APM261: Quiz 9. Transportation Problems

Quiz 9. Transportation Problems

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Each question has only one correct answer. The results of the quiz do not affect the final marks.

1: What is the difference between minimal cost network flows and transportation problems?

The minimal cost network flows are special cases of transportation problems
The transportation problems are special cases of the minimal cost network flows
There is no difference
The transportation problems are formulated in terms of tableaus, while the minimal cost network flows are formulated in terms of graphs

2: Consider the following minimal cost network flow:

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The supply vector b has the values:

b₁ = 2, b₂ = -1, b₃ = 2, b₄ = -3

The cost coefficients are

c₁₂ = 1, c₃₂ = 3, c₁₄ = 10
c₂₄ = 1, c₃₄ = 5

What is the status of the following distribution?

x₁₂ = x₃₄ = 0
x₃₂ = x₁₄ = 2, x₂₄ = 1

The distribution is optimal and final
The route 3->4 should be used with the distribution: x₁₂ = x₂₄ = 0, x₁₄ = 2, and x₃₂ = x₃₄ = 1
The route 1->2 should be used with the distribution: x₁₄ = x₃₄ = 0, x₁₂ = x₃₂ = 2, and x₂₄ = 3
The distribution is not feasible

3-4: Cost matrix C for a transportation problem is given by

( 2 3 6 )
C = ( 4 3 1 )
( 1 2 3 )

Find the missing entries A and B in the non-degenerate transportation tableau:

	stock 1	stock 2	stock 3	supply	dual
plant 1	3	5	0	8	0
plant 2	0	0	6	6	-3
plant 3	0	1	1	2	`B`
demand	3	`A`	7
dual	2	3	4

A = 4
A = 5
A = 6
A = 10 B = -1
B = 0
B = 1
B = 2

5: The cutting plane method is designed for ...

Developing another simplex algorithm that combines the primal and dual simplex methods
Solving zero-one programming problems
Eliminating integer optimal solutions from the feasible space of linear programming problems
Eliminating non-integer optimal solutions from the feasible space of linear programming problems

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