Transportation Management
Operational Networks
Chris Caplice
ESD.260/15.770/1.260 Logistics Systems
Nov 2006
Agenda
Economic vs Traditional Modes
Operational Networks
„
„
„
One to One
One to Many
Many to Many
Example of Approximate Analysis
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Traditional Transport Modes (US)
US Transportation By Mode 2003 (702 $B)
Mode
Trucking
Rail
Intermodal
Pipeline
Air Freight
Barge
2003 revenue ($B)
610
87%
36
5%
8
1%
27
4%
13
2%
8
1%
702
100%
Rail
5%
Intermodal
1%
Pipeline
4%
Air Freight
2%
Trucking
87%
Barge
1%
100%
Trucking By Sub-Mode
90%
80%
70%
Trucking
Rail
Air Freight
Barge
60%
50%
40%
LTL, 10%
Private , 46%
30%
20%
Truckload, 44%
10%
0%
1975
1987
1999
2003
Note that these modes are all technology based –
according to the type of power unit and guideways used.
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The Transportation Product
Four Primary Transportation Components
„
„
„
„
Loading/Unloading
Line-Haul
Local-Routing (Vehicle Routing)
Sorting
Basic Forms of Consolidation
„
„
„
Vehicle
Temporal
Spatial
Driving Influences
„
„
„
Economies of Scale
Economies of Scope (Balance )
Economies of Density
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The Transportation Product
B
B
B
B
B
B
Plant A
Customer B
Loading
Linehaul
Loading/Unloading
„
Linehaul
Key drivers:
„
Key drivers:
Š Number of items
Š Distance
Š Time
Š Balance / Backhaul
Š Stowability (Packaging)
„
Unloading
„
Not always symmetric
Impacted by network
Š Congestion
Š Connectivity
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Regression of Long Haul TL Rates
95% Confidence Limits
Independent
Variable
Coefficient
Value
Lower
Bound
Upper
Bound
(Constant)
116.84
107.57
126.12
Distance
1.10
1.097
1.101
OutBound Flag
9.04
5.48
12.61
Private Fleet Dist
(0.17)
(0.21)
(0.13)
Spot Mkt Dist
0.29
0.26
0.32
Intermodal Dist
(0.29)
(0.30)
(0.29)
Expedited Dist
0.15
0.13
0.16
High Frequency Flag
(72.49)
(78.44)
(66.54)
Monthly Flag
(60.96)
(64.44)
(57.49)
Quarterly Flag
(36.33)
(38.96)
(33.69)
$100M Buy Flag
(19.2840)
(23.85)
(14.71)
Regional Values
XXX
XX
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Explains ~77%
Explains ~ 2%
Explains ~ 7%
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The Transportation Product
C
C
D
B
B
Plant A
Customer B
Vehicle Routing
„
Key drivers:
Š Number/Density of stops
Š Vehicle Capacity
Š Time
„
Customer D
Origin or Destination
Š One to Many
Š Many to One
Š Interleavened
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Customer C
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The Transportation Product
Sorting
Key drivers:
„
Š Stowability (Packaging)
Š Number of items
Š Timing (Banking)
E
From A
D
F
E
F
E
From B
From C
E
E
To D
E
E
E
F
D
F
E
E
F
F
F
D
D
D
E
F
Outbound vehicles
D
D
D
D
D
E
Outbound loading
Inbound unloading
Inbound vehicles
To E
F
F
F
F
To F
Cross-Dock Terminal
Material Adapted from Yossi Sheffi
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The Transportation Product
Four Primary Transportation Components
„
„
„
„
Loading/Unloading
Line-Haul
Local-Routing (Vehicle Routing)
Sorting
Basic Forms of Consolidation
„
„
„
Vehicle
Temporal
Spatial
Driving Influences
„
„
„
Economies of Scale
Economies of Scope (Balance )
Economies of Density
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Economies of Scale
For an individual shipment –
„
„
Captures allocation of fixed costs over many items
Follows lot sizing logic – drives mode selection
Cost per Item
Moving Cost
Holding Cost
vMAX
2vMAX
Shipment Size
Across a network – this is less clear
„
„
„
Volume on all lanes increase in the same proportion
It depends on directionality (mainly direct carriers)
Consolidated carriers have more fixed costs - more terminals
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Economies of Scope (Balance)
Reverse flow mitigates the cost of repositioning.
