Push-Pull Production Planning

We study a manufacturing system with a two-stage production referred to as the Fabrication and Fulfillment processes. The first stage (Fabrication) is a Build-to-Plan (Push) process in which the parts are replenished, tested, and assembled into subassemblies according to the product level build plan. The subassembly inventory is kept in stock ready for the final assembly of the end products. The second stage (Fulfillment) is an Assembly-to-Order (Pull) process, which means that final assembly starts after the customer order is received and no finished goods inventory is kept for end products.

One important issue in the planning process is to address the trade-off between the capacity utilization and inventory cost reduction while striving 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 machine capacity constraints. This results in a convex program with linear constraints. Efficient solution algorithms are developed using piecewise linear approximation, and heuristics are developed based on the Dynamic Programming formulation of the problem. Several variations of the model are formulated to incorporate additional features in practice. Numerical analyses are presented to show the performance improvement generated by the optimal solutions over the “as is” production-smoothing strategy.