Design and Control of a
Home Delivery Logistics Network
Michael G. Kay
North Carolina State University
Goal of Research
To eliminate the need for all non-recreational
shopping by making it possible to have a hot
pizza and a vehicle-load of other stuff
delivered to your home, exactly when you
want, for the price of what you would have
tipped the pizza delivery guy.
Dirt-to-Dirt Logistics Costs
($/ton-mi relative to water)
Economics of Driverless Vehicles
• Average cost (wage + benefits) of FedEx driver (UPS = $45/hr)
= $27/hr x 2000 hr/yr = $54,000 per year
 1  1.0175 
• Max investment = $54,000 
  $54,000  4.75   $256,500
 0.017 
Driverless Delivery Vehicle
Home Delivery Logistics Network
36.1
35.79
Durham
36
4
35.78
3
35.77
2
35.9
Raleigh
35.76
Or
de
r
35.8
er
35.75
Tr
ig
g
1
Local DC
35.7
35.74
DDV
-79.1
-79
-78.9
-78.8
-78.7
-78.6
-78.5
-78.78
-78.77
-78.76
-78.75
-78.74
-78.73
-78.72
34 miles
4 miles
(a) DCs covering Raleigh-Durham metro area.
(b) Delivery of four orders to a home.
-78.71
5 Modules
(1.25 m)
Fixed Array
in Facility
Array onboard vehicle moves to
interface with array in facility
Movable Array
Onboard Vehicle
Automated Loading/Unloading
10 Modules (2.5 m)
Module and Container Design
25 cm (9.84 in)
Track
Pop-up
wheel
(a) Top view of single module.
(b) Bottom view of 1 x 1 container.
(c) 2 x 1 container
(shown half scale).
Container
(a) First pair of wheels moves
container moves onto module.
(b) Container stops and second
pair of wheels is raised.
(c) First pair of wheels is lowered and second
pair moves container in orthogonal direction.
Container Accessibility
(a) Storage area prior to retrieval of
shaded container.
(b) Storage area after path cleared for
shaded container.
DC (top view of one level)
Elevator
Array
L/U Dock
Array
DDV Array
DC (side view)
Drone
Delivery
Pad
Elevators
Frozen
Storage
Refrigerated
Storage
General
Merchandise
Storage
L/U and
Sortation
Current Research Areas
1. Storage System Control
–
Unload, store, and load each container in a DC (joint
work with Peerapol Sittivijan)
2. Module Design
–
Design module prototype to estimate cost vs transit-time
tradeoff
3. Network Coordination
–
Develop mechanism to coordinate the operation of each
container, vehicle, and DC in the network
4. Performance Analysis
–
Estimate delivery times and associated cost for given
logistic network
Area 1: Storage System Control
vehicle departure and
load information
vehicle arrival and
load information
expected load
arrival time
load configuration,
destination and
deadline
Priority Assignment
confirm or report
deadlock
container priority
and destination
Path Planning and Execution
confirm
movement
signal
movement
Module
Elevator
signal and confirm movement
Load Planning and Control
Path Planning and Execution
• Module ≤ Container ≤ Shipment ≤ Load
• 3-D (x,y,t) A* used for planning path of each container
• Each container assigned unique priority that determines
planning sequence
– Paths of higher-priority containers become obstacles for
subsequent containers
– First-in-last-out loading/unloading → must change container
priority from when it is unloaded to when it is loaded
• Adaptive priority adjustment to correct for:
– Delay along planned path
– Deadlock detection
• Destination of containers in long-term storage is maxmin
distance to other containers
2-D Paths
2-D Paths
3-D Paths
Example: Loads on DDVs Arrive to DC
Example: Loads Unloaded into DC
Example: Containers Move to Staging
Example: Containers Loaded on DDVs
Area 2: Module Design
• Develop prototype modules and containers to determine
performance vs cost tradeoff
– Container transit time (target 5 sec)
– Module cost (target $50-$100 at scale)
• Economies of scale: 2.5 billion modules in 100,000 DCs
covering U.S.
25 cm (9.84 in)
Pop-up
wheel
(a) Top view of single module.
Track
(b) Bottom view of 1 x 1 container.
(c) 2 x 1 container
(shown half scale).
Prototype Module
• Mix of off-the-shelf and custom components
• 3D printing/additive manufacturing to be used to prototype
custom components and housing
Area 3: Network Coordination
• Separate firm can
own each DC and
DDV → coordination
more difficult than
private network
• Local load is a single
shipment
• Containers in
linehaul load part of
different shipments
each owned by a
separate firms
• Containers pay DC for
storage time
Load Bids
Multiple Loads at DC
Single (1-D) Load
• Load bid is sum of
container bids in load
• Loads in a lane ordered
by decreasing bid
• Containers bid for
services of the DDVs
used for their transport
– Containers going to same
DC compete to be in next
transported load
– Loads to different DCs
competing to be selected
by a DDV
– DDVs competing with
each other to select loads
DDV Protocol
•
•
Determines which DDV is used to transport what load at
what DC
Goal for DDV operation:
–
•
Try to match the load that values transport the highest with the DDV
that can provide that transport service at the least cost
Protocol:
1.