Strong for direct carriers – but present in all
„
„
Subadditivity - the costs of serving a set of lanes by a single
carrier is lower than the costs of serving it by a group of
carriers
Cost Complementarity - the effect that an additional unit
carried on one lane has on other lanes
BOS
CHI
NYC
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Economies of Density
Strong for Consolidated Carriers
„
Location Density
Š Number of customers per unit area
„
Shipment Density
Š Average number of shipments at a customer location
Š Daily average volume is critical
Which is better?
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Economic Modes
Consolidated Carrier’s Core Activities
Pick up
cycle
Sorting
Line-haul
move
EOL
Delivery
cycle
EOL
Sorting
Line-haul
move
HUB
Sorting
Direct Carrier’s Core Activities
Pick up
cycle
Delivery
Line-haul
move
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Economic Modes
Direct operations (DO)
Consolidated operations (CO)
Bus/rail transit
LTL
Rail
Airlines
Ocean carriers/liner service
Taxi
TL
Unit trains
Charter/private planes
Tramp services
Package delivery
Courier
DO conveyances on CO carriers (sub-consolidation)
Š Rail cars
Š Ocean containers
Š Air “igloos”
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Operational Network (ONW) Structure
One to One
„
Direct Network
One to One
One to One
P
P
D
P
D
P
D
D
One to Many / Many to One
„
„
Direct with Milk Runs
Consolidation within the Vehicle
One to Many
P
D
Pool / Zone Skipping
D
D
D
P
Pool
D
D
P - Pickup Location
D
M21 w/Tranship
P
P
Con
D
P
P
D - Delivery Location
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Operational Network (ONW) Structure
Many to Many
„
No Transhipment Point
Š Direct with Milk Runs
„
M2M Interleavened
Many to Many
P
P
P
P
D
P
D
D
D
D
P
D
With Transhipment Point
Š Direct with DC (Cross Docking)
Š Direct with Milk Runs
Direct w/ DC
P
P
P
P
X-Dock
Direct w/ Milk Runs
D
P
D
D
P
D
P - Pickup Location
X-Dock
P
P
Hub w/ Directs
D
P
D
P
D
D
P
P
D
X-Dock
D
D
D
D - Delivery Location
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Decisions – Contract Type
What type of relationship do you need to establish with
your carriers?
Continuum of relationships from one-off to ownership
„
„
„
„
Ownership of Assets versus Control of Assets
Responsibility for utilization
On-going commitment / responsibilities
Shared Risk/Reward – Flexible contracts
Spot
Market
Alternate
Carriers
Use for random &
distressed traffic
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Core
Carriers
Dedicated
Fleet
Private
Fleet
Use for most reliable
and steady flows
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Solution Approaches for ONW
Math Programming / Algorithmic Approach
„
„
„
Develop detailed objective function and constraints
Requires substantial data
Solve MILP to optimality
Simulation Approach
„
„
„
Develop detailed rules and relationships
Simulate the expected demand patterns
Observe results and rank different scenarios
Approximation Approach
„
„
„
Develop a Total Cost Function that incorporates the relevant
decision variables
Obtain reasonable results with as little information as possible in
order to gain insights
Detailed data can actually make the optimization process harder
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Total Cost Per Item Function
Cost per item = Holding Costs + Moving Costs
= (Inventory Cost) + (Transport Cost + Handling Cost)
Nomenclature
⎛D⎞
⎛Q⎞
TC (Q ) = vD + A ⎜ ⎟ + rv ⎜ ⎟
⎝2⎠
⎝Q⎠
TC (Q )
A
⎛T ⎞
CostPerItem =
= v + + rv ⎜ ⎟
D
Q
⎝2⎠
ShipmentCost = c f + cvQ
c f = cs (1 + ns ) + cd d
cv = cvs + cvd d
ShipmentCost = ⎣⎡ cs (1 + ns ) + cd d ⎦⎤ + ⎡⎣Q ( cvs + cvd d ) ⎤⎦
⎛ 1 + ns ⎞
⎛d ⎞
TransportCPI = cs ⎜
