Optimal supply chain design and management over a multi-period horizon under demand uncertainty. Part II: A Lagrangean decomposition algorithm

In Part I (Rodriguez, et al., 2013) an optimization model was proposed to redesign the supply chain of spare parts industry under demand uncertainty in a specified planning horizon. To address large industrial problems, a Lagrangean scheme is proposed to decompose the MINLP of Part I according to the warehouses by dualizing the logic constraints that assign the warehouses to different customers, together with the demand constraints and factory capacity constraints. The subproblems are first approximated by an adaptive piece-wise linearization scheme that provides lower bounds, and the MILP is further relaxed to an LP to improve solution efficiency while providing a valid lower bound. An initialization scheme is designed to obtain good initial Lagrange multipliers, which are scaled to accelerate the convergence. The results from an illustrative problem and two real world industrial problems show that the method can obtain optimal or near optimal solutions in modest computational times.