Dynamic colour dynamics: markov decision processes for fashion inventory management

Abstract Efficient inventory management is essential for fashion retailers seeking to reduce waste, curb stock-outs, and protect margins. Because colour is a defining product attribute in apparel, balancing inventories across colour variants is both an economic and a sustainability challenge. We propose two complementary Markov-decision-process (MDP) tools to address this problem: (1) the Stochastic Risk‑Adjusted Markov Optimizer (SRAMO), a reinforcement‑learning procedure that samples prospective future states and rewards actions that minimize the expected deviation from a uniform colour distribution; and (2) Stochastic Risk Inventory Analysis (SRIA), a diagnostic test that flags colours whose steady-state probabilities differ significantly from the uniform benchmark, signaling latent over- or under-stock risk. Using a dataset of products and their recommendation‑link transitions from five global e‑commerce platforms, we built two transition matrices and benchmarked SRAMO against classical Q‑learning and a deep Q‑network (DQN). SRAMO reduced the average absolute deviation from uniformity to 0.042 ± 0.001, a 55% improvement over both baselines ( p = 0.003). Structural analyses show that anchor colours such as black centralize the MDP and mask substitution effects; removing black yields a more uniform steady state and elevates navy by 4.6%. These findings demonstrate that the SRAMO–SRIA framework can both optimize dynamic replenishment policies and provide interpretable diagnostics for attribute‑level inventory risk in volatile fashion markets.