Stochastic Due-Date Lot-Streaming Flowshop Scheduling with Benders Decomposition and Branch-and-Bound

Abstract

The lot-streaming flowshop scheduling problem with stochastic due time is addressed in this paper, with the objective of minimizing the sum of expected job delays. Closed-form expressions for the expected delays of jobs are derived under three classical distribution conditions. A mathematical model is then formulated, considering set-up times and stochastic due time. To address the highly nonlinear nature of the model, a linearization is performed. Furthermore, an optimization algorithm is designed using a Logic-based Benders decomposition (LBBD) approach combined with branch-and-bound. Two effective acceleration strategies are introduced to improve the efficiency of the algorithm. The numerical experiments demonstrate the effectiveness of the proposed algorithm, and the necessity of considering stochastic lead times is verified by comparing the results with those obtained from deterministic due time.

Keywords

• stochastic due time
• lot-streaming
• benders decomposition
• branch-and-bound