CUSTOMER_CODE
SMUDE
DIVISION_CODE
SMUDE
EVENT_CODE
OCTOBER15
ASSESSMENT_CODE MC0079_OCTOBER15
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
4340
QUESTION_TEXT
Write the algorithm for Hungarian method
SCHEME OF
EVALUATION
Step 1: locate the smallest cost element in each row of the cost table.
Step 2: in the reduced cost table obtained, considered each column and
locate the smallest element in the subtract the smallest value from
every other entry in the column.
Step 3: Draw the minimum number of horizontal and vertical lines that
are require to cover all the ‘zero’ elements.
Step 4: Select the smallest uncovered cost element.
Step 5: Repeat steps 3 An 4 until an optimal solution is obtained.
Step 6: Given the optimal solution. Make the job assignments as
indicated by the zero elements.
(10 marks with explanation)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
116760
a.
List out the characteristics of the standard form of LPP.
b.
Explain simplex algorithm.
QUESTION_TEXT
a.
The Standard form of LPP
The characteristics of the standard form are :
i.
All constraints are equations except for the non-negativity
condition which remain inequalities (, 0) only.
SCHEME OF
EVALUATION
ii.
The righthand side element of each constraint equation is nonnegative.
iii.
All variables are non-negative.
iv. The objective function is of the maximization or minimization
type.
(4 marks)
b.
Simplex Algorithm
i.
Locate the most negative number in the last (bottom) row of the
simplex table, excluding that of last column and call the column in which
this number appears as the work (pivot) column.
ii.
Form ratios by dividing each positive number in the work column,
excluding that of the last row into the element in the same row and last
column. Designate that element in the work column that yields the
smallest ratio as the pivot element. If more than one element yields the
same smallest ratio choose arbitrarily one of them. If no element in the
work column is non negative the program has no solution.
iii. Use elementary row operations to convert the pivot element to
unity (1) and then reduce all other elements in the work column to zero.
iv. Replace the x -variable in the pivot row and first column by xvariable in the first row pivot column. The variable which is to be replaced
is called the outgoing variable and the variable that replaces is called the
incoming variable. This new first column is the current set of basic
variables.
v.
Repeat steps 1 through 4 until there are no negative numbers in the
last row excluding the last column.
vi. The optimal solution is obtained by assigning to each variable in
the first column that value in the corresponding row and last column. All
other variables are considered as non-basic and have assigned value zero.
The associated optimal value of the objective function is the number in
the last row and last column for a maximization program but the
negative of this number for a minimization problem.
(6 marks)
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
116761
QUESTION_TEXT
Write a note on operating characteristics of Queuing system.
SCHEME OF
EVALUATION
Queue length: The average number of customers in the queue waiting to
get service. Large queues may indicate poor server performance while
small queues may imply too much server capacity.
System length: The average number of customers in the system, those
waiting to be and those being serviced. Large values of this statistic
imply congestion and possible customer dissatisfaction and a potential
need for greater service capacity.
Waiting time in the queue: The average time that a customer has to wait
in the queue to get service. Long waiting times are directly related to
customer dissatisfaction and potential loss of future revenues, while very
small waiting times may indicate too much service capacity.
Total time in the system: the average time that a customer spends in the
system, from entry in the queue to completion of service. Large values
of this statistic are indicative of the need to make adjustment in the
capacity.
Server idle time: The relative frequency with which the service system
is idle. Idle time is directly related to cost. However, reducing idle time
may have adverse effects on the other characteristics mentioned above.
(2 Marks each )
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
116762
Define the following
QUESTION_TEXT
a.
Redundant constraint
b.
Basic solution
c.
A basic feasible solution
d.
Optimal feasible solution
e.
Convex polygon
1. A redundant constraint is a constraint which does not affect the feasible
region
SCHEME OF
EVALUATION
2. A basic solution of a system of n equation and n variables (M<n) is a
solution where at least n-n variables are zero
3. A basic feasible solution of a system of n equations and n variables (m<n)
is a solution where n variables are non negative (≥0) & n-n variables are
zero
4. Any feasible solution that optimizes the objective function is called an
optimal feasible solution
5. A convex polygon is a convex set formed by the inter section of finite
number of closed half planes
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
116765
Explain the terms:
i.
Saddle point
ii.
Max–min and min–max principle
iii.
Principle of dominance
i.
Saddle point definition: (4marks)
QUESTION_TEXT
For any game, if the max–min and the min–max are equal, then such
games are said to have saddle point
Steps to detect a saddle point: 5 steps
ii.
SCHEME OF
EVALUATION
Max–min and min–max principle: (3 marks)
Suppose player A and player are to play a game without knowing what
the other player would do. However, player A would like to maximize
his profit and player B would like to minimize his loss. And thus each
player would expect his opponent to be calculative
Explanation
iii.
Principle of dominance:
(3 marks)
The dominance rule for columns: every value in the dominating
column(s) must be less than or equal to the corresponding value of the
dominated column
The dominance rule for row: every value in the dominating row(s) must
be greater than or equal to the corresponding value of the dominated row
QUESTION_TYPE
DESCRIPTIVE_QUESTION
QUESTION_ID
116766
QUESTION_TEXT
What are the steps involved in Gomory’s All IPP algorithm
The iterative procedure for the solution of an all integer programming
problem is as follows:
Step 1: Convert the minimization IPP into that of maximization, if it is
in the minimization form. The integrality condition should be ignored.
Step 2: Introduce the slack or surplus variables, wherever necessary to
convert the in equations into equations and obtain the optimum solution
of the given LPP by using simplex algorithm.
Step 3: Test the integrality of the optimum solution
a.
If the optimum solution contains all integer values, an optimum
basic feasible integer solution has been obtained.
b.
If the optimum solution does not include all integer values then
proceed onto next step.
SCHEME OF
EVALUATION
Step 4: Examine the constraint equations corresponding to the current
optimum solution. Let these equations be represented by
ij
, xj = bi ,(i=0,1,2,…..m 1)
Where n1 denotes the number of variables and m1 the number of
equations.
Choose the largest fraction of bi
Let it be [b k1]I
s i.e ..to find max {bi }
or write is as fk0
Step 5: Express each of the negative fractions if any, in the kth row of
the optimum simplex table as the sum of a negative integer and a nonnegative integer and a non-negative fraction.
Step 6: Find the Gomorian constraint
kj
, xj ≥fk0
And add the equation
Gsla(1) = -fko +
kj
. xj
to the current set of equation constraints.
Step 7: Starting with this new set of equation constraints, find the new
optimum solution by dual simplex algorithm.
(So that Gsla (1) is the initial leaving basic variable).
Step 8: If this new optimum solution for the modified LPP is an integer
solution. It is also feasible and optimum for the given IPP otherwise
return to step 4 and repeat the process until an optimum
Obtained
(1.25*8 10 marks)