Exam 6: Integer Linear Programming

An investor has $500,000 to invest and wants to maximize the money they will receive at the end of one year. They can invest in condos, apartments and houses. The profit after one year, the cost and the number of units available are shown below. Based on this ILP formulation of the problem and the indicated optimal integer solution values what values should go in cells B5:F12 of the following Excel spreadsheet? ​

A cellular phone company wants to locate two new communications towers to cover 4 regions. The company wants to minimize the cost of installing the two towers. The regions that can be covered by each tower site are indicated by a 1 in the following table: ​ Based on this ILP formulation of the problem and the solution (X₁, X₂, X₃, X₄) = (1, 1, 0, 0) what values should go in cells B6:G14 of the following Excel spreadsheet?

The following ILP is being solved by the branch and bound method. You have been given the initial relaxed IP solution. Complete the entries for the 3 nodes and label the arcs when you branch on X2. Initial solution X₁ = 5.0 X₂ = 7.5 Obj = 550

The concept of an upper bound in IP is associated with:

An ILP problem has 5 binary decision variables. How many possible integer solutions are there to this problem?

Pure IP formulation requires that:

What does the Analytic Solver Platform integer tolerance factor of 0 accomplish?

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. ​ The decision variables are defined as X_i = the amount of product i produced Y_i = 1 if X_i > 0 and 0 if X_i = 0 Using the approach discussed in the text, what is the appropriate value for M₁ in the linking constraint for product A?

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. ​ What is the appropriate formula to use in cell E8 of the following Excel implementation of the ILP model for this problem?

Suppose you want to minimize an objective function z=2x₁+3x₂. Both decision variables must be integer. The optimal solution to the LP relaxation will:

A company is developing its weekly production plan. The company produces two products, A and B, which are processed in two departments. Setting up each batch of A requires $60 of labor while setting up a batch of B costs $80. Each unit of A generates a profit of $17 while a unit of B earns a profit of $21. The company can sell all the units it produces. The data for the problem are summarized below. ​ What is the appropriate formula to use in cell B15 of the following Excel implementation of the ILP model for this problem?

In the B & B algorithm, B & B stands for

A manufacturing company has costs associated with production preparation and with per unit production. The per unit production costs are referred to as

The objective function value for the ILP problem can never

A city wants to locate 2 new fire fighting ladder trucks to maximize the number of tall buildings which they can cover within a 3 minute response time. The city is divided into 4 zones. The fire chief wants to locate no more than one of the trucks in either Zone 1 or Zone 2. The number of tall buildings in each zone and the travel time between zones is listed below. Formulate the ILP for this problem. ​

Binary variables are useful for modeling

A practical way of dealing with the complexity of IP problems is to:

An integrality condition indicates that some (or all) of the

Exhibit 6.1 The following questions pertain to the problem, formulation, and spreadsheet implementation below. A research director must pick a subset of research projects to fund over the next five years. He has five candidate projects, not all of which cover the entire five-year period. Although the director has limited funds in each of the next five years, he can carry over unspent research funds into the next year. Additionally, up to $30K can be carried out of the five-year planning period. The following table summarizes the projects and budget available to the research director. The following is the ILP formulation and a spreadsheet model for the problem. -Refer to Exhibit 6.1. What formula should go in cell D15 of the above Excel spreadsheet?

How is the integer tolerance factor set in the Analytic Solver Platform (ASP)?