Exam 19: Integer Programming: the Branch and Bound Method

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

In using the branch and bound method, if a branch gives an infeasible solution to the associated linear programming problem, then the particular branch is fathomed and is not considered any further.

In using rounding of a linear programming model to obtain an integer solution, the solution is

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 Give the constraints for the problem.

An infeasible solution is ensured by rounding down non-integer solution values.

The production manager for the Rusty soft drink company is considering the production of two kinds of soft drinks: regular and diet. Two of her resources are constraint production time (8 hours = 480 minutes per day) and syrup (1 of the ingredients), limited to 675 gallons per day. To produce a regular case requires 2 minutes and 5 gallons of syrup, while a diet case needs 4 minutes and 3 gallons of syrup. Profits for regular soft drink are $3 per case and profits for diet soft drink are $2 per case. What are optimal daily profits?

Solve the following integer LP using branch and bound: MAX Z=+5 subject to: +10\leq20 \leq2 ,\geq0 and integer

Solve the following integer LP using branch and bound: MAX +5 subject to: +10\leq20 \leq2 ,\geq0 and integer The optimal value of Z is:

Solve the following integer linear program: MAX    $\quad Z = 2 x _ { 1 } + x _ { 2 }$ subject to:     $2 x _ { 1 } + 2 x _ { 2 } \leq 7$           $4 x _ { 1 } + x _ { 2 } \leq 11$           $x _ { 1 }$ and $x _ { 2 } \geq 0$ What are the optimal values of x1 and x2?

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

We begin the branch and bound method by first solving the problem as a regular ________ model without integer restrictions.

In implicit enumeration the feasible integer solutions closest to the optimal non-integer solution are evaluated to see which is best.

The production manager for Beer etc. produces two kinds of beer: light and dark. Two of his resources are constrained: malt, of which he can get at most 4800 oz per week; and wheat, of which he can get at most 3200 oz per week. Each bottle of light beer requires 12 oz of malt and 4 oz of wheat, while a bottle of dark beer uses 8 oz of malt and 8 oz of wheat. Profits for light beer are $2 per bottle, and profits for dark beer are $1 per bottle. What are the optimal weekly profits?

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

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

The branch and bound method is a solution technique specifically limited to integer programming problems.

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

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

Solve the following integer linear program using implicit enumeration. MAX Z= subject to: -+\leq0.5 +\leq3.5 ,\geq0 and integer

The branch and bound method can be used for 0-1 integer programming problems by adding a ________ 1 constraint for each 0-1 variable.