From Hatchbacks to Minivans: Optimizing Acceptance and Packing Decisions on Two-Sided Car-Shipping Platforms

Abstract

We analyze a two-sided platform facilitating car-shipping services, where both demand and supply are stochastic. On the demand side, customers submit requests to ship cars of varying types; on the supply side, truckers offer their available capacity for shipping. The platform also has access to an expensive outside supply option for additional trucking capacity. The platform's objective is to maximize the long-run average profit rate by optimally accepting or rejecting demand and supply requests, hiring outside trucks, and matching accepted cars with trucks, subject to packing capacity and timing constraints. We first formulate the static packing problem, which is an integer program. We utilize the linear relaxation of this integer program to formulate a fluid model that respects the capacity constraints. The properties of the fluid problem's solution allow us to upper bound the optimal profit of the platform and categorize the platform's problem into two cases: excess-trucks and excess-cars. We propose an asymptotically optimal policy for each case faced by the platform, where the relative optimality gap of our policy approaches zero as arrival rates increase by a factor of n: the excess-trucks policy has an optimality gap of O(1), while the excess-cars policy has an optimality gap of O(√ n).