Manufacturing Planning over Alternative Facilities: Modeling, Analysis and Algorithms

We propose a planning model for multiple products manufactured across multiple manufacturing facilities sharing similar production capabilities. The need for crossfacility capacity management is most evident in high-tech industries that have capitalintensive equipment and short technology life cycle. Our model is based on an emerging practice in these industries where product managers from business units dictate manufacturing planning in facilities that are equipped to produce their products. We propose a multicommodity flows network model where each commodity represents a product and the network structure represents linked manufacturing facilities capable of producing the products. We analyze in depth the product-level (single-commodity, multifacility) subproblem. We prove that even the uncapacitated, general-cost version of this subproblem is NP-complete. We develop a shortest-path algorithm for this problem and show that it achieves optimality under special cost structures. We analyze and pinpoint specific cases where the algorithm fails to produce optimal solutions. To solve the overall (multicommodity) planning problem we develop a Lagrangian decomposition scheme, which separates the planning decisions into a number of single-product, multifacility subproblems and a resource subproblem. Through extensive computational testing, we demonstrate that in the context of product-based decomposition the shortest path algorithm is an effective heuristic for the MIP subproblem, yielding high quality solutions with only a fraction (roughly 2%) of the computer time.