Joint Order Picking and Packaging Optimization for E-Warehouse with Multiple Zones

E-commerce orders frequently contain items stored in distinct zones or even separate facilities, necessitating the coordination of multiple pickers, which often results in additional waiting time. This research investigates the joint order picking and packaging optimization problem for a multi-zone e-commerce warehouse. We formulate the integrated batching, picker assignment, sequencing, and packaging decisions as a mixed-integer nonlinear programming (MINLP) model and further reformulate the nonlinear relationships into a solvable mixed-integer linear programming (MILP) model for exact-solver validation. Due to the computational intractability of large-scale instances, we introduce a two-stage heuristic framework that combines spatial-first and temporal-first batching rules with an RP-VNS improvement procedure. Computational experiments compare the proposed algorithms with Gurobi on small-scale instances and with two greedy benchmarks and an ALNS-based metaheuristic on large-scale instances. The results show that the spatial-first heuristic (SFH) consistently achieves the lowest total cost, while the temporal-first heuristic (TFH) also improves upon ALNS in most settings. Relative to ALNS, SFH and TFH reduce total operational costs by up to 28.85% and 20.93%, respectively. Additional VNS ablation and routing-policy experiments further demonstrate the contribution of VNS on the tested instances and the robustness of the proposed framework under alternative routing assumptions.