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25 Nov
2019

FAM Formulation | Good Grade Guarantee!

Tutorial:FAM FormulationCheng-Lung Wu, Tomasz Drabas, Pedram KesharvarzianFAM formulation is summarised as follows:
min Xj2JX i2Fci;jxi;j
(1)
s.t.:X j2Jxi;j = 1 8i 2 F (2)Gk-;j + Xi2FSi;kxi;j = Gk;j 8k 2 M and j 2 J (3)X k2CGk;j ≤ Nj 8j 2 J (4)xi;j 2 f0; 1g 8i 2 F and j 2 J (5)Gk;j 2 Z+ 8k 2 M and j 2 J (6)where:sets:
F
= Set of flights
J
= Set of fleet-types
C
= Set of last-nodes, representing all nodes with aricraftgrounded overnight at an airport in the network
M = Number of nodes in the networkindices:
ij
= Flight index= Fleet-type index
NjSi;k
= Number of available aircraft in fleet-type j= ( +1 if flight i is an arrival at node k
k = Node indexparameters:Ci;k = Cost of assigning fleet-type k to flight i-1 if flight i is a departure flight from node kdecision variables:xi;j = ( 10 if flight otherwise i is assigned to fleet-type j
Gk;j
= Integer decision variable representing numberof aircraft of fleet-type j on ground at node k
1

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