Tactical Design of Same-Day Delivery Systems; Dynamic relocation of vehicles and staff for a car sharing service

Alan Erera

Tactical Design of Same-Day Delivery Systems

We study tactical models for the design of same-day delivery (SDD) systems. Same-day fulfillment in e-commerce has seen substantial growth in recent years, and the underlying management of such a service is complex. While the literature includes operational models to study SDD, they tend to be detailed, complex, and computationally difficult to solve, and thus may not provide any insight into tactical SDD design variables and their impact on the average performance of the system. We propose a simplified vehicle dispatching model that captures the “average” behavior of an SDD system from a single stocking location by utilizing continuous approximation techniques. We analyze the structure of optimal vehicle dispatching policies given our model for two important instance families, the single-vehicle case and the case in which the delivery fleet is large, and develop techniques for finding best configurations of these policies that require only simple computations. We then demonstrate with several example problem settings how this model and these policies can help answer various tactical design questions, including how to select a fleet size, determine an order cutoff time, and combine SDD and overnight order delivery operations. We also validate the predictions of the model and policies for example problem instances against a detailed operational model and demonstrate that our simple approximation model can predict the average number of orders served and minutes driven to within about 1%. (This is joint work with Georgia Tech Ph.D. student Alex Stroh and colleague Alejandro Toriello.)

Mathias Klapp

Dynamic relocation of vehicles and staff for a car sharing service

Recently, urban transport systems based on the shared economy have experienced significant growth driven by customers demanding flexible transportation options and the continuous search for efficiency and vehicle utilization. Nowadays, it is common to see services of shared vehicles, such as bikes (Mobike, Ofo), scooters (Lime, Bird) and automobiles (Zipcar, Shared Now, Car2go).

We study the daily operation of a one-way-car-sharing (OWCS) service offering the customer to pick-up and return a shared car in two different geographic locations (stations). Such a service poses major operational challenges. First, it is common to observe asymmetric demand patterns in space producing a tendency to geographical imbalance of vehicle inventory. If vehicles are not dynamically relocated over time, this will cause some stations to suffer shortages (loss of demand), while other stations could fill up with cars and lack empty parking spots for future vehicle returns. Also, unlike a bike/scooter-sharing service that repositions multiple vehicles in one trip, each car must be repositioned by a driver who should also be dynamically relocated over space and time.

We formulate a dynamic optimization model to jointly relocate cars and company staff throughout the operating day and propose different online policies ranging from a simple inventory band control policy at each station to a more sophisticated Approximate Dynamic Programming based policy estimating a loss function, i.e., expected future cost of shortage and overparking, for each station using a simplified stochastic model that disregards network effects and assumes memoryless properties of the underlying vehicle net arrival process. The value of our strategies is estimated in computationally simulated instances and in a study performed for a car-sharing company in Santiago, Chile.