transportation_lecture_1

transportation_lecture_1 - SENSITIVITY ANALYSIS TRANS...

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SENSITIVITY ANALYSIS TRANS PROBLEM I Changing the obj coeff of a nonbasic variable. Changing the obj coeff of a basic variable. Increasing a single supply by Δ and a single demand by Δ. Saigal (U of M) IOE 310 1 / 14

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THE OPTIMUM TABLEAU I v j = 6 6 10 2 8 6 10 9 u 1 = 0 10 25 9 12 13 7 u 2 = 3 45 5 14 9 16 5 u 3 = 3 10 30 Saigal (U of M) IOE 310 2 / 14
OBJ COEFF OF NON-BASIC VAR I Since the RHS remains unchanged, the u i s and v j s will not change. Also, c T BV B - 1 is also not changed. The change allowed is ¯ c ij . Saigal (U of M) IOE 310 3 / 14

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OBJ COEF OF BASIC VAR I Now c T BV B - 1 changes, so we need to re-calculate u i s and v j s. Change c 13 from 10 to 10+Δ. Saigal (U of M) IOE 310 4 / 14
INCREASE s i AND d j BY Δ I If x ij is a basic variable, increase the value of this variable by Δ. If x ij is a non-basic variable, find loop. Increase cell in row i by Δ and adjust along loop. Saigal (U of M) IOE 310 5 / 14

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ASSIGNMENT PROBLEM I An Example: A company has purchased 3 new machines of different types that they need to install in a factory. They have identified 4 locations for these three
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