+
c
⎟ d ⎜ Q ⎟ + cvs
Q
⎝
⎠
⎝ ⎠
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A= Fixed order cost ($/shipment)
r= Inventory holding cost ($/yr)
v= Purchase cost ($/item)
Q = Shipment size (items)
T = Shipment frequency (yr) = Q/D
L = Lead time for transport (yr)
cf = Fixed transport cost ($/shipment)
cv = Variable transport cost (#/item)
cs = Fixed cost per stop ($/stop)
cd = Cost per distance ($/distance)
cvd = Marginal cost / item / distance
cvs = Marginal cost / item / stop
ns = Number of delivery stops
© Chris Caplice, MIT
One to One System
Cost per Item
⎛ 1 + ns ⎞
⎛d⎞
⎛T
⎞
TotalCPI = rv ⎜ + L ⎟ + cs ⎜
+ cd ⎜ ⎟ + cvs
⎟
⎝2
⎠
⎝ Q ⎠
⎝Q⎠
rvL
QMAX
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2QMAX
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Shipment Size
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Handling Costs
Handling Costs ($/item)
„
„
„
„
Loading items into boxes, pallets, containers, etc.
If handled individually – linear with each item
If handled in batches – fixed & variable components
Generally subsumed w/in transportation (move) costs as long
as Q>>QhMAX (total shipment size is greater than pallet)
HandlingCost = c fh + cvhQh
c fh
⎛
MovementCost = c f + ⎜ cv + cvh +
QhMAX
⎝
⎞
⎟Q
⎠
c fh ⎤
⎛ 1 + ns ⎞
⎛d⎞ ⎡
Transport & Handling = cs ⎜
+ cd ⎜ ⎟ + ⎢ cvs + cvh +
⎥
⎟
Q
Q
Q
⎝
⎠
⎝ ⎠ ⎣
hMAX ⎦
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One to Many System
Single Distribution Center:
• Products originate from one origin
• Products are demanded at many destinations
• All destinations are within a specified Service Region
• Ignore inventory (service standards given)
Service Region
Assumptions:
• Vehicles are homogenous
• Same capacity, QMAX
• Fleet size is constant
Origin
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Destinations
Figure by MIT OCW.
Based on Hernandez MLOG Thesis 2003
© Chris Caplice, MIT
One to Many System
Finding the estimated total distance:
• Divide the Service Region into Delivery Districts
• Estimate the distance required to service each district
Delivery
District
Service
Region
Origin
Destinations
Figure by MIT OCW.
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Based on Hernandez MLOG Thesis 2003
© Chris Caplice, MIT
One to Many System
Local Delivery
Back Haul
Line Haul
Figure by MIT OCW.
Route to serve a specific district:
• Line haul from origin to the 1st customer in the district
• Local delivery from 1st to last customer in the district
• Back haul (empty) from the last customer to the origin
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Based on Hernandez MLOG Thesis 2003
© Chris Caplice, MIT
An Aside: Routing & Scheduling
Problem:
„
„
How do I route vehicle(s) from one or many origins to one or
many destinations at a minimum cost?
A HUGE literature and area of research
Traveling Salesman Problem / Vehicle Routing Problem
„
„
„
„
„
One origin, many destinations, sequential stops
Stops may require delivery & pick up
Vehicles have different capacity (capacitated)
Stops have time windows
Driving rules restricting length of tour, time, number of stops
Discussed next lecture – Dr. Edgar Blanco
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© Chris Caplice, MIT
One to Many System
Find the estimated distance for each tour, dTOUR
„
„
Capacitated Vehicle Routing Problem (VRP)
Cluster-first, Route-second Heuristic
dTOUR ≈ 2d LineHaul + d Local
dLineHaul = Distance from origin to center of gravity (centroid) of delivery district
dLocal = Local delivery between c customers in district (TSP)
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One to Many System
What can we say about the expected TSP
distance to cover n stops in district of area X?
