Integer Programming And Goal Programming

40 Questions | Total Attempts: 755

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Programming Quizzes & Trivia

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.


Questions and Answers
  • 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