application of linear programming in operations management
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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