1. Same-day delivery systems that provide instant delivery are becoming more common and changing consumer expectations and retail logistics. 2. Very short delivery times require new approaches for efficient last-mile delivery logistics. 3. Understanding modern last-mile delivery systems can be helped by quantitative models, but more study is still needed as these systems evolve rapidly.

1. Building Understanding of Modern
Last-mile Delivery Systems
Alan Erera
School of Industrial and Systems Engineering, Georgia Tech
Transportation Symposium to Honor Carlos, Berkeley, June 2018

2. The impact of an advisor
• Inspire with guiding principles
• Before seeking solutions, be sure to understand the problem
• Arm with diverse toolkit
• “I can teach you things that no one else can!”
• Coach but also cheerlead
• Root for your students and prioritize them professionally and personally
• Be a role model
• The impact of an advisor is primarily delivered through her students

3. The impact of an advisor
Team Carlos
Team Erera

4. Last-mile delivery logistics collaborators
• Georgia Tech collaborators:
• Alex Stroh, Ramon Auad, Damian Reyes (Amazon), Mathias Klapp (PUC Chile)
• AE, Alejandro Toriello, Martin Savelsbergh
• Industry collaborators
• Grubhub, SF Express

5. What to remember
1. Same-day delivery systems with short delivery deadlines are here
to stay, providing consumers instant acquisition and large selection
2. Very short click-to-door times may require different approaches for
last-mile delivery logistics to consumers
3. Building an understanding of modern last-mile delivery logistics
systems can rely on a variety of different quantitative models
4. Much work remains to be done in the study of evolving delivery
logistics systems

6. What to remember
1. Same-day delivery systems with short delivery deadlines are here
to stay, providing consumers instant acquisition and large selection
2. Very short click-to-door times may require different approaches for
last-mile delivery logistics to consumers
3. Building an understanding of modern last-mile delivery logistics
systems can rely on a variety of different quantitative models
4. Much work remains to be done in the study of evolving delivery
logistics systems

7. Fundamental change in commerce
• Diminishing role of retail stores
• Delivery of product directly to
consumers
• Product “definition” includes a
service element
• When and how can I get it?
• Last mile logistics
• Increasing complexity!

8. Same-day delivery retailing
• Order (click) and
receive (to door)
• on the same day
• within a few hours
• within an hour
• Best of both worlds
• No trip to store
• Much larger product
catalog than store

9. What to remember
1. Same-day delivery systems with short delivery deadlines are here
to stay, providing consumers instant acquisition and large selection
2. Very short click-to-door times may require different approaches for
last-mile delivery logistics to consumers
3. Building an understanding of modern last-mile delivery logistics
systems can rely on a variety of different quantitative models
4. Much work remains to be done in the study of evolving delivery
logistics systems

10. Same-day delivery
• Order placement and ready time processes
Ready
time r
time
today’s orders begin order deadline
o4
ready for dispatch
from depot
o4
Placement
time a
Order placed
by customer
“click time”

11. Same-day delivery
• Order placement and ready time processes
ready time process realization
timeo1 o2 o3
today’s orders begin
on
order deadline
o4

12. Same-day delivery
• Vehicle operating deadline
• Order delivery deadlines (click- or ready-to-door)
time
vehicle operating
deadline TOrder delivery deadline
o1 o2 o3 o4 on

13. • Consolidation and vehicle dispatching
• Dispatch one or more vehicles over time, serving orders by delivery deadlines
Same-day delivery
time
Driver 1
o1 o2 o3
o1
o2
o3
Single depot system for now

14. • Consolidation and vehicle dispatching
• Dispatch one or more vehicles over time, serving orders by delivery deadlines
• Vehicles may be reused, must return from last dispatch by operating deadline
Same-day delivery dispatching
time
Driver 1 Driver 1Driver 2
Single depot system for now

15. What to remember
1. Same-day delivery systems with short delivery deadlines are here
to stay, providing consumers instant acquisition and large selection
2. Very short click-to-door times may require different approaches for
last-mile delivery logistics to consumers
3. Building an understanding of modern last-mile delivery logistics
systems can rely on a variety of different quantitative models
4. Much work remains to be done in the study of evolving delivery
logistics systems

16. Single depot, single deadline setting
time
deadline T
o1 o2 o3 o4 on
last order N
depot
o1
service area A

17. Dedicated vehicle fleet: how many?
time
deadline Tlast order NContinuous arrival rate 1 per scaled time

18. Dedicated vehicle fleet: how many?
time
deadline Tlast order NContinuous arrival rate 1 per scaled time
depot
service area A Approximate travel time to serve n customers across service area

19. Dedicated vehicle fleet: how many?
time
TNContinuous arrival rate 1 per scaled time
depot
service area A Approximate travel time to serve n customers across service area
One vehicle can serve all requests for if (T – N) large enough!

