Lecture 5 (and some l7 questions)

Rounding Issue: Integer Solutions

- Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution. - A feasible solution is ensured by rounding down non-integer solution values but may result in a less than optimal (sub-optimal) solution.

In formulating a mixed integer programming problem, the constraint x1 + x2 ≤ 500y1 where y1 is a 0-1 variable and x1 and x2 are continuous variables, then x1 + x2 = 500 if y1 is:

1

True or False: A long period of real time cannot be represented by a short period of simulated time.

False

True or False: Simulation results will always equal analytical results if 1000 trials of the simulation have been conducted.

False

True or False: The "certainty" linear programming (LP) hypothesis (LP are deterministic models) is violated by integer programming.

False

True or False: The constraint x1 + x2 ≤ 1 is named as "conditional constraint" in 0-1 integer programming problems.

False

Define Corequisite Constraint

If one event occurs, the other will occur, and vice versa.

Define Conditional Constraint

Occurrence of one outcome is dependent on the previous outcome of another

What is the Branch and Bound Method

Traditional approach to solving integer programming problems: i) Feasible solutions can be partitioned into smaller subsets; ii) Smaller subsets evaluated until best solution is found; iii) Methods is a tedious and complex mathematical process;

True or False: For a "Primal maximization problem" with Z equal to 2,570, its respective "Dual minimization problem " would also have a Z of 2,570.

True

If Xba = the production of product a in period b, then to indicate that the limit on production of the company's 3 products in period 1 is 250, we write:

X11 + X12 + X13 ≤ 250

The constraint (x1 + x2 + x3 + x4 + x5 greater than or equal to 3) means that ________ out of the ________ projects must be selected.

at least 3, 5

In a 0-1 integer programming model, if the constraint , it means when project is selected, project ________ be selected.

can sometimes

Integer Programming

i) Total Integer Model: all decision variables required to have integer solution variables. ii) 0-1 Integer Model: all decision variables required to have integer values of zero or one. iii) Mixed Integer Model: some of the decision variables (but not all) required to have integer values.

For a minimization integer linear programming problem, a feasible solution is ensured by rounding ________ non-integer solution values if all of the constraints are the greater-than-or-equal-to type.

up

In a "capital budgeting" problem, if either project 1 or project 2 is selected, then project 5 cannot be selected. Which of the alternatives listed below correctly models this situation?

x1 + x5 ≤ 1, x2 + x5 ≤ 1