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Balancing a trip matrix
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sumAiOi 21361,83333311 32161,59 23271,57142911 766 1399
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sumAiOi 21361,83333311 32161,59 23271,57142911 766 1399 Initial guess
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sumAiOi 21361,83333311 32161,59 23271,57142911 766 1399 Column sum Row sum
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sumAiOi 21361,83333311 32161,59 23271,57142911 766 1399 Desired Column sum Dj Desired Row sum Oi Doubly constrained model
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sumAiOi 21361,83333311 32161,59 23271,57142911 766 1399 Balancing factor
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sumAiOi 21361,83333311 32161,59 23271,57142911 766 1399 Balancing factor 11/6=1.8333
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sumAiOi 21361,83333311 32161,59 23271,57142911 766 1399 Balancing factor 11/6=1.8333 We need to multiply first row with 1.8333
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iteration 1Oi 3,6666671,8333335,511 4,531,599 3,1428574,7142863,14285711 11,309529,54761910,14286 1,1494740,9426430,887324 1399 Applying balancing factor Ai on initial guess, we get a new trip matrix in the first iteration Exactly balanced Row sum
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iteration 1Oi 3,6666671,8333335,511 4,531,599 3,1428574,7142863,14285711 11,309529,54761910,14286 1,1494740,9426430,887324 1399 Applying balancing factor Ai on initial guess, we get a new trip matrix in the first iteration Exactly balanced Row sum Column sum still off
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iteration 1Oi 3,6666671,8333335,511 4,531,599 3,1428574,7142863,14285711 11,309529,54761910,14286 1,1494740,9426430,887324 1399 Applying balancing factor Ai on initial guess, we get a new trip matrix in the first iteration Exactly balanced Row sum Balancing factor Bj
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iteration 1Oi 3,6666671,8333335,511 4,531,599 3,1428574,7142863,14285711 11,309529,54761910,14286 1,1494740,9426430,887324 1399 Applying balancing factor Ai on initial guess, we get a new trip matrix in the first iteration Exactly balanced Row sum Balancing factor Bj 13/11.309=1.149
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iteration 2 sumAiOi 4,2147371,728184,88028210,82321,01633511 5,1726322,827931,3309869,3315480,964479 3,6126324,443892,78873210,845251,01426911 1399 99 Column sum exactly balanced
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iteration 2 sumAiOi 4,2147371,728184,88028210,82321,01633511 5,1726322,827931,3309869,3315480,964479 3,6126324,443892,78873210,845251,01426911 1399 99 Column sum exactly balanced But now Row sum off!
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iteration 2 sumAiOi 4,2147371,728184,88028210,82321,01633511 5,1726322,827931,3309869,3315480,964479 3,6126324,443892,78873210,845251,01426911 1399 99 But now Row sum off! New balancing factors for the rows
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