Real-Time Personalized Order Holding

Abstract

E-commerce retailers have a buffer to “hold” some orders before dispatching them for warehouse picking, which has benefits such as consolidating with another order placed by the same customer. Some e-retailers have begun using personalization to decide which orders to hold, based on a customer’s predicted probability of making another order. However, due to the real-time nature in which orders arrive and the dispatching deadlines imposed, e-tailers still face a non-trivial tradeoff in deciding which orders to hold.

We introduce a parsimonious online decision-making model for studying this tradeoff, yielding intuitive index-based policies that decide in real-time which orders to hold. We provide constant-factor competitive ratio guarantees for these policies’ performances, which do not require any forecasts regarding future incoming orders. In particular, we show that two naive index-based policies have competitive ratios of 1/2 and 1−1/e ≈ 0.63. Our main methodological contribution is to develop a flexible framework for defining “quasi-utilities” that couples the states of an online vs. offline algorithm, which reduces the design of online index-based policies to an offline geometrical problem. The framework allows us to optimize the index function, leading to an exponential-index-based policy that has an improved competitive ratio of 0.68. We also consider various extensions and prove that most of our analyses are tight.

Finally, we conduct a concise numerical study to demonstrate the strong average-case performance of the proposed policies, under non-worst-case stochastic demand sequences.

Keywords: order holding, consolidation, personalization, index-based policies, online algorithms, competitive ratio, e-commerce, fulfillment, online allocation, online scheduling, reusable resources, cloud computing