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12th Business Maths Monthly Test - 1 ( Operations Research )

MABS Institution

12th Business Maths Monthly Test - 1 ( Operations Research )-Aug 2020

Time : 2.30 Hours

Part - A

Multiple Choice Question - Answer All Question

In a non – degenerate solution number of allocations is

Equal to m+n–1
Equal to m+n+1
Not equal to m+n–1
Not equal to m+n+1

The transportation problem is said to be unbalanced if _________

Total supply ≠ Total demand
Total supply = Total demand
m = n
m+n–1

Decision theory is concerned with

analysis of information that is available
decision making under certainty
selecting optimal decisions in sequential problem
All of the above

A type of decision –making environment is

certainty
uncertainty
risk
all of the above

The purpose of a dummy row or column in an assignment problem is to

prevent a solution from becoming degenerate
balance between total activities and total resources
provide a means of representing a dummy problem
none of the above

North-West Corner refers to ________

top left corner
top right corner
bottom right corner
bottom left corner

Number of basic allocation in any row or column in an assignment problem can be

Exactly one
at least one
at most one
none of these

Solution for transportation problem using __________method is nearer to an optimal solution.

NWCM
LCM
VAM
Row Minima

The Penalty in VAM represents difference between the first ________

Two largest costs
Largest and Smallest costs
Smallest two costs
None of these

In an assignment problem the value of decision variable x_ij is _________

1
0
1 or 0
none of them

If number of sources is not equal to number of destinations, the assignment problem is called____________

balanced
unsymmetric
symmetric
unbalanced

The solution for an assignment problem is optimal if

each row and each column has no assignment
each row and each column has atleast one assignment
each row and each column has atmost one assignment
each row and each column has exactly one assignment

In an assignment problem involving four workers and three jobs, total number of assignments possible are

4
3
7
12

Part - B

Generic 2 - Answer All Question

A car hire company has one car at each of five depots a,b,c,d and e. A customer in each of the fine towers A,B,C,D and E requires a car. The distance (in miles) between the depots (origins) and the towers(destinations) where the customers are given in the following distance matrix.

How should the cars be assigned to the customers so as to minimize the distance travelled?

what is feasible solution and non degenerate solution in transportation problem?

Obtain an initial basic feasible solution to the following transportation problem by using least- cost method.

Three jobs A, B and C one to be assigned to three machines U, V and W. The processing cost for each job machine combination is shown in the matrix given below. Determine the allocation that minimizes the overall processing cost.

(cost is in Rs. per unit)

Following pay-off matrix, which is the optimal decision under each of the following rule
(i) maxmin
(ii) minimax

Act States of nature

S₁ S₂ S₃ S₄

A₁ 14 9 10 5

A₂ 11 10 8 7

A₃ 9 10 10 11

A₄ 8 10 11 13

Explain Vogel’s approximation method by obtaining initial feasible solution of the following transportation problem

Consider the following transportation problem

Determine an initial basic feasible solution using (a) Least cost method (b) Vogel’s approximation method.

Give mathematical form of assignment problem.
A departmental head has four subordinates and four tasks to be performed. The subordinates differ in efficiency and the tasks differ in their intrinsic difficulty. His estimates of the time each man would take to perform each task is given below

How should the tasks be allocated to subordinates so as to minimize the total man-hours?

Determine an initial basic feasible solution of the following transportation problem by north west corner method

Determine an initial basic feasible solution to the following transportation problem by using (i)North West Corner rule (ii) least cost method.

Part - C

Generic 3 - Answer All Question

Determine an initial basic feasible solution to the following transportation problem using North West corner rule.

Here O_i and D_j represent ith origin and jth destination.

Obtain an initial basic feasible solution to the following transportation problem using least cost method.

Here O_iand D_j denote i^th origin and j^th destination respectively.

Consider the following pay-off (profit) matrix Action States

Action States

(s₁) (s₂) (s₃) (s₄)

A₁ 5 10 18 25

A₂ 8 7 8 23

A₃ 21 18 12 21

A₄ 30 22 19 15

Determine best action using maximin principle.

Find the initial basic feasible solution for the following transportation problem by VAM

Consider the following pay-off matrix

Alternative Pay – offs (Conditional events)

A₁ A₂ A₃ A₄

E₁ 7 12 20 27

E₂ 10 9 10 25

E₃ 23 20 14 23

E₄ 32 24 21 17

Using minmax principle, determine the best alternative.

Obtain the initial solution for the following problem

Determine how much quantity should be stepped from factory to various destinations for the following transportation problem using the least cost method

Cost are expressed in terms of rupees per unit shipped.

A business man has three alternatives open to him each of which can be followed by any of the four possible events. The conditional pay offs for each action - event combination are given below:

Alternative Pay – offs (Conditional events)

A B C D

X 8 0 -10 6

Y -4 12 18 -2

A₃ 21 18 12 21

Obtain an initial basic feasible solution to the following transportation problem using Vogel’s approximation method.

Part - D

Generic 5 - Answer All Question

Solve the following assignment problem. Cell values represent cost of assigning job A, B, C and D to the machines I, II, III and IV.

Consider the problem of assigning five jobs to five persons. The assignment costs are given as follows. Determine the optimum assignment schedule.

Solve the following assignment problem.

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