# Integer Programming And Goal Programming

40 Questions | Total Attempts: 755  Settings  This is a quiz on 'Integer Programming and Goal Programming'. You have to answer 40 questions in 80 minutes. Each question carries 2 marks making the total equal to 80 marks.

Related Topics
• 1.
Mark the correct statement about integer programming problems (IPPs):
• A.

Pure IPPs are those problems in which all the variables are non-negative integers.

• B.

The 0-1 IPPs are those in which all variables are either 0 or all equal to 1.

• C.

Mixed IPPs are those where decision variables can take integer values only but the slack/surplus variables can take fractional values as well.

• D.

In real life, no variable can assume fractional values. Hence we should always use IPPs.

• 2.
Consider the following problem: Max. Z = 28x1 + 32x2, subject to 5x1 + 3x2 ≤ 23, 4x1 + 7x2 ≤ 33, and x1 ≥ 0, x2 ≥ 0. This problem is:
• A.

A pure IPP.

• B.

A 0-1 IPP.

• C.

A mixed IPP.

• D.

Not an IPP.

• 3.
Mark the correct statement:
• A.

A facility location problem can be formulated and solved as a 0-1 IPP.

• B.

Problems involving piece-wise linear functions can be modeled as mixed linear programming problems.

• C.

Solution to an IPP can be obtained by first solving the problem as an LPP then rounding off the fractional values.

• D.

If the optimal solution to an LPP has all integer values, it may or may not be an optimal integer solution.

• 4.
1.      Mark the wrong statement:
• A.

To solve an IPP using cutting plane algorithm, the integer requirements are dropped in the first instance to obtain LP relaxation.

• B.

A cut is formed by choosing a row in the optimal tableau that corresponds to a non-integer variable.

• C.

A constraint picked from the optimal tableau is: 0x1 + x2 + 1/2 S1 – 1/3 S2 = 7/2. With S3 being a slack variable introduced, the cut would be: -1/2 S1 – 2/3 S2 + S3 = -1/2

• D.

The optimal solution to LPP satisfies the cut that is introduced on the basis of it.

• 5.
In cutting plane algorithm, each cut which is made involves the introduction of
• A.

An ‘=’ constraint

• B.

An artificial variable

• C.

A ‘≤’ constraint

• D.

A ‘≥’ constraint

• 6.
Which of the following effects does the addition of a Gomory have? (i) adding a new variable to the tableau; (ii) elimination of non-integer solutions from the feasibility region; (iii) making the previous optimal solution infeasible by eliminating that part of the feasible region which contained that solution.
• A.

(i) only

• B.

(i) and (ii) only

• C.

(i) and (iii) only

• D.

All the above

• 7.
• A.

It is not a particular method and is used differently in different kinds of problems.

• B.

It is generally used in combinatorial problems.

• C.

It divides the feasible region into smaller parts by the process of branching.

• D.

It can be used for solving any kind of programming problem.

• 8.
Mark the wrong statement:
• A.

Goal programming deals with problems with multiple goals.

• B.

Goal programming realizes that goals may be under-achieved, over-achieved, or met exactly.

• C.

The inequalities or equalities representing goal constraints are flexible.

• D.

The initial tableau of a goal programming problem should never have a variable in the basis which is an under-achievement variable.

• 9.
• A.

A travelling salesman problem can be solved using Branch and Bound method.

• B.

An assignment problem can be formulated as a 0-1 IPP and solved using Branch and Bound method.

• C.

The Branch and Bound method terminates when the upper and lower bounds become identical and the solution is that single value.

• D.

The Branch and Bound method can never reveal multiple optimal solutions to a problem, if they exist.

• 10.
If two deviational variables, d- or d+ for over-achievement, are introduced in a goal constraint, then which of the following would not hold:
• A.

Each of them can be positive or zero.

• B.

Either d- or d+ is zero.

• C.

Both are non-zero.

• D.

Both are equal to zero.

• 11.
Mark the wrong statement:
• A.

A ‘lower’ one-sided goal sets a lower limit that we do not want to fall under.

