Design and Control of aHome Delivery Logistics Network

Michael G. KayNorth 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

• Max investment =

51 1.017$54,000 $54,000 4.75 $256,500

0.017

Driverless Delivery Vehicle

Home Delivery Logistics Network

-79.1 -79 -78.9 -78.8 -78.7 -78.6 -78.5

35.7

35.8

35.9

36

36.1

Raleigh

Durham

-78.78 -78.77 -78.76 -78.75 -78.74 -78.73 -78.72 -78.71

35.74

35.75

35.76

35.77

35.78

35.79

4 miles 34 miles

1

2

43

Local DC Trigge

r Ord

er

DDV

(a) DCs covering Raleigh-Durham metro area. (b) Delivery of four orders to a home.

Automated Loading/UnloadingFi

xed

Arra

y in

Fac

ility

Mov

able

Arr

ayO

nboa

rd V

ehic

le

Arra

y on

boar

d ve

hicl

e m

oves

to

inte

rfac

e w

ith a

rray

in fa

cilit

y

5 M

odul

es(1

.25

m)

10 Modules (2.5 m)

Module and Container Design

(a) Top view of single module. (b) Bottom view of 1 x 1 container. (c) 2 x 1 container (shown half scale).

TrackPop-up wheel

25 cm (9.84 in)

(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

Container Accessibility

(b) Storage area after path cleared for shaded container.

(a) Storage area prior to retrieval of shaded container.

DC (top view of one level)

L/U DockArray

DDV Array

Elevator Array

DC (side view)

Elevators

General Merchandise Storage

L/U and Sortation

Refrigerated Storage

Frozen Storage

DroneDeliveryPad

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

load configuration, destination and deadline

Path Planning and Execution

Priority Assignment

Load Planning and Control

confirm or report deadlock

container priority and destination

expected load arrival time

vehicle departure and load information

vehicle arrival and load information

confirmmovement

signal movement

Modulesi

gn

al a

nd

co

nfi

rm m

ove

men

tElevator

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.

(a) Top view of single module. (b) Bottom view of 1 x 1 container. (c) 2 x 1 container (shown half scale).

TrackPop-up wheel

25 cm (9.84 in)

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• 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

Single (1-D) Load

Mu

ltip

le L

oad

s at

DC

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. Priority for Accepting Loads: Opportunity to accept or reject load

based on DDV’s expected arrival time at DC2. Reneging: After reneging, DDV cannot again accept same load until

all other DDVs have rejected it

1. Priority for Accepting Loads

7

9

8

5

6

1st2nd

• 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• After reneging, DDV

cannot again accept same load until all other DDVs have rejected it

Near and far DDV accept high and low bids, respectively

DC 9

DC 7

DC 8

DC 5DC 6

2. Reneging• After reneging, DDV

cannot again accept same load until all other DDVs have rejected it

Near and far DDVs accept high and low bids, respectively

Low bid now increases beyond high bid

DC 9

DC 7

DC 8

DC 5DC 6

Bid Increases$50 to $200

2. Reneging• After reneging, DDV

cannot again accept same load until all other DDVs have rejected it

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)

DC 9

DC 7

DC 8

DC 5DC 6

2. Reneging• After reneging, DDV

cannot again accept same load until all other DDVs have rejected it

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

DC 9

DC 7

DC 8

DC 5DC 6

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. Load Formation: Bid per unit area of each container used by

2-D bin-packing heuristic to form loads2. 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

3. Withdrawal and Rebidding: Containers that withdraw or rejoin load charged their previous bid amounts in addition to current bid

