Exam 19: Integer Programming: the Branch and Bound Method

If an integer linear programming problem has no feasible solution, then its relaxed solution (LP relaxation) must also have no feasible solution

Consider a capital budgeting example with five projects from which to select. Let xi = 1 if project a is selected, 0 if not, for i = 1, 2, 3, 4, 5. Write the appropriate constraint(s) for the following condition: If project 3 is chosen, project 4 must be chosen.

The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same and not all four machines have to be used to produce all of the garden hoses. Fixed Cost to\nobreakspaceSetup Variable\nobreakspaceCost Machine Production Run per Hose Capacity 1 750 1.25 6000 2 500 1.50 7500 3 1000 1.00 4000 4 300 2.00 5000 Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.

When the branch and bound approach is applied to an integer programming problem, it is used in conjunction with the normal non-integer solution approach.

The branch and bound method of solving linear integer programming problems is an enumeration method.

The branch and bound method of solving linear integer programming problems is

A linear programming model solution with integer restrictions is called a relaxed solution.

Rounding large values of decision variables to the nearest integer value causes ________ problems than rounding small values.

A feasible solution is ensured by rounding down non-integer solution values.

When using branch and bound for a maximization integer programming problem, the lower bound at the initial node can always be determined by rounding down the LP relaxation solution values regardless of the types of constraints in the problem.

The branch and bound method can be used for ________ integer problems except only variables with integer restrictions are rounded down to achieve an initial lower bound and only integer variables are branched on.

The ________ integer solution will always be between the upper bound of the relaxed solution and a lower bound of the rounded-down solution.

Solve the following integer linear program: MAX + subject to: 4+6\leq22 +5\leq15 2+\leq9 ,x\geq0, integer

The Wiethoff Company has a contract to produce 10,000 garden hoses for a customer. Wiethoff has four different machines that can produce this kind of hose. Because these machines are from different manufacturers and use differing technologies, their specifications are not the same and not all four machines have to be used to produce all of the garden hoses. Fixed Cost to\nobreakspaceSetup Variable\nobreakspaceCost Machine Production Run per Hose Capacity 1 750 1.25 6000 2 500 1.50 7500 3 1000 1.00 4000 4 300 2.00 5000 Write a constraint to ensure that if machine 4 is used, machine 1 will not be used.

In implicit enumeration, all feasible solutions are evaluated to see which is best.

The branch and bound method uses a tree diagram of ________ and ________ to organize the solution partitioning.

The ________ method evaluates all feasible and infeasible solutions to determine the optimal solution.

The ________ method is a solution approach that partitions the feasible solution space into smaller subsets of solutions.

Rounding non-integer solution values up to the nearest integer value can result in an infeasible solution.

The branch and bound method is a solution approach that partitions the infeasible solution space into smaller subsets of solutions.