transportation_lecture

transportation_lecture - FORMULATING TRANSPORTATION...

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FORMULATING TRANSPORTATION PROBLEMS An electric company has three plants that supply four cities. Supply demand data follow: To From City 1 City 2 City 3 City 4 Supply Plant 1 $8 $6 $10 $9 35 Plant 2 $9 $12 $13 $7 50 Plant 3 $14 $9 $16 $5 40 Demand 45 20 30 30 Saigal (U of M) IOE 310 1 / 13
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THE MODEL Decision Variables: x i , j = number of (million) KWH produced at plant i and shipped to City j . The model: Constraints: x 11 + x 12 + x 13 + x 14 35 (Supply Constraints) x 21 + x 22 + x 23 + x 24 50 x 31 + x 32 + x 33 + x 34 40 x 11 + x 21 + x 31 45 (Demand Constraints) x 12 + x 22 + x 32 20 x 13 + x 23 + x 33 30 x 14 + x 24 + x 34 30 Objective Function: min z = 8 x 11 + 6 x 12 + 10 x 13 + 9 x 14 + 9 x 21 + 12 x 22 + 13 x 23 + 7 x 24 + 14 x 31 + 9 x 32 + 16 x 33 + 5 x 34 . Non-negativity: x 0 for all i = 1 , ··· , 3 and j = 1 , , 4. Saigal (U of M) IOE 310 2 / 13
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A SMALL EXAMPLE x 11 x 12 x 13 x 21 x 22 x 23 x 31 x 32 x 33 1 1 1 = s 1 1 1 1 = s 2 1 1 1 = s 3 1 1 1 = d 1 1 1 1 = d 2 1 1 1 = d 3 Each column has exactly two non-zeros. Adding all supply constraints generates the same equation as adding all demand constraints.
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transportation_lecture - FORMULATING TRANSPORTATION...

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