Last-100-Meter Vertical Delivery

<div> Problem Definition: On-demand delivery platforms increasingly distinguish themselves through faster and more reliable order fulfillment, yet the final delivery stage inside high-rise buildings can remain time-consuming and uncertain.&nbsp;We identify this overlooked stage as the last-100-meter vertical delivery problem and formalize it as the Elevator Delivery Problem with Deadlines (EDPD) under uncertain elevator waiting times.&nbsp;Elevator waiting-time data from Beijing office buildings show substantial dispersion, pronounced right tails, and systematic heterogeneity across call floors, requested travel directions, and elevator loading states.&nbsp;Methodology/results: To capture these empirical patterns, we use a directed network to distinguish elevator calls by call floor and requested travel direction and a scenario-wise ambiguity set to characterize each loading state with conditional moment and support information.&nbsp;To quantify delay risk, we propose the Flexible Essential Riskiness Index (FERI), which extends the Essential Riskiness Index (ERI) by allowing the ERI feasibility condition to be relaxed with a penalty.&nbsp;FERI jointly accounts for the probability and magnitude of lateness while remaining finite and informative in delay-prone instances, where ERI is inapplicable.&nbsp;Integrating these elements, we propose a last-100-meter vertical delivery model, derive an equivalent mixed-integer second-order cone reformulation, develop a Benders decomposition algorithm to solve the model exactly, and design a hybrid heuristic that combines a residual-capacity-based Label strategy with the Deadline and Floor strategies for real-time sequencing decisions.&nbsp;Managerial implications: Simulation experiments show that the Benders decomposition substantially improves tractability and that our proposed model provides more reliable out-of-sample performance than sample-average approximation under distributional misspecification.&nbsp;A case study using real elevator data from Weiya Building shows that the exact solution approach and the Label strategy outperform practical Floor and Deadline strategies.&nbsp;The results also show that reliable delivery sequences may accept additional but more predictable in-elevator riding time to avoid long and volatile waits.&nbsp;Mechanisms for platform--building coordination, including anticipatory elevator calling and dedicated elevator access, can further reduce vertical delivery delay risk.&nbsp;More broadly, this work highlights the role of vertical logistics in enabling reliable urban on-demand fulfillment. </div>