1. UPS Optimizes Its Air Network
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2. Background
UPS is the world’s leading package-delivery company, carrying an average of more than 14 million packages daily to nearly 8 (1.8 millions pickup; 6.1 millions delivery) million customers in over 200 countries and territories. It owns 3,700 Stores, 1,500 mailboxes, 1,000 UPS service center, and 40,000 UPS Drop Boxes. 384 thousands of employees are working in it. (328 thousands in USA; 56 thousands in other areas)

3. UPS Airlines
With 256 aircraft and 78 more on order, UPS Airlines, a wholly owned subsidiary of UPS, is the 11th largest commercial airline in the world and the ninth largest in the United States. The daily flights in USA are 1,082, and 1,140 for international routes. The delivery equipments involve 88,000 transportations, trucks, trailers, and motorcycles
Hubs: Louisville, Ky, USA (Hub center)－local America
Bonn, Germany－Europe
Taipei; Singapore－Asia
Hamilton, Canada－N. America

4. Delivery Services 1 Same-day-air: SonicAir
2 Next-day-air: Like the examples of this report
3 Second day air: No timely restrict
Each aircraft transports its packages directly to an air hub or stops at one intermediate airport to pick up additional packages.
Each aircraft positioned at the air hub until it is fully loaded for its delivery route.
The aircraft fly to at most two airports.

5. UPS network of a next-day-air service
A two-leg pickup route runs from airport 1 to airport 2 to the hub and a two-leg delivery route runs from the hub to airport 3 to airport 1

6. Next-day-air package flows
1 Origin → Ground center (truck)
2 Ground center → Airport (truck)
3 Airport → Hub (airplane)
4 Hub → Airport (airplane)
5 Airport → Ground center (truck)
6 Ground center → Destination (truck)

7. VOLCANO of UPS
The team from UPS and MIT developed and implemented “Volume, Location, and Aircraft Network Optimizer,” an optimization-based planning system that is transforming the planning and business processes within UPS Airlines.
This innovative modeling and algorithmic approach to an intractable network-design problem has been a tremendous success within the airline and the academic community.
By this technique, we simultaneously determine the minimum-cost set of routes, fleet assignment, and package flows.

8. An Example of two-location network Conventional formulations
The LP feasible solution for the examples will be:
of aircraft type 1
2 0.5 of aircraft type 2
This two-location network consists of an airport, g, and an air hub, h. The objective is to move 5,000 packages from g to h using one of two aircraft types with different capacities

9. An Example of two-location network Composite-Variable formulations
The LP feasible solution for the examples:
of aircraft type 1
2 0.5 of aircraft type 2
is not feasible because the composite variable is defined as 2 of aircraft type 1 or 1 of aircraft type 2
With composite-variable formulations, we define new variables, called composites, which combine the original aircraft and package-flow decision variables to provide sufficient

10. The composite-variable approach
The composite-variable approach yields a set-covering formulation with appealing computational properties. It requires preparatory work to generate the feasible set of composite variables.

11. Conventional Model for next-day-air network

12. Conventional Model for next-day-air network
Demand ≦
Capacity * number of aircraft
The summation of fraction of commodity k

13. Conventional Model for next-day-air network
The amount of packages through h ≦ capacity of h
The number of planes for pickup and delivery should be the same

14. Conventional Model for next-day-air network
The number of assigned planes have to be less than the number of this type of plane
Total number of planes to the hub must be less than the number of aircraft that can land at hub h

15. Simple Example (1) →

16. Composite-Variable model for next-day-air network
Composite variable (c) =
number of aircrafts of each type + package-flow
We must find the composite first to implement the model

17. Composite-Variable model for next-day-air network
All the paths from airports and hubs can not be wholly infeasible
All the paths from hubs and airports can not be wholly infeasible

18. Composite-Variable model for next-day-air network
The number of planes for pickup and delivery should be the same

19. Composite-Variable model for next-day-air network
The number of assigned planes have to be less than the number of this type of plane
Total number of planes to the hub must be less than the number of aircraft that can land at hub h

20. Simple Example (2) →
C has been determined before the formulation. At least 2 of type 1 or at least 1 of type 2

21. Easy Test Results
We obtain similar results when planning the entire next-day-air network. One scenario tested during the development phase included 101 airports, seven of which were hubs, and 160 aircraft available from seven fleet types. We conservatively estimated the nightly volume at packages on the pickup side and packages on the delivery side.

22. Complicated Examples 1 3 2

23. Conclusions The goal of formulations → minimize the cost
The constraints are:
1 Total demand ≦ total capacity of the hub
2 Demand of each route or path ≦ capacity of a fleet
3 The amount of aircrafts of an airport or hub is steady
4 Number of planes to hubs ≦ the apron capacity of hubs
5 Number of assigned planes ≦ number of standby planes
6 Demand on the path ≦ demand on the route
UPS has saved over $87 million from 2000 through 2002, and planners estimate UPS’s savings over the next decade at $189 million.

24. References Barnhart, Cynthia, Niranjan Krishnan, Daeki Kim, Keith A.
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