Discrete-Time MDP Modeling for Multi-Item Capacitated Lot Sizing with Stochastic Demand Timing
Affected assets and topics
Why it matters
The article presents a new discrete-time Markov decision process (DTMDP) model for multi-item capacitated lot-sizing problems with stochastic demand timing, demonstrating that stochastic demand arrival timing increases computational complexity and memory requirements compared to deterministic models. The proposed genetic algorithm (GA) achieves near-optimal solutions with an average optimality gap of 3.44% and significant speedups in optimization.
- stochastic demand timing increases computational complexity in lot-sizing models
- genetic algorithm achieves near-optimal solutions with a 3.44% average optimality gap
- optimization speedup of 6.89±1.41x demonstrated in computational experiments
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Expected market reaction
The research may indirectly affect supply chain management software providers and industrial automation firms by validating the need for advanced optimization tools to handle stochastic demand timing, potentially increasing demand for AI-driven logistics and inventory management solutions. However, no direct market impact is evident from the article alone.
Risks
- the study is theoretical and does not address commercial deployment or market adoption
- no evidence of direct commercial applications or revenue impact
- hardware limitations may restrict scalability of the proposed model
Evidence trail
Evidence
AI provenance
Technical identifiers
- Provider tag
- mistral-small-latest
- Analysis version
- mistral-small-latest
- Article id
- 125688
Original source
arXiv:2609.00004v1 Announce Type: new Abstract: This paper studies a finite-horizon multi-item capacitated lot-sizing problem in which demand quantities are deterministic, while demand-arrival periods are stochastic. Each demand occurs once within a known time window and must be satisfied no later than its deadline. The proposed model makes production and allocation decisions at the demand level, allowing it to represent capacity competition, demand-specific backlog, and allocation-dependent inventory dynamics. The stochastic problem is formulated as a discrete-time Markov decision process (DTMDP), including the state space, feasible actions, transition kernel, and one-period cost function. To isolate the computational effect of stochastic timing, each stochastic instance is first compared with a deterministic counterpart in which each arrival distribution is replaced by its most likely arrival period. This comparison shows that stochastic timing substantially increases the number of states, the number of transitions, solution time, and memory pressure. 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 the GA remains close to the exact stochastic solution whenever the latter is available, with an average optimality gap of about $3.44\%$. On the difficult benchmark instances, comprising 90 test cases, the GA remains below the $5\%$ optimality-gap threshold and achieves an average optimization 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 is used to estimate the missing exact resolution time and extrapolate the expected GA speedup.
Read the full article on arXiv
Original article published by arXiv on September 2, 2026. Analysis and insights provided by AnalystMarkets AI.