Pure IPPs are those problems in which all the variables are non-negative integers.
The 0-1 IPPs are those in which all variables are either 0 or all equal to 1.
Mixed IPPs are those where decision variables can take integer values only but the slack/surplus variables can take fractional values as well.
In real life, no variable can assume fractional values. Hence we should always use IPPs.
A pure IPP.
A 0-1 IPP.
A mixed IPP.
Not an IPP.
A facility location problem can be formulated and solved as a 0-1 IPP.
Problems involving piece-wise linear functions can be modeled as mixed linear programming problems.
Solution to an IPP can be obtained by first solving the problem as an LPP then rounding off the fractional values.
If the optimal solution to an LPP has all integer values, it may or may not be an optimal integer solution.
To solve an IPP using cutting plane algorithm, the integer requirements are dropped in the first instance to obtain LP relaxation.
A cut is formed by choosing a row in the optimal tableau that corresponds to a non-integer variable.
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
The optimal solution to LPP satisfies the cut that is introduced on the basis of it.
An ‘=’ constraint
An artificial variable
A ‘≤’ constraint
A ‘≥’ constraint
(i) and (ii) only
(i) and (iii) only
All the above
It is not a particular method and is used differently in different kinds of problems.
It is generally used in combinatorial problems.
It divides the feasible region into smaller parts by the process of branching.
It can be used for solving any kind of programming problem.
Goal programming deals with problems with multiple goals.
Goal programming realizes that goals may be under-achieved, over-achieved, or met exactly.
The inequalities or equalities representing goal constraints are flexible.
The initial tableau of a goal programming problem should never have a variable in the basis which is an under-achievement variable.
A travelling salesman problem can be solved using Branch and Bound method.
An assignment problem can be formulated as a 0-1 IPP and solved using Branch and Bound method.
The Branch and Bound method terminates when the upper and lower bounds become identical and the solution is that single value.
The Branch and Bound method can never reveal multiple optimal solutions to a problem, if they exist.
Each of them can be positive or zero.
Either d- or d+ is zero.
Both are non-zero.
Both are equal to zero.
A ‘lower’ one-sided goal sets a lower limit that we do not want to fall under.
A two-sided goal sets a specific target missing which from either side is not desired.
In goal programming, an attempt is made to minimize deviations from targets.
In using goal programming, one has to specify clearly the relative importance of the various goals involved by assigning weights to them.
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.
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.
Existence of (multiple ∆j rows) Net Evaluation containing priority terms indicate a prioritized goal-programming problem.
A lower priority is never sought to be achieved at the expense of higher-priority goal.
The co-efficients, Pi’s are not assigned any actual values.
An explicit objective function
0 - 1
All of the above
Prioritization of goals
A single objective function
Linear objective function
None of the above
Pure integer programming
Zero-one integer programming
The values of decision variables obtained by rounding off are always very close to the optimal values.
The value of the objective function for a maximization problem will likely be less than that for the simplex solution.
The value of the objective function for a minimization problem will likely be less than that for the simplex solution.
All constraints are satisfied exactly.
None of the above.
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.
None of the above
None of the above
Pure integer programming problem
Zero-one programming problem
Mixed-integer programming problem
It may never converge to a solution.
It can be used only for problems with two dimensions.
It may 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.
Both c and d