Bi-Objective Routing Optimization for Instant Delivery with an Active Customer Rejection Strategy Considering Delivery Cost and Customer Satisfaction

Faced with capacity-demand mismatch and customer churn during order surges in instant delivery, selective veh[]icle routing provides a promising alternative by actively rejecting low-value orders instead of passively accepting all requests. This study constructs a bi-objective routing optimization model that minimizes delivery cost while maximizing the satisfaction of retained customers. First, a game-theoretic AHP–entropy weighting framework is built for multi-dimensional customer-rejection loss assessment, with an adaptive screening threshold and robustness validated via ±15% weight perturbation. Second, a piecewise exponential satisfaction function derived from cumulative prospect theory characterizes user loss aversion; dual hard constraints for maximum rejection rate and per-customer minimum satisfaction are incorporated to maintain the basic service level among retained customers, though rejected customers receive zero satisfaction and the full-population mean satisfaction decreases with the rejection ratio. An improved MA-NSGA-II with adaptive genetic operators and phased incremental memetic local search is proposed to solve this NP-hard problem. Numerical experiments on scaled benchmark and real-world instant-delivery instances with statistical hypothesis tests indicate that reasonable rejection thresholds reduce delivery costs without degrading basic service levels. For our test instances, a 10% rejection cap yields the most favorable trade-off for both the large-scale and the small-scale test cases, as it significantly reduces delivery costs while improving the satisfaction of retained customers. The generated Pareto trade-off schemes support quantitative peak-period scheduling decisions for instant-delivery platforms.