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G-2025-02

Integrated lot sizing and blending problems under demand uncertainty

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Blending problems occur when different components are mixed to form an end product. The recipe typically has some flexibility as long as specific quality conditions are met. We consider the blending problem as a multi-period, multi-level lot sizing problem. The problem involves determining the setup periods for purchasing the components and producing the products, along with their respective quantities and blending. A two-stage stochastic programming formulation is introduced to account for demand uncertainty for the end products. In the first stage, before demand is realized, decisions are made on the setup periods for both production and purchase, and their corresponding quantities. In the second stage, after demand is revealed, the inventory and lost sales decisions are made. The goal is to minimize the expected total cost incurred by the decisions made in both stages. Heuristic approaches are proposed to solve the problem, using the expected demand through the deterministic formulation and sets of demand scenarios in the application of the sample average approximation method. Finally, numerical experiments are conducted with test instances to evaluate the modeling results for the expected cost and computational time using the proposed heuristics.

, 34 pages

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