Risk-Based Optimization of Driver Allocation in Urban Last-Mile Delivery

Uncertainty in last-mile delivery complicates day ahead driver staffing. We propose a single-period stochastic optimization model that jointly chooses base (pre-booked) and surge (backup) capacity. The model combines the newsvendor overage / underage tradeoff, dual-sourcing cost differentiation, and exogenously specified risk-based route classes to represent heterogeneous demand. Given counts of high, medium, and low risk routes and unit costs, it computes the cost with the objective of finding the optimal numbers of pre-booked and backup drivers. An illustrative example shows how risk segmentation and dual sourcing shape the optimal mix and quantify the tradeoff between higher upfront staffing and lower shortfall exposure. We use finite convolution formulas for the distribution of total driver demand under independent per route needs, enabling efficient evaluation of expected penalties across candidate staffing plans. The model can be extended to rolling horizon and multi-period settings.