An Improved L-Shaped Method for Solving Process Flexibility Design Problems

Process flexibility, where a plant is able to produce different types of products, is introduced to mitigate mismatch risk caused by demand uncertainties. The long chain design proposed by Jordan and Graves in 1995 has been shown to be able to reap most benefits of full-flexibility structure (where each plant is able to produce all products) in balanced systems (where the numbers of products and plants are equal). However, when systems are not balanced or asymmetric or when response dimension is taken into consideration, long chain design may not be the best configuration. Therefore, this paper models the process flexibility design problem in more general settings. The paper considers both balanced and unbalanced systems with asymmetric plants considering response dimension. The problem is formulated as a two-stage stochastic program which is solved by an adapted L-shaped method, combining it with several enhancements. To the best of our knowledge, this is the first time L-shaped method is used to solve the process flexibility design problem. The effectiveness and efficiency of the proposed method and enhancements are evaluated. Finally, the comparison between design methods proposed in this paper and in existing literature shows the superiority of the former.