2.
Priority for Accepting Loads: Opportunity to accept or reject load
based on DDV’s expected arrival time at DC
Reneging: After reneging, DDV cannot again accept same load until
all other DDVs have rejected it
1. Priority for Accepting Loads
9
2nd 1st
8
7
3rd
6
4th
5
• Opportunity to accept or
reject load based on DDV’s
arrival time at DC
• DDV’s portion of load bid
fixed after acceptance
• If all DDVs reject load, then
it’s posted at DC and
available for any DDV to
accept
Load at DC 7
2. Reneging
DC 9
A c ce p
t
DC 8
Bid =
$ 1 00
Near and far DDV accept high
and low bids, respectively
DC 7
Bid =
DC 6
e
A cc
pt
• After reneging, DDV
cannot again accept
same load until all
other DDVs have
rejected it
$5 0
DC 5
2. Reneging
DC 9
A c ce p
t
DC 8
Bid =
$ 1 00
Bid Increases
$50 to $200
DC 7
Bid
DC 6
e
A cc
pt
• After reneging, DDV
cannot again accept
same load until all
other DDVs have
rejected it
= $2
00
DC 5
Near and far DDVs accept high
and low bids, respectively
Low bid now increases beyond
high bid
2. Reneging
R ene
ge
DC 8
Bid =
Sid
e Ag
reem
ent
DC 9
$ 1 00
DC 7
Bid
DC 6
e
Re n
ge
• After reneging, DDV
cannot again accept
same load until all
other DDVs have
rejected it
= $2
00
DC 5
Near and far DDVs accept high
and low bids, respectively
Low bid now increases beyond
high bid
DDVs agree to renege (since
far DDV’s portion fixed at
$50)
2. Reneging
DC 8
DC 9
ep
Bid =
t
Ac
ce
pt
Ac
c
DC 6
$ 1 00
DC 7
Bid
• After reneging, DDV
cannot again accept
same load until all
other DDVs have
rejected it
= $2
00
DC 5
Near and far DDVs accept high
and low bids, respectively
Low bid now increases beyond
high bid
DDVs agree to renege (since
far DDV’s portion fixed at
$50)
Near DDV accepts $200 bid
and far DDV $100 bid
Container Protocol
•
•
Determines which containers selected to join load
Goal for container selection:
–
•
Encourage a container to submit a bid that represents its true value
for transport as soon possible, thereby allowing DDVs to be more
responsive and discouraging multiple-bid auction-like behavior
Protocol:
1.
2.
3.
Load Formation: Bid per unit area of each container used by
2-D bin-packing heuristic to form loads
Allocation of Load Bid: After acceptance, DDV’s portion of load bid
does not increase and bids of any subsequent containers joining load
allocated to original containers
Withdrawal and Rebidding: Containers that withdraw or rejoin load
charged their previous bid amounts in addition to current bid
1. Load Formation
$3
9
nd
ou
b
In
$2
$4
• Containers assigned to load that
maximizes resulting load bid
• Containers can bid as soon as they
are at or inbound to DC
8
At DC
ETA =
7
1
Time
Index
Load
Bid
0
$3
$2
$1
1
$9
$4
$3
$2
$1
$1
2
$12
$5
$4
$3
$3
$2
First Load
Load
Bid
Second Load
$1
ETA
6
Inbo
und
=2
$5
5
$1
2. Allocation of Load Bid
• DDV’s portion of load bid fixed after acceptance
• Subsequent increases in bid allocated to container in load
(and remain in load) at time of acceptance
Container
Event
DDV
Response
Load
Bid
DDV
Portion
Allocated
Portion
Load
(Bid / Cost)
Bid & Join
Reject
8
8
0
8/8
Bid & Join
Accept
10
10
0
8/8
2/2
Bid & Join
—
15
10
5
8/4
5/5
2/1
Bid, Join,
& Drop
—
16
10
6
8/2
5/5
3/3
2/0
3. Withdrawal and Rebidding
• Containers that withdraw or rejoin load are charged
previous bid amounts
Container
Event
DDV
Response
Load
Bid
DDV
Portion
Allocated
Portion
Load
(Bid / Cost)
Bid & Join
Reject
8
8
0
8/8
Bid & Join
Accept
10
10
0
8/8
2/2
Bid & Join
—
15
10
5
8/4
5/5
2/1
Bid, Join,
& Drop
—
16
10
6
8/2
5/5
3/3
2/0
Rebid, Rejoin,
& Drop
—
19
10
9
8 /-1
5/5
4/6
3/0
Rebid, Rejoin,
& Drop
—
24
10
14
8 /-6
6/9
5/5
4/2
Withdraw
& Rejoin
—
28
10
18
8 /-10
6/9
4/6
0/5
—
Renege
28
28
0
8/8
6/9
4/6
0/5
Agent-based Coordination
• Each container and each DDV controlled by a software agent
• Agents:
– provided with all load bids at DC and all DDV locations
– can make side payments with each other
2-D Load Formation: Select Containers
• Containers
sorted based on
decreasing perunit bid value
• Selected until
cumulative area
= 50, capacity of
module array
Cont.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Length
4
2
1
2
3
2
1
1
1
1
2
3
1
1
4
1
2
1
Width
3
3
2
2
2
1
1
2
1
1
2
1
1
2
4
1
1
1
Area
12
6
2
4
6
2
1
2
1
1
4
3
1
2
16
1
2
1
Cum.
