Analysis of Real-Time Order Fulfillment Policies: When to Dispatch a Batch?

This paper considers orders that arrive one-by-one over time to a fulfillment center. Each order requests a product with some degree of customization that needs to be delivered expeditiously to a nearby location using a delivery vehicle. However, each vehicle can batch multiple orders together for delivery within a single trip. The benefits of batching include more efficient capacity utilization, lower total vehicle ownership requirements, and reduced environmental impact. The main drawback of batching is the consequent reduced average quality of service due to associated delivery delays when waiting for additional orders to arrive and executing a delivery route. To address this trade-off, we consider a set of threshold policies for batching and dispatching groups of orders, and characterize the associated long-run average cost per unit time for each policy that explicitly accounts for the customer’s total order lead time, including the time between order dispatch and delivery to the customer which, in turn, depends on route sequencing policies. For the threshold policies, our state variable may not only include the number of outstanding orders, but may also incorporate information on order arrival times and delivery locations. We model the stochastic dynamics of the system and obtain the long-run average cost per unit time, which we compute using a renewal-reward approach. We also consider different delivery sequencing approaches, including first-come, first-served and shortest traveling salesperson. In addition, we evaluate the effectiveness of accounting for all order information in the decision-making process, as opposed to just the number of outstanding orders or the time in the system for each order. Our analysis shows that a generalized class of cost- and quantity-based threshold policies often outperforms existing policies in the literature with the additional benefits of being robust to overestimates of the optimal cost threshold value and achieving strong delay cost performance.