lec4_mcfs_linear_and_integer_2003

lec4_mcfs_linear_and_integer_2003 - 1 .206J/16.77J/ESD.215J...

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Unformatted text preview: 1 .206J/16.77J/ESD.215J Airline Schedule Planning Cynthia Barnhart Spring 2003 1.206J/16.77J/ESD.215J Airline Schedule Planning: Multi- commodity Flows Outline Applications Problem definition Formulations Solutions Computational results Integer multi-commodity network flow problems Integer multi-commodity network flow solutions Branch-and-price: combination of branch-and-bound and column generation Results Application I Package flow problem (express package delivery operation) Shipments have specific origins and destinations and must be routed over a transportation network Each set of packages with a common origin- destination pair is called a commodity Time windows (availability and delivery time) associated with packages The objective might be to minimize total costs, find a feasible flow, ... Application II Passenger mix problem Given a fixed schedule of flights, a fixed fleet assignment and a set of customer demands for air travel service on this fleeted schedule, the airline's objective is to maximize revenues by accommodating as many high fare passengers as possible For some flights, demand exceeds seat supply and passengers must be spilled to other itineraries of either the same or another airline Application III Message routing problem In a telecommunications or computer network, requirements exist for transmission lines and message requests, or commodities. The problem is to route the messages from their origins to their respective destinations at minimum cost MCF Networks Set of nodes Each node associated with the supply of or demand for commodities Set of arcs Cost per unit commodity flow Capacity limiting the total flow of all commodities and/ or the flow of individual commodities MCF Commodity Definitions A commodity may originate at a subset of nodes in the network and be destined for another subset of nodes A commodity may originate at a single node and be destined for a subset of the nodes A commodity may originate at a single node and be destined for a single node MCF Objectives Flow the commodities through the networks from their respective origins to their respective destinations at minimum cost Expressed as distance, money, time, etc. Ahuja, Magnanti and Orlin (1993)-- survey of multi-commodity flow models and solution procedures MCF Problem Formulations -- Linear Programs Network flow problems Capacity constraints limit flow of individual commodities Conservation of flow constraints ensure flow balance for individual commodities...
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lec4_mcfs_linear_and_integer_2003 - 1 .206J/16.77J/ESD.215J...

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