
DOI: 10.2139/ssrn.4617620
url
https://doi.org/10.2139/ssrn.4617620View
Preprint (Author's original)This preprint has not been evaluated by subject experts through peer review. Preprints may undergo extensive changes and/or become peer-reviewed journal articles. Open Access

Abstract

With ever changing market dynamics and growing supply chain networks (i.e., warehouses and stores) for large retailers, it is crucial to study the inventory replenishment and allocation decision with unknown demand under a multi-warehouse multi-store (MWMS) network. This paper proposes a novel primal-dual learning algorithm, named PD-LaBS, to tackle this challenge when demand is censored. In particular, we adapt a classic volumetric cutting plane method for the dual problem in a non-trivial manner, whose separating oracle is given by a primal learning algorithm which jointly optimizes the replenishment and allocation decision at each store on the fly. Regret analysis shows that our algorithm achieves a regret of $\tilde O(NM^{3.5}\times \sqrt{T})$ (where $N$ is the number of stores, $M$ is the number of warehouses, and $T$ is the length of the time horizon), generalizing the results in the literature of one-warehouse multi-store (OWMS) problem. Crucially, the designed primal learning algorithm uses a novel LP formulation to approximately optimize primal objectives penalized by Lagrangian multiplies and simultaneously satisfy (approximately) primal feasibility constraints, which is not necessary from a pure optimization perspective but essential to upper bound the cumulative regret of our designed algorithm. Numerical experiments further demonstrated the effective empirical performance of our algorithm.

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