Question

1. What is linear programming?
2. What is the purpose of sensitivity analysis?
3. When might you have multiple optimal solutions? How do you identify it? What does it mean to you, the operations manager?
4. What is an unbounded problem? How do you identify it? What does it mean to you, the operations manager

Answer 1

1)

What is linear programming?

Linear programming is a mathematical method that is used to determine the best possible outcome or solution from a given set of parameters or list of requirements, which are represented in the form of linear relationships. It is most often used in computer modeling or simulation in order to find the best solution in allocating finite resources such as money, energy, manpower, machine resources, time, space and many other variables. In most cases, the "best outcome" needed from linear programming is maximum profit or lowest cost.

Because of its nature, linear programming is also called linear optimization.

2)

What is the purpose of sensitivity analysis?

Sensitivity Analysis is a tool used in financial modeling to analyze how the different values of a set of independent variables affect a specific dependent variable under certain specific conditions. In general, Sensitivity Analysis is used in a wide range of fields, ranging from biology and geography to economics and engineering.

It is especially useful in the study and analysis of a “Black Box Processes” where the output is an opaque function of several inputs. An opaque function or process is one which for some reason can’t be studied and analyzed. For example, climate models in geography are usually very complex. As a result, the exact relationship between the inputs and outputs are not well understood.

3)

When might you have multiple optimal solutions? How do you identify it? What does it mean to you, the operations manager?

he concept of multiple optimal solutions is associated with the linear programming problems. The multiple optimal solutions will arise in a linear program with more than one set of basic solutions that can minimize or maximize the required objective function. Sometimes, the multiple optimal solutions are called the alternative basic solution.

In case of an assignment problem, it is likely to have two or additional ways to remove an assured number of zeros. This situation shows multiple optimal solutions with the identical optimal value of objective function. Therefore, it can be said that the total cost or total profit will remain identical for different sets of allocation in an assignment problem.

In case of the simplex method, the presence of multiple optimal solutions is specified by a condition under which a non-basic variable in the last simplex table displays the optimal solution to the problem and the net amount of contribution is zero.

The decision creator will use the most suitable set of the basic solution as the solution of the linear program when the problem has multiple optimal solutions.

The occurrence of the multiple optimal solutions is not a big problem because the occurrence of the alternative solutions does not prevent the researcher from discovering one optimal solution for the problem.

The linear problem can be solved by using the software like MS Excel, but it only provides one optimal solution among many optimal solutions. So, it is reasonable to solve the problem manually for obtaining all the basic solutions when there is a possibility of occurrence of multiple optimal solutions.

4)

Unbounded solution

The solutions of a linear programming problem which is feasible can be classified as a bounded solution and an unbounded solution.

The unbounded solution is a situation when the optimum feasible solution cannot be determined, instead there are infinite many solutions. It is not possible to solve the problem in which this situation occurs.