Lagrangian decomposition and second-order cone programming based warehouse storage planning problem

In this paper we consider a warehouse storage planning problem which is widely appeared in process industry as well as logistics companies. Products came from production line are initially stored in production-end warehouse of each production line and will be transported to different warehouses for further production or delivery according to customers´ requests. Warehouse storage planning is to decide where and when to transport the products to make the matching degree maximized while considering capability restrictions and equilibrium of logistics. We formulate this problem and transform it to a mixed integer second-order cone program (MISOCP). We perform a Lagrangian decomposition algorithm to derive an upper bound, and a randomized rounding heuristic is applied to gain near optimal solutions. We also construct valid inequalities to improve the upper bound. Experimental results based on practical data show that the proposed method outperforms optimization software both on solution quality and computing efficiency.