Balancing a trip matrix. sumAiOi 21361,83333311 32161,59 23271,57142911 766 1399.

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Presentation transcript:

Balancing a trip matrix

sumAiOi 21361, , ,

sumAiOi 21361, , , Initial guess

sumAiOi 21361, , , Column sum Row sum

sumAiOi 21361, , , Desired Column sum Dj Desired Row sum Oi Doubly constrained model

sumAiOi 21361, , , Balancing factor

sumAiOi 21361, , , Balancing factor 11/6=1.8333

sumAiOi 21361, , , Balancing factor 11/6= We need to multiply first row with

iteration 1Oi 3, , ,511 4,531,599 3, , , ,309529, , , , , Applying balancing factor Ai on initial guess, we get a new trip matrix in the first iteration Exactly balanced Row sum

iteration 1Oi 3, , ,511 4,531,599 3, , , ,309529, , , , , 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

iteration 1Oi 3, , ,511 4,531,599 3, , , ,309529, , , , , Applying balancing factor Ai on initial guess, we get a new trip matrix in the first iteration Exactly balanced Row sum Balancing factor Bj

iteration 1Oi 3, , ,511 4,531,599 3, , , ,309529, , , , , 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

iteration 2 sumAiOi 4, ,728184, ,82321, , ,827931, , , , ,443892, ,845251, Column sum exactly balanced

iteration 2 sumAiOi 4, ,728184, ,82321, , ,827931, , , , ,443892, ,845251, Column sum exactly balanced But now Row sum off!

iteration 2 sumAiOi 4, ,728184, ,82321, , ,827931, , , , ,443892, ,845251, But now Row sum off! New balancing factors for the rows