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L13_10 - ESI 6314 Deterministic Methods in Operations...

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1/21 ESI 6314 Deterministic Methods in Operations Research Lecture Notes University of Florida Department of Industrial and Systems Engineering / REEF

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2/21 Solving transportation problems (TPs) A property of TPs : If a set of decision variables ( x ij ’s) satisfy all but one constraint, the values for x ij ’s will satisfy that remaining constraint automatically. We will consider three basic solution methods: 1 Northwest Corner Method 2 Minimum Cost Method 3 Vogel’s Method
3/21 Northwest Corner (NWC) Method To ﬁnd the bfs by the NWC method: ± Begin in the upper left (northwest) corner of the transportation tableau and set x 11 as large as possible: x 11 = min { d 1 , s 1 } ± Cross out the ﬁrst column (if d 1 s 1 ) or the ﬁrst row (if d 1 s 1 ), set d 1 = d 1 - x 11 , s 1 = s 1 - x 11 , and repeat the previous step. ± Stop when all cells are crossed out.

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4/21 Northwest Corner Method Using the NWC method, we can set x 11 = 3 (meaning demand of demand point 1 is satisﬁed by supply point 1).
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L13_10 - ESI 6314 Deterministic Methods in Operations...

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