Transportation

1
Transportation

• Mode Selection
• Route Selection
• Shortest Path
• Minimum Spanning Tree
• Transportation
• Assignment
• TSP
• Route Sequencing
• Tanker Scheduling

2
Mode Selection

• Ship
• Rail
• Truck
• Plane...

Faster
Cheaper
More Variable
3
Mode that minimizes Total Cost

• Transportation Cost
• Inventory Costs
• Source
• Pipeline
• Destination - including safety stock

4
Costs

• Transportation Cost
• Cost per unit Units
• Cost per unit
• /CWT (based on origin, destination, freight,
  weight)
• /Time (leased, dedicated transportation)

5
Inventory

• At the plant
• 1/2 cycle quantity
• At the warehouse
• 1/2 cycle quantity
• Safety stock depends on lead time variability
• In the pipeline
• Annual Volume Days in Transit
• Days per year

6
Example (page 187)
7
Multi-Modal Systems

• Ship from Japan to Los Angeles
• Rail from Los Angeles to Terminals
• Truck from Terminals to Dealerships
• Where to change mode?
• How many channels to operate?

8
Route Selection

• Getting From A to B
• Underlying Network
• Roads
• Airports
• Telecommunication links
• Costs of using each link
• Find the cheapest (shortest) path

9
Example (page 192)
I
84
E
B
84
90
A
132
66
138
120
C
126
90
H
F
60
348
126
156
132
48
J
150
48
D
G
10
Shortest Path Model
11
Applicability

• Single Origin
• Single Destination
• No requirement to visit intermediate nodes
• No negative cycles

12
Tree of Shortest Paths

• Find shortest paths from Origin to each node
• Send n-1 units from origin
• Get 1 unit to each destination

13
Shortest Path Problem
14
Minimum Spanning Tree

• Find the cheapest total cost of edges required to
  tie all the nodes together

I
84
E
B
84
90
A
132
66
138
120
C
126
90
H
F
60
348
126
156
132
48
J
150
48
D
G
15
Greedy Algorithm

• Consider links from cheapest to most expensive
• Add a link if it does not create a cycle with
  already chosen links
• Reject the link if it creates a cycle.

16
Whats the difference

• Shortest Path Problem
• Riders version
• Consider the number of riders who will use it
• Spanning Tree Problem
• Builders version
• Consider only the cost of construction

17
Transportation Problem

• Sources with limited supply
• Destinations with requirements
• Cost proportional to volume
• Multiple sourcing allowed
• Example Regal Company (Tools)

18
Special Case

• Assignment Problem
• Supply at each source 1
• Requirement at each destination 1
• Match up suppliers with destinations
• Hows this different from single sourcing
• Assigning workers to tasks

19
Application

• Truckload shipping
• Loads waiting at customers
• Trucks sitting at locations
• Which truck should handle which load?
• No concern for what to do after that.
• What are sources
• What are destinations
• What are costs?

20
Traveling Salesman Problem

• Vehicle at depot
• Customers to be served (visited)
• Vehicle must visit all and return to depot
• Minimize travel cost

21
Example

• Full Service Business
• Driver at Service Center
• Assigned vending machines to visit
• What order should he visit to minimize the time
  to complete the work and get back to the depot?

22
Extensions

• If the customers involve transportation
• Customers truck load shipments
• If more than one salesman involved
• Construct routes for the 7 drivers at the North
  Metro Service center
• If the vehicle has capacity
• LTL deliveries
• If we intersperse pickups and deliveries
• If there are time windows on service

23
Basic TSP

• Data issues
• Estimate distance by location
• Calculate point to point distances
• Calculate point to point costs

24
Heuristics

• Cluster first Route Second
• Build delivery zones with approximately equal
  work.
• Route a vehicle in each zone
• Clustering Approaches
• Assign most distant blocks first
• Sweep
• Space-filling curve

25
Space-Filling Curve

• Each point (X,Y) on the map
• Express X string of 0s and 1s
• X 16.5 10000.10
• 12402302202102012-1
  02-2
• Express Y string of 0s and 1s
• Y 9.75 01001.11
• 02412302202112012-1
  12-2
• Space Filling Number - interleave bits
• ?(X,Y) 1001000001.1101

26
Properties

• Every pair (X,Y) has a unique point ?(X,Y)
• Every point on the line corresponds to a single
  point (X,Y)
• If ?(X,Y) and ?(X, Y) are close together, (X,Y)
  and (X,Y) tend to be close together.

27
Clustering

• Compute ?(X,Y) for each customer
• Sort the customers by their ? values
• To build N routes
• Give first 1/Nth of customers to first route
• Give second 1/Nth of customers to second route
• ...

28
Routing

• Each route visits the customers in order of their
  ? values.
• ? defines a route on the plane that visits every
  point. We visit the customers in the same order
  as that route

29
Route First

• Build a single large route
• Assign each vehicle a segment of the route

30
Routing Heuristics

• Space-Filling Curve
• Clarke-Wright Savings
• Nearest Neighbor
• Nearest Insertion
• Farthest Insertion
• 2-interchange

31
2-Interchange
32
2-Interchange
33
2-Interchange
34
2-Interchange
35
Route Sequencing
36
Tanker Scheduling
37
Consolidation

• Cross docking
• Multi-stop shipments
• Larger Orders
• Delay shipments
• Consolidate Production