Time-Dependent Shipment Options and Shipment Fees for E-Commerce Fulfillment Centers

We build a parsimonious model of a stochastic e-commerce fulfillment center offering time-dependent shipment options and corresponding fees to utility-maximizing customers that arrive according to a Poisson process. For this time-dependent policy, we present an exact analysis based on the underlying periodic Markov chain as well as monotonicity results for the optimal time-dependent shipment fee structure. We then propose a simple time-dependent shipment policy with an attractive two-level fee structure, and study it alongside two benchmarks that are prevalent in practice. Both benchmarks rely on static, time-independent fees for the offered shipment options, but differ in whether they stop offering same-day shipment after a certain cutoff time. Our numerical analysis indicates that including such a cutoff point under static shipment fees increases profits significantly, and that moving to time-dependent shipment fees increases profits by another substantial amount. Our time-dependent policy provides e-commerce companies with an easily implementable mechanism to better manage online demands for same-day or next-day shipment with the available capacity in the fulfillment centers responsible for collecting and shipping those orders.