Order assignment and scheduling under processing and distribution time uncertainty

In response to increasingly fierce competition and highly customized demands, many companies adopt a distributed production model but manage their orders in a centralized manner. Coordination between multiple factories requires unified information and resources to provide a close match between supply and demand. One of the crucial tasks is to solve the order assignment and scheduling problem with uncertainties introduced by unexpected changes in upstream supply, labor supply, and transportation capacity. Managing uncertainties in production and distribution is important, as they can significantly interrupt and delay the timely and constant supply of orders if not appropriately managed. We address an order assignment and scheduling problem with direct distribution under uncertainties in processing and distribution time. The aim is to achieve a minimum of weighted sum cost and timeliness, which involves the optimization of the order assignments to multi-factory and production scheduling for orders at each site. We first formulate the problem as a two-stage stochastic programming model. To manage a large scale of possible scenarios, we apply a sample average approximation (SAA) method to approximate the model. We propose a novel model with fewer binary variables and big-M constraints. An exact logic-based Benders decomposition (LBBD) method is developed to deal with practical-sized instances. Numerical results indicate the superiority of our new model and the LBBD method. Managerial implications are discussed to demonstrate its advantages and potential applicability in practice.