UPS Optimizes Its Air Network 937814 林蒼威. Background UPS is the world’s leading package-delivery company, carrying an average of more than 14 million.

UPS Optimizes Its Air Network

937814 林蒼威

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)

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

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.

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

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)

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.

An Example of two-location network

Conventional formulations

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

The LP feasible solution for the examples will be:

1 1.25 of aircraft type 1


An Example of two-location network

Composite-Variable formulations

With composite-variable formulations, we define new variables, called composites, which combine the original aircraft and package-flow decision variables to provide sufficient

The LP feasible solution for the examples:



is not feasible because the composite variable is defined as 2 of aircraft type 1 or 1 of aircraft type 2

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.

Conventional Model for next-day-air network


Demand ≦

Capacity * number of aircraft

The summation of fraction of commodity k


The amount of packages through h capacity of h≦

The number of planes for pickup and delivery should be the same


Total number of planes to the hub must be less than the number of aircraft that can land at hub h

The number of assigned planes have to be less than the number of this type of plane

Simple Example (1)

→

21 15001000min rr yy

21 1000040005000.. rr yyts

he5000

22

11

ny

ny

r

r

hfr ay 0kpx

Nyy fr

fr ,0

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


All the paths from airports and hubs can not be wholly infeasible

All the paths from hubs and airports can not be wholly infeasible


The number of planes for pickup and delivery should be the same


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

Simple Example (2)

→

21 15001000min rr yy

C has been determined before the formulation. At least 2 of type 1 or at least 1 of type 2

fcfc nvr

hc－

fc avr h )(

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 926268 packages on the pickup side and 967172 packages on the delivery side.

Complicated Examples

1

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.

References

Barnhart, Cynthia, Niranjan Krishnan, Daeki Kim, Keith A. Ware. 2002b. Network design for express shipment delivery. Computer Optimal Application. 21(3) 239–262.Crainic, Teodor G. 2000. Service network design in freight transportation. European Journal of Operation Research 122(2) 272–288.Kim, Daeki, C. Barnhart, Keith A. Ware, G. Reinhardt. 1999. Multimodal express package delivery: A service network design approach. Transportation Science 33(4) 391–407.Magnanti, Thomas L., Richard T. Wong. 1984. Network design and transportation planning: Models and algorithms. Transportation Science 18(1) 1–55.

UPS Optimizes Its Air Network 937814 林蒼威. Background UPS is the world’s leading package-delivery company, carrying an average of more than 14 million.

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