• B.

A two-sided goal sets a specific target missing which from either side is not desired.

• C.

In goal programming, an attempt is made to minimize deviations from targets.

• D.

In using goal programming, one has to specify clearly the relative importance of the various goals involved by assigning weights to them.

• 12.
Mark the wrong statement:
• A.

Goal programming assumes that the decision-maker has a linear utility function with respect to the objectives.

• B.

Deviations for various goals may be given penalty weights in accordance with the relative significance of the objectives.

• C.

The penalty weights measure the marginal rate of substitution between the objectives.

• D.

A goal programming problem cannot have multiple optimal solutions.

• 13.
Mark the wrong statement:
• A.

In goal programming, the goals are ranked from the least important (goal 1) to the most important (goal n), with objective function co-efficients Pi.

• B.

Existence of (multiple ∆j rows) Net Evaluation containing priority terms indicate a prioritized goal-programming problem.

• C.

A lower priority is never sought to be achieved at the expense of higher-priority goal.

• D.

The co-efficients, Pi’s are not assigned any actual values.

• 14.
Which of the following is not an essential condition in a situation for linear programming to be useful?
• A.

An explicit objective function

• B.

Uncertainty

• C.

Linearity

• D.

Limited resources

• E.

Divisibility

• 15.
There are other related mathematical programming techniques that can be used instead of linear programming if the problem has a unique characteristic. If the problem has multiple objectives we should use which of the following methodologies?
• A.

Goal programming

• B.

Orthogonal programming

• C.

Integer programming

• D.

Multiplex programming

• E.

Dynamic programming

• 16.
There are other related mathematical programming techniques that can be used instead of linear programming if the problem has a unique characteristic. If the problem prevents divisibility of products or resources we should use which of the following methodologies?
• A.

Goal programming

• B.

Primary programming

• C.

Integer programming

• D.

Unit programming

• E.

Dynamic programming

• 17.
Types of integer programming models are _____________.
• A.

Total

• B.

0 - 1

• C.

Mixed

• D.

All of the above

• 18.
Which of the following is not an integer linear programming problem?
• A.

Pure integer

• B.

Mixed integer

• C.

0-1integer

• D.

Continuous

• 19.
Which of the following is not a requirement for a goal programming problem?
• A.

Prioritization of goals

• B.

A single objective function

• C.

Linear constraints

• D.

Linear objective function

• E.

None of the above

• 20.
If we wish to develop a stock portfolio wherein we maximize return and minimize risk, we would have to use
• A.

Pure integer programming

• B.

Goal programming

• C.

Zero-one integer programming

• D.

Mixed-integer programming

• E.

Nonlinear programming

• 21.
Solving an integer programming problem by rounding off answers obtained by solving it as a linear programming problem (using simplex), we find that
• A.

The values of decision variables obtained by rounding off are always very close to the optimal values.

• B.

The value of the objective function for a maximization problem will likely be less than that for the simplex solution.

• C.

The value of the objective function for a minimization problem will likely be less than that for the simplex solution.

• D.

All constraints are satisfied exactly.

• E.

None of the above.

• 22.
When using the branch and bound method in integer programming maximization problem, the stopping rule for branching is to continue until
• A.

The objective function is zero.

• B.

The new upper bound exceeds the lower bound.

• C.

The new upper bound is less than or equal to the lower bound or no further branching is possible.

• D.

The lower bound reaches zero.

• E.

None of the above

• 23.
• A.

300

• B.

-300

• C.

3300

• D.

0

• E.

None of the above

• 24.
Which of the following is not a type of integer programming problem?
• A.

Pure integer programming problem

• B.

Blending problem

• C.

Zero-one programming problem

• D.

Mixed-integer programming problem

• 25.
Potential problems with the cutting plane method include
• A.

It may never converge to a solution.

• B.

It can be used only for problems with two dimensions.

• C.

It may take a great deal of computer time to find a solution.

• D.

It does not produce a good integer solution until the final solution is reached.

• E.

Both c and d