„
Hard bound and some network specific estimates:
E [ d TSP ] ≤ 1.15 nX
E [ d TSP ] ≈ k nX
For n>25 over Euclidean space, k=.7124
For grid (Manhattan Metric), k=.7650
n
δ=
X
Density, δ, number of stops per area
Average distance per stop, dstop
Source: Larson & Odoni Urban Operations Research 1981
http://web.mit.edu/urban_or_book/www/book/index.html, see section 3.87
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d stop
d TSP
nX
k
=
=k⋅
=
n
n
δ
© Chris Caplice, MIT
One to Many System
Length of local tours
„
„
Number of customer stops, c, times dstop over entire
region
Exploits property of TSP being sub-divided –
Š TSP of disjoint sub-regions ≥ TSP over entire region
Delivery District
Traveling salesman
tours in the subregions
Connections
between subregions
Figure by MIT OCW.
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One to Many System
Finding the total distance traveled on all, l, tours:
E [ dTOUR ] = 2d LineHaul +
ck
δ
E [ d AllTours ] = lE [ dTOUR ] = 2ld LineHaul +
nk
δ
Minimize number of tours by maximizing vehicle capacity
⎡ D ⎤
l=⎢
⎥
Q
⎣ MAX ⎦
+
+
⎡ D ⎤
nk
E [ d AllTours ] = 2 ⎢
d LineHaul +
⎥
δ
⎣ QMAX ⎦
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[x]+ is lowest integer value greater
than x – a step function
Estimate this with continuous
function:
E([x]+ ) ~ E(x) + ½
© Chris Caplice, MIT
One to Many System
So that expected distance is:
E [n] k
⎡ E [ D] 1 ⎤
E [ d AllTours ] = 2 ⎢
+ ⎥ d LineHaul +
δ
⎣ QMAX 2 ⎦
Note that if each delivery district has a different density,
then:
E [ ni ]
⎡ E [ Di ] 1 ⎤
+ ⎥ d LineHauli + k ∑ i
E [ d AllTours ] = 2∑ i ⎢
δi
⎣ QMAX 2 ⎦
For identical districts, the transportation cost becomes:
⎛ ⎡ E [ D] 1 ⎤
E [ D] 1 ⎤
E [n] k ⎞
⎡
TransportCost = cs ⎢ E [ n ] +
+ ⎥ + cd ⎜ 2 ⎢
+ ⎥ d LineHaul +
⎟ + cvs E [ D ]
QMAX 2 ⎦
δ ⎠
⎣
⎝ ⎣ QMAX 2 ⎦
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One to Many System
Fleet Size
„
„
Find minimum number of vehicles required, M
Base on, W, amount of required work time
Š
Š
Š
Š
Š
tw = available worktime for each vehicle per period
s = average vehicle speed
l = number of shipments per period
tl =loading time per shipment
ts = unloading time per stop
d AllTours
Mtw ≥ W =
+ ltl + nts
s
⎛ k
⎞
⎛ 2d LineHaul
⎞ ⎡ E [ D] 1 ⎤
W =⎜
+ tl ⎟ ⎢
+ ⎥ + E [n] ⎜
+ ts ⎟
s
⎝
⎠ ⎣ QMAX 2 ⎦
⎝s δ
⎠
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One to Many System
Note that W is a linear combination of two random variables, n
and D
E[aX + bY ] = aE[ X ] + bE[Y ]
Var[aX + bY ] = a 2Var[ X ] + b 2Var[Y ] + 2abCov[ X , Y ]
Substituting in, we can find E[W] and Var[W]
⎛ 2d
a = ⎜ LineHaul
s
⎝
Given a service level, CSL
P[W<Mtw]=CSL Thus,
⎞⎡ 1 ⎤
+ tl ⎟ ⎢
⎥
Q
⎠ ⎣ MAX ⎦
⎛ k
⎞
+ ts ⎟
b=⎜
⎝s δ
⎠
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M= (E[W] + k(CSL) StDev[W])/tw
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© Chris Caplice, MIT
Questions?