A Two-Stage Push-Pull Production Planning Model

We study a hybrid push-pull manufacturing system that the IBM Systems Group implemented as a response to a complex configuration environment and increasing pressure for responsive order fulfillment lead times. This is a two-stage (fabrication and fulfillment center) manufacturing process, which builds and stocks tested subassemblies for justin-time configuration of the final product when a specific customer order is received. The first production stage (fabrication) is a push process where parts are replenished, tested, and assembled into subassemblies according to product-level build plans. The subassembly inventory is kept in stock ready for the final assembly of the end products. The second production stage (fulfillment) is a pull-based assemble-to-order process where the final assembly process is initiated when a customer order is received and no finished goods inventory is kept for end products. One important planning issue is to find an optimal trade-off between capacity utilization and inventory cost reduction that strives to meet the quarter-end peak demand. We present a nonlinear optimization model to minimize the total inventory cost subject to the service level constraints and the production capacity constraints. This results in a convex program with linear constraints. An efficient algorithm using decomposition is developed for solving the nonlinear optimization problem. Other numerical methods including a piece-wise linearization method and a general purpose nonlinear solver are also tested along with the decomposition method. Several variations of the model are formulated to incorporate additional features in practice. Numerical results are presented to show the performance improvement generated by the optimal solutions over a production-smoothing strategy.