20. Large fleet: simple “whole area” strategy
time
TNTo minimize total duration of all routes: “wait as long as possible”
depot
service area A To find first dispatch time:
each vehicle serves
customers in “whole area”

21. Large fleet: simple “whole area” strategy
time
TNTo minimize total duration of all routes: “wait as long as possible”
depot
service area A To find first dispatch time:
each vehicle serves
customers in “whole area”
To find the j-th dispatch time:

22. Large fleet: simple “whole area” strategy
time
TNTo minimize total duration of all routes: “wait as long as possible”
depot
service area A For some large enough m:
each vehicle serves
customers in “whole area”
Under this strategy, you need only m vehicles:
and the m-th vehicle may complete its work before T

23. Large fleet: simple “divide area” strategy
time
TN
depot
service area A Each vehicle accumulates N/m customers, and
operates in a smaller zone of size A/m
each vehicle serves zone
with area A/m
m vehicles
Dispatch all m vehicles at time N

24. Large fleet: simple “divide area” strategy
time
TNDispatch all m vehicles at time N
depot
service area A Each vehicle accumulates N/m customers, and
operates in a smaller zone of size A/m
each vehicle serves zone
with area A/m
m vehicles

25. Single vehicle: serving more customers!
time
TN
depot
service area A
We can move N closer to T, but only by
reusing vehicle for multiple trips

26. Single vehicle: serving more customers!
time
TN
depot
service area A
Dispatching Policy Minimizing Total Route Duration:
Suppose that there is some enforced minimum dispatch size
such that, for larger dispatches, q >= f(q).
Then an optimal dispatch policy for a single vehicle is to initially
wait, and then dispatch consecutively shorter duration trips
without any additional waiting.
We can move N closer to T, but only by
reusing vehicle for multiple trips

27. Single vehicle: serving more customers!
time
TN
depot
service area A
We can move N closer to T, but only by
reusing vehicle for multiple trips
Vehicle arrives back at depot for final dispatch after last order:
Vehicle can complete final dispatch before deadline:

28. Single vehicle: serving more customers!
time
TN
depot
service area A
Dispatching Policy Minimizing Total Route Duration:
Using fewest dispatches D in this scheme leads to minimizing
costs
A simple iterative root-finding algorithm can be used to find D
and its associated initial waiting time
We can move N closer to T, but only by
reusing vehicle for multiple trips

29. Single vehicle: serving more customers!
time
TN
depot
service area A
Dispatching Policy Minimizing Total Route Duration:
Using minimal number of dispatches D in this scheme leads to
minimizing costs
A simple iterative root-finding algorithm can be used to find
minimum D and its associated initial waiting time
We can move N closer to T, but only by
reusing vehicle for multiple trips

30. Building understanding with other models
• Simplified half-line geometry provides maximum consolidation benefit
• Eliminates need for combinatorial route sequencing (TSP)
timeo1 o2 o3 ono4
Distance
depot

31. Building understanding with other models
• Simplified half-line customer geography
• Polynomial algorithms for single-vehicle multiple-trip dispatch
optimization with known orders (Reyes, E, Savelsbergh, 2018)
• Can orders be served by deadlines?
• What dispatches minimize total duration of all dispatches?
• Polynomial algorithms for single-vehicle multiple-trip order
accept/reject with known orders
• How many orders can be served? (Reyes, 2018 thesis)
• Balancing orders served with route travel costs? (Klapp, E, Toriello, 2016)
Distance
depot

32. Building understanding with other models
• Simplified half-line customer geography
• A priori rollout policies for single-vehicle multiple-trip dispatching with
dynamic and uncertain orders
• Balancing orders served with route travel costs? (Klapp, E, Toriello, 2016)
• Time-expanded network integer programs for multiple vehicle
accept/reject policy analysis with known orders
• Can simple reject schemes based on distance-from-depot perform close to
complex optimal schemes? (Auad, E, Savelsbergh, TBP)
Distance
depot

33. Building understanding with other models
• Full detailed dynamic programming for problems
with “network” geography
• Single-vehicle multiple-trip prize-collecting TSP for
deterministic and a priori expected cost minimization
• A priori rollout policies for single-vehicle multiple trip
dispatching with dynamic and uncertain orders
• Balancing orders served with route travel costs? (Klapp, E,
Toriello, to appear)
depot

34. Orders served versus routing costs
time
TN
time
TN

35. Orders served versus routing costs
Balance Cost with Orders Served Maximize Orders Served

36. What to remember
1. Same-day delivery systems with short delivery deadlines are here
to stay, adding instant acquisition to large selection for consumers
2. Very short click-to-door times require different approaches for last-
mile delivery logistics to consumers
3. Building an understanding of modern last-mile delivery logistics
systems can rely on a variety of different quantitative models
4. Much work remains to be done in the study of evolving delivery
logistics systems

37. Questions still needing better answers
• “Traditional” capacity management
• What mix of dedicated versus on-demand delivery resources?
• How and when to add on-demand capacity?
• How to decide when adding on-demand capacity is preferable to
dynamically suppressing demand?
• How and when to integrate “Uber-like” on-demand delivery couriers?
• How to provide “soft control” incentives to independent couriers to get
capacity when and where you need it?

38. Massive scale, shortest click-to-door
• Online food ordering, shared
delivery network across
restaurants
• Not one or two vehicles
• Not one or two goods pickup
points (depots)
• Variation and uncertainty in
operating conditions
• order processing (click-to-ready)
• travel and service times
• order demand rates
• capacity availability

39. Questions still needing answers
• Large-scale urban pickup-and-delivery systems
• How to scale high velocity last-mile systems to large numbers of orders?
• How to enable simple coordination of multi-layer last-mile systems?
• How and when to integrate new automated technologies (both storage
and transport) into large-scale systems?
When we pursue these problems, let’s not forget:
Before seeking answers, understand the problem

40. What to remember
1. Same-day delivery systems with short delivery deadlines are here
to stay, adding instant acquisition to large selection for consumers
2. Very short click-to-door times require different approaches for last-
mile delivery logistics to consumers
3. Building an understanding of modern last-mile delivery logistics
systems can rely on a variety of different quantitative models
4. Much work remains to be done in the study of evolving delivery
logistics systems