Area
12
18
20
24
30
32
33
35
36
37
41
44
45
47
48
50
51
Bid
4.03
1.99
0.64
1.27
1.80
0.56
0.27
0.54
0.27
0.26
0.95
0.55
0.17
0.35
2.64
0.15
0.27
0.12
Per Unit
Bid
0.3361
0.3322
0.3195
0.3180
0.3000
0.2787
0.2737
0.2715
0.2650
0.2628
0.2379
0.1843
0.1750
0.1731
0.1651
0.1500
0.1366
0.1220
2-D Load Formation: Order Containers
• Order sequence determined
based on:
1. Length
2. Width
3. Bid
• Upper Bound (UB) = sum of bids
of all containers
• May not be feasible to fit (pack)
all containers into array (bin)
Cont.
1
5
12
2
4
11
6
17
3
8
14
7
9
10
13
16
18
Length
4
3
3
2
2
2
2
2
1
1
1
1
1
1
1
1
1
Width
3
2
1
3
2
2
1
1
2
2
2
1
1
1
1
1
1
UB =
Bid
4.03
1.80
0.55
1.99
1.27
0.95
0.56
0.27
0.64
0.54
0.35
0.27
0.27
0.26
0.17
0.15
0.12
14.09
2-D Load Formation: Bin Packing
1.
2.
3.
4.
5.
Initial: Add
containers based on
order sequence
Re-check: try adding
any cont. left out of
initial load
Add more efficient:
replace if more
efficient cont. can be
added
Add extras: insert
cont. in any available
space
Final
Diseconomies of Scale
Yellow containers spend/bid less on a per-unit basis to join
a load leaving earlier due to their smaller size
(Containers 1-40 numbered in decreasing total bid; Loads 1-6 in increasing departure time)
Area 4: Performance Analysis
Home Delivery Cost Estimate
Module Cost
L/U Time (min)
DC Space Util.
Household Demand (trips/week)
50
50
5
5
0.6
0.8
1
2
1.46 2.27
1.29 2.10
0.23 9
0.21 10
2.27 3.19
1.93 2.84
0.16 17
0.14 18
0.73 1.54
0.64 1.45
0.15 25
0.15 26
1.14
0.96
2.05 0.10
1.88 0.09
50
50
10
10
0.6
0.8
3
4
1.46 2.27
1.29 2.10
0.23 11
0.21 12
2.27 3.19
1.93 2.84
0.16 19
0.14 20
1.32 2.13
1.32 2.13
0.21 27
0.21 28
1.64
1.64
2.56 0.13
2.56 0.13
100
100
5
5
0.6
0.8
5
6
2.51 3.39 0.34 13
2.16 3.05 0.30 14
4.01 5.02
3.32 4.32
0.25 21
0.22 22
1.25 2.14
1.08 1.97
0.21 29
0.20 30
2.01
1.66
3.01 0.15
2.66 0.13
100
100
10
10
0.6
0.8
7
8
2.51 3.39
2.16 3.05
4.01 5.02
3.32 4.32
0.25 23
0.22 24
2.12 3.01
2.12 3.01
0.30 31
0.30 32
2.71
2.71
3.71 0.19
3.71 0.19
2
4
Modules per Trip
10
DC
Modules per Trip
10
20
Trip Mod
0.34 15
0.30 16
DC
Trip Mod
DC
Trip Mod
20
DC
Trip Mod
(DC cost in $, DC + vehicle cost = Trip cost in $, Mod = cost per module delivered in $)
Available 2016: Starship Technologies
• Started by Skype cofounders
• 99% autonomous
(human operators are
available to take control)
• Goal: “deliver ‘two
grocery bags’ worth of
goods (weighing up to
20lbs) in 5-30 minutes for
‘10-15 times less than
the cost of current lastmile delivery
alternatives.’”
• http://www.engadget.co
m/2015/11/02/starshiptechnologies-localdelivery-robot/