Exam 10: Integer Programming, Goal Programming, and Nonlinear Programming

Terms that are minimized in goal programming are called ________.

In goal programming, our goal is to drive the deviational variables in the objective function as close to zero as possible.

Allied Manufacturing has three factories located in Dallas, Houston, and New Orleans. They each produce the same 281 products and ship to three regional warehouses - #1, #2, and #3. The cost of shipping one unit of each product to each of the three destinations is given in the table below: There is no way to meet the demand for each warehouse. Therefore, the company has decided to set the following equally weighted goals: (1) each source should ship as much of its capacity as possible, (2) the number shipped to each destination should be as close to the demand as possible, (3) the capacity of New Orleans should be divided as evenly as possible between warehouses #1 and #2, and (4) the total cost should be less than $1,400. Formulate this as a goal program, which includes a strict requirement that capacities cannot be violated.

A transportation problem is an example of

Table 10-4 A company has decided to use 0−1 integer programming to help make some investment decisions. There are three possible investment alternatives from which to choose, but if it is decided that a particular alternative is to be selected, the entire cost of that alternative will be incurred (i.e., it is impossible to build one-half of a factory). The integer programming model is as follows: -Table 10-4 presents an integer programming problem. What is the meaning of Constraint 2?

An integer programming solution can never produce a greater profit objective than the LP solution to the same problem.

Allied Manufacturing has three factories located in Dallas, Houston, and New Orleans. They each produce the same product and ship to three regional warehouses: #1, #2, and #3. The cost of shipping one unit of each product to each of the three destinations is given below. There is no way to meet the demand for each warehouse. Therefore, the company has decided to set the following goals: (1) the number shipped from each source should be as close to 100 units as possible (overtime may be used if necessary), (2) the number shipped to each destination should be as close to the demand as possible, (3) the total cost should be close to $1,400. Formulate this as a goal programming problem.

Classify the following problems as to whether they are pure-integer, mixed-integer, zero-one, goal, or nonlinear programming problems. (a) Maximize Z = 5 X₁ + 6 X₁ X₂ + 2 X₂ Subject to: 3 X₁ + 2 X₂ ≥ 6 X₁ + X₂ ≤ 8 X₁, X₂ ≥ 0 (b) Minimize Z = 8 X₁ + 6 X₂ Subject to: 4 X₁ + 5 X₂ ≥ 10 X₁ + X₂ ≤ 3 X₁, X₂ ≥ 0 X₁, X₂ = 0 or 1 (c) Maximize Z = 10 X₁ + 5 X₂ Subject to: 8 X₁ + 10 X₂ = 10 4 X₁ + 6 X₂ ≥ 5 X₁, X₂ integer (d) Minimize Z = 8 X₁² + 4 X₁ X₂ + 12 X₂² Subject to: 6 X₁ + X₂ ≥ 50 X₁ + X₂ ≥ 40