Multiple lot‐sizing decisions in a two‐stage production with an interrupted geometric yield and non‐rigid demand

In a production system with random yield, it may be more cost effective to release lots multiple times towards fulfilling a customer order. Such a decision, called the multiple lot‐sizing problem, has been investigated in various contexts. This paper proposes an efficient algorithm for solving a new multiple lot‐sizing problem defined in the context of a two‐stage production system with non‐rigid demand when its process yields are governed by interrupted geometric distributions. We formulate this problem as a dynamic program (DP) and develop lemmas to solve it. However, solving such a DP may be computationally extensive, particularly for large‐scale cases with a high yield. Therefore, this study proposes an efficient algorithm for resolving computational issues. This algorithm is designed to reduce the DP network into a much simpler algorithm by combining a group of DP branches into a single one. Extensive experiments were carried out. Results indicate that the proposed reduction algorithm is quite helpful for practitioners dealing with large‐scale cases characterized by high‐yield.