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

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--> [Submitted on 5 Jul 2026] Title:Discrete-Time MDP Modeling for Multi-Item Capacitated Lot Sizing with Stochastic Demand Timing View a PDF of the paper titled Discrete-Time MDP Modeling for Multi-Item Capacitated Lot Sizing with Stochastic Demand Timing, by L\'ea Bayati and Mohamed Dahmoune and Melek Rodoplu View PDF 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. Subjects: Artificial Intelligence (cs.AI); Neural and Evolutionary Computing (cs.NE); Optimization and Control (math.OC) Cite as: arXiv:2609.00004 [cs.AI] (or arXiv:2609.00004v1 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2609.00004 arXiv-issued DOI via DataCite Submission history From: Lea Bayati [view email] [v1] Sun, 5 Jul 2026 23:37:57 UTC (1,122 KB) Full-text links: Access Paper: View a PDF of the paper titled Discrete-Time MDP Modeling for Multi-Item Capacitated Lot Sizing with Stochastic Demand Timing, by L\'ea Bayati and Mohamed Dahmoune and Melek Rodoplu View PDF TeX Source view license Current browse context: cs.AI new | recent | 2026-09 Change to browse by: cs cs.NE math math.OC References & Citations NASA ADS Google Scholar Semantic Scholar Loading... Data provided by: Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv (What is alphaXiv?) Links to Code Toggle CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub Toggle DagsHub (What is DagsHub?) GotitPub Toggle Gotit.pub (What is GotitPub?) Huggingface Toggle Hugging Face (What is Huggingface?) ScienceCast Toggle ScienceCast (What is ScienceCast?) Demos Demos Replicate Toggle Replicate (What is Replicate?) Spaces Toggle Hugging Face Spaces (What is Spaces?) Spaces Toggle TXYZ.AI (What is TXYZ.AI?) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower (What are Influence Flowers?) Core recommender toggle CORE Recommender (What is CORE?) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs. Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)