This paper investigates a finite‑horizon multi‑item lot‑sizing problem with capacity limits where demand quantities are known but the periods in which demands arrive are stochastic. Each demand occurs once within a known time window and must be satisfied no later than its deadline. By making production and allocation decisions at the demand level, the model captures capacity competition, demand‑specific backlogs, and the way allocation influences inventory dynamics.\ \ The stochastic problem is formulated as a discrete‑time Markov decision process (DTMDP) that specifies the state space, feasible actions, transition kernel, and one‑period cost function. To isolate the computational impact of stochastic timing, each stochastic instance is first compared with a deterministic counterpart obtained by replacing each arrival distribution with its most likely period. The comparison reveals that stochastic timing dramatically enlarges the number of states, transitions, solution time, and memory usage.\ \ A genetic algorithm (GA) is then proposed for the stochastic‑timing problem. The GA searches over feasible state‑feedback policies and evaluates each policy exactly under the DTMDP transition model. Computational experiments on 330 benchmark instances show that when an exact stochastic solution is available, the GA’s average optimality gap is about $3.44\%$. On the hardest 90 test cases, the GA stays below a $5\%$ gap and achieves an average speedup of $6.89 \pm 1.41$ at the $95\%$ confidence level. For instances that cannot be solved exactly on the available hardware, an empirical Bellman‑time regression estimates the missing exact resolution time and extrapolates the expected GA speedup.\ \ Review: The study precisely models the effect of uncertain demand timing via DTMDP and demonstrates that a well‑designed genetic algorithm can deliver high‑quality near‑optimal solutions with substantial computational savings, offering a practical approach for stochastic production planning.