Discrete-Time MDP Modeling for Multi-Item Capacitated Lot Sizing with Stochastic Demand Timing

The paper introduces a discrete‑time Markov decision process (DTMDP) model for a finite‑horizon, multi‑item capacitated lot‑sizing problem where demand quantities are deterministic but demand‑arrival times are stochastic. It compares stochastic instances to deterministic counterparts, showing that stochastic timing significantly enlarges the state space, transitions, solution time, and memory usage. A genetic algorithm (GA) is proposed to search feasible state‑feedback policies, achieving an average optimality gap of about 3.44 % and a speedup of roughly 6.89× on challenging benchmark instances.

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• reinforcement-learning
• benchmarks