Last-Mile Shared Delivery: A Discrete Sequential Packing Approach

We propose a model for optimizing the last-mile delivery of n packages from a distribution center to their final recipients, using a strategy that combines the use of ride-sharing platforms (e.g., Uber or Lyft) with traditional in-house van delivery systems. The main objective is to compute the optimal reward offered to private drivers for each of the n packages such that the total expected cost of delivering all packages is minimized. Our technical approach is based on the formulation of a discrete sequential packing problem, in which bundles of packages are picked up from the warehouse at random times during the interval $\left[0,\mathit{T}\right]$. Our theoretical results include both exact and asymptotic (as $n\to \mathrm{\infty }$) expressions for the expected number of packages that are picked up by time T. They are closely related to the classical Rényi’s parking/packing problem. Our proposed framework is scalable with the number of packages.