1. Load Formation

• Containers assigned to load that maximizes resulting load bid

• Containers can bid as soon as they are at or inbound to DC

7

9

8

5

6$5

$3

$2

$1

At DC

Inbound

Inbound

ETA = 2

ETA = 1

$4

Time Index

Load Bid First Load

Load Bid Second Load

0 $3 $2 $1

1 $9 $4 $3 $2

$1 $1

2 $12 $5 $4 $3

$3 $2 $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 amountsContainer

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 6 / 9 0 / 54 / 68 /-10

— Renege 28 28 0 8 / 8 6 / 9 0 / 54 / 6

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 per-unit bid value

• Selected until cumulative area = 50, capacity of module array

Cont. Length Width Area Cum. Area Bid

Per Unit Bid

1 4 3 12 12 4.03 0.3361 2 2 3 6 18 1.99 0.3322 3 1 2 2 20 0.64 0.3195 4 2 2 4 24 1.27 0.3180 5 3 2 6 30 1.80 0.3000 6 2 1 2 32 0.56 0.2787 7 1 1 1 33 0.27 0.2737 8 1 2 2 35 0.54 0.2715 9 1 1 1 36 0.27 0.2650 10 1 1 1 37 0.26 0.2628 11 2 2 4 41 0.95 0.2379 12 3 1 3 44 0.55 0.1843 13 1 1 1 45 0.17 0.1750 14 1 2 2 47 0.35 0.1731 15 4 4 16 2.64 0.1651 16 1 1 1 48 0.15 0.1500 17 2 1 2 50 0.27 0.1366 18 1 1 1 51 0.12 0.1220

2-D Load Formation: Order Containers

• Order sequence determined based on:1. Length2. Width3. Bid

• Upper Bound (UB) = sum of bids of all containers

• May not be feasible to fit (pack) all containers into array (bin)

Cont. Length Width Bid

1 4 3 4.03 5 3 2 1.80

12 3 1 0.55 2 2 3 1.99 4 2 2 1.27

11 2 2 0.95 6 2 1 0.56

17 2 1 0.27 3 1 2 0.64 8 1 2 0.54

14 1 2 0.35 7 1 1 0.27 9 1 1 0.27

10 1 1 0.26 13 1 1 0.17 16 1 1 0.15 18 1 1 0.12

UB = 14.09

2-D Load Formation: Bin Packing1. Initial: Add

containers based on order sequence

2. Re-check: try adding any cont. left out of initial load

3. Add more efficient: replace if more efficient cont. can be added

4. Add extras: insert cont. in any available space

5. Final

Diseconomies of ScaleYellow 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 M

odu

le C

ost

L/U

Tim

e (m

in)

DC

Sp

ace

Uti

l. Household Demand (trips/week)

2 4

Modules per Trip Modules per Trip

10 20 10 20

DC Trip Mod DC Trip Mod DC Trip Mod DC Trip Mod

50 5 0.6 1 1.46 2.27 0.23 9 2.27 3.19 0.16 17 0.73 1.54 0.15 25 1.14 2.05 0.10 50 5 0.8 2 1.29 2.10 0.21 10 1.93 2.84 0.14 18 0.64 1.45 0.15 26 0.96 1.88 0.09

50 10 0.6 3 1.46 2.27 0.23 11 2.27 3.19 0.16 19 1.32 2.13 0.21 27 1.64 2.56 0.13 50 10 0.8 4 1.29 2.10 0.21 12 1.93 2.84 0.14 20 1.32 2.13 0.21 28 1.64 2.56 0.13

100 5 0.6 5 2.51 3.39 0.34 13 4.01 5.02 0.25 21 1.25 2.14 0.21 29 2.01 3.01 0.15 100 5 0.8 6 2.16 3.05 0.30 14 3.32 4.32 0.22 22 1.08 1.97 0.20 30 1.66 2.66 0.13

100 10 0.6 7 2.51 3.39 0.34 15 4.01 5.02 0.25 23 2.12 3.01 0.30 31 2.71 3.71 0.19 100 10 0.8 8 2.16 3.05 0.30 16 3.32 4.32 0.22 24 2.12 3.01 0.30 32 2.71 3.71 0.19

(DC cost in $, DC + vehicle cost = Trip cost in $, Mod = cost per module delivered in $)

Home Delivery Cost Estimate

Available 2016: Starship Technologies

• Started by Skype co-founders• 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 last-mile delivery alternatives.’”

• http://www.engadget.com/2015/11/02/starship-technologies-local-delivery-robot/