MTH601 Quiz 3 Solution and Discussion

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While solving a Transportation problem by Vogel’s approximation method, if the row has two elements of the same magnitude say ‘x’ as the smallest element then the opportunity(penalty) cost of that row or column is ----------. MTH601

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For calculating the penalty cost of a row in Vogel’s approximation method, if the smallest element is ‘3’ and other elements are 3, 4, 5 then which of the following will be taken as next highest?

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If the cost matrix in an Assignment problem is not square then which the following modification will be made to balance the given problem?

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In the Vogel’s approximation Method for solving a Transportation problem, Penalty measure for any row or column, is given by which of the following?

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The North – West Corner Rule

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The solution of an Assignment problem can be arrived by using which of the following method?

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For North West Corner method, in the first row and first column, each resource and sink contain ‘5’ units; then after allocating the appropriate amount ‘x11’ in the cell (1,1), in which of the following cell the next allocation will be zero?

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In North West Corner method, the first step after choosing the appropriate cell in 1st row, we allocate -------------so that the capacity of first row or first column is exhausted.
as much as possible

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The Transportation Problem is one of the sub-class of -------------.

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The column, which is introduced in the matrix to balance an unbalanced Transportation problem, is known as-------

dummy column

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When the total allocations in a transportation model of m*n size is not equals to “m + n – 1”, the situation is known as:

Unbalanced situation

In North West Corner method, the first step after choosing the appropriate cell in 1st row, we allocate -------------so that the capacity of first row or first column is exhausted.
as much as possible

For an unbalanced Transportation problem, if the total demand is MORE than total supply then which of the following is true in order to balance the problem?
a dummy sink…

In the assignment problem, the decision variable ‘xij’ can attain which of the following value?
Only ‘1’

The row, which is introduced in the matrix to balance an unbalnced Transportation problem, is known as ----------.
dummy row (confirm)

The solution of a transportation problem with m rows (supplies) and n (destinations) is feasible if numbers of positive allocations are
m+n-1 (confirm)

While solving an Assignment problem by Hungarian’s method, in the modified cost matrix if the minimum number of horizontal and vertical lines to cover zeros are not equal to the number of rows (or columns), then which of the following operation is done?
Subtract smallest element of uncovered rows from all other elements of uncovered cells

The amounts shipped from a dummy source represent shortages at the receiving destinations
True (confirm)

In the Vogel’s approximation Method for solving a Transportation problem, Penalty measure for any row or column, is given by which of the following?
Difference between the smallest unit cost to the next smallest cost in the same row(column)

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1_ If a balanced Transportation problem with ‘m’ sources and ‘n’ sinks then degeneracy will arise only if there are less than ---------- independent allocations in the solution.

m–n–1
(In this question all options are in (-) negative range like m–n–1 , m–n–2 m–n–3, m–n–4 )
and there was no one true. correct was m+n–1 .however i select m–n–1 ).

2_In a Transportation Problem, the objective function ’Z’ gives ----------.
Total Cost of transportation

3_Which of the following type of Elementary matrix operations are performed while solving an Assignment problem by Hungarian’s method?
Column operations (not sure)

4_For North West Corner method, in the first row and first column, resource and sink contain ‘5’ and ‘7’ units respectively; then after allocating the appropriate amount ‘x11’ in the cell (1,1), we will move towards which of the following cell?
missed

5_To convert an Assignment problem into a maximization problem, which of the following operations would have to apply?
Deduct all elements of the row from highest element in that row

6_In the assignment problem, the decision variable ‘xij’ can attain which of the following value?
Only ‘1’
Ref:
Pg 97
Optimization for Decision Making: Linear and Quadratic Models
By Katta G Murty
https://books.google.com.pk/books?id=HWZXs1rkVxEC&pg=PA97&l…
7_In

Hungarian method of solving assignment problem, the cost matrix is obtained by----------.
subtracting the smallest element from all other elements of the row.

8_If the total demand is equal to total supply as per requirement of a balanced transportation problem i-e “a1+a2±–+an = b1+b2±–+bn” then which of the following is true?
“a1=b1, a2=b2,—, an=bn” is necessarily implied (not sure)

9_In case the cost elements of one or two cells are not given in the problem, it means that ---------
the routes connected by those cells are not available

10_ If the cost matrix in an Assignment problem is not square then which the following modification will be made to balance the given problem?
Add a dummy row(column) with negative cost elements (not sure)

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In the assignment problem, the cost matrix is ------------. MTH601
rectangular

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In the Vogel’s approximation Method for solving a Transportation problem, Penalty measure for any row or column, is given by which of the following? MTH601
Difference between the largest unit cost to the next largest cost in the same row(column)