CME -II Test 2

Potential problems with the cutting plane method include

• It may never converge to a solution.

• It can be used only for problems with two dimensions.

• It may not take a great deal of computer time to find a solution.

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

Mark the wrong statement:

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

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

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

• A goal programming problem cannot have multiple optimal solutions.

The first step in a branch and bound approach to solving integer programming problems is to

• Graph the problem

• Change the objective function coefficients to whole integer numbers.

• Solve the original problem using LP by allowing continuous noninteger solutions.

• Compare the lower bound to any upper bound of your choice.

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

• The objective function is zero.

• The new upper bound exceeds the lower bound.

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

• The lower bound reaches zero.

Which of the following is not a type of integer programming problem?

• Pure integer programming problem

• Blending problem

• Zero-one programming problem

• Mixed-integer programming problem

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 pure IPP.

• A 0-1 IPP.

• A mixed IPP.

• Not an IPP.

The _______________ divides a set of feasible solutions into subsets that are examined systematically.

• Cutting plane method

• Simplex method

• Branch and bound method

• Mixed-integer method

An integer programming solution can never produce ______________ solution than the solution to the same LP problem.

• The same

• A better

• A worse

• An integer

In cutting plane algorithm, each cut which is made involves the introduction of

• An ‘=’ constraint

• An artificial variable

• A ‘≤’ constraint

• A ‘≥’ constraint

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?

• Goal programming

• Primary programming

• Integer programming

• Dynamic programming