The vehicle routing problem with cross-docking for perishable products under freshness-life and travel time uncertainties

This research extends the vehicle routing problem with cross-docking (VRPCD) by incorporating perishable products under freshness-life and travel time uncertainties, resulting in VRPCD-PP-2U. A robust optimization (RO) approach with budget sets is derived to address these uncertainties. While the RO model is tractable for small-scale instances, an adaptive large neighborhood search (ALNS) algorithm integrated with a dynamic programming feasibility-checking procedure under worst-case scenarios is proposed to address large-scale instances. Numerical experiments demonstrate that the proposed ALNS effectively solves all benchmark instances with up to 200 requests, achieving stable performance over 10 runs within reasonable computational times. Sensitivity analysis further shows that incorporating freshness considerations reduces freshness loss by 47.12% compared with the baseline setting, whereas introducing robustness increases the total cost by 9.61% on average across the benchmark instances. It highlights the trade-off among cost, product quality, and robustness, and provide managerial insights under uncertainties.