application of linear programming in operations management

Application of Linear Programming in

“Operations Management”

Sachin Soni, MBA, BITS Pilani

A Mixed-Integer Programming

Approach to Air Cargo Fleet Planning

Roy E. Marsten, Michael R. MullerManagement Science, Vol.26, No.11 (Nov. 1980), pp. 1096-1107

Institute for Operations Research and the Management Sciences (INFORMS)

The Approach

The Flying Tiger – A cargo airline carrier company

Addressed two problems: Design of the Service Network and Selection and Deployment of the aircraft fleet

A Cargo Airline is not constrained by passenger routes and schedules

Fast delivery is the existence of a cargo airline company

Assumptions

The Context

Suppose the airline is servicing n cities Then the no. of pairs would be n(n-1) The Simplest network design would be having n(n-1)/2 nodes. Which very expensive The reasonable design is to have a HUB where all the bags are

sorted into n piles to reach one of the n destinations respectively. (used by FedEx)

HUB

City 1

City 2

City 3

City 4

City 5

City 6

City 7

Single Hub Spider Graph

11

Formulation of Single Hub Spider Graph

Heavy traffic between major cities should not pass through intermediate hubs (to avoid delay). Single hub model was meant for medium sized cities as overnight freight can be transferred.

The Issue with the model

Therefore there should be: More than one hub Major cities should be made hub for domestic

spiders so as to help in overnight transit of freight amongst major cities.

A round trip for each route on the graph. Change of cargo only at hubs

Hence

Hub 1

City 1

City 2City 4

City 3

Multiple Hub Model

Hub 2

City 5

City 8

City 7

City 6

Formulation of Multiple Hub Model

The Objective Function:

The Constraints

where:

Thank You