Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/313815 
Year of Publication: 
2024
Citation: 
[Journal:] OR Spectrum [ISSN:] 1436-6304 [Volume:] 46 [Issue:] 3 [Publisher:] Springer Berlin Heidelberg [Place:] Berlin/Heidelberg [Year:] 2024 [Pages:] 639-668
Publisher: 
Springer Berlin Heidelberg, Berlin/Heidelberg
Abstract: 
Abstract Using scenarios to model a stochastic system’s behavior poses a dilemma. While a large(r) set of scenarios usually improves the model’s accuracy, it also causes drastic increases in the model’s size and the computational effort required. Multi-period descriptive sampling (MPDS) is a new way to generate a small(er) set of scenarios that yield a good fit both to the periods’ probability distributions and to the convoluted probability distributions of stochastic variables (e.g., period demands) over time. MPDS uses descriptive sampling to draw a sample of S representative random numbers from a period’s known (demand) distribution. Now, to create a set of S representative scenarios, MPDS heuristically combines these random numbers (period demands) period by period so that a good fit is achieved to the convoluted (demand) distributions up to any period in the planning interval. A further contribution of this paper is an (accuracy) improvement heuristic, called fine-tuning, executed once the fix-and-optimize (FO) heuristic to solve a scenario-based mixed integer programming model has been completed. Fine-tuning uses linear programming (LP) with fixed binary variables (e.g., setup decisions) generated by FO and iteratively adapts production quantities so that compliance with given expected service level constraints is reached. The LP is solved with relatively little computational effort, even for large(r) sets of scenarios. We show the advancements possible with MPDS and fine-tuning by solving numerous test instances of the stochastic capacitated lot-sizing problem under a static uncertainty approach.
Subjects: 
Scenario generation
Stochastic lot-sizing
Service level constraints
Sample average approximation
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
Document Version: 
Published Version
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