Operation Analysis w5 discussions - Essay Example

Linear Programming vs. Simplex Method Question Introduction Linear programming (LP) is a branch of mathematical programming designed to find solutions to problems of optimization where all constraints are expressed as linear function (Hillier, Mark and Gerald 2000). LP is a good tool for making choices under certain conditions i.e. all constraints and objectives, and courses of alternatives are known and quantified. The course of action yielding optimal results is chosen out of all possible alternatives available.

Therefore, LP can be used as a checking mechanism and verification tool to determine the reliability and accuracy of decisions made by managers based on experience without help of any mathematical model.Graphical solutions in linear programming have limited number of decision variables. The technique of LP plots constraints on graph paper and then identifies the feasible region that is represented by the constraints. The objective function is then drawn and used to identify optimal points in the feasible region.

However, graphically, linear programming can only be done in one two variables. Thus, the maximum number of variables in LP model is two. However, it can be done in more than three variables using special algorithms. Business managers use linear programming models to come up with concrete and measurable performance improvements. The kind of decisions that are arrived at using LP models represent the optimal solutions or decisions that are possible with the given constraint variables at the disposal of managers.

For instance, the optimal decision would be the maximum profit that a business can generate using available limited resources or the minimum costs that the business can incur to produce products in order to maintain its current maximum level of profits. Therefore, LP can help managers use available limited resources effectively, reduce costs, improve profitability, and reduce risks among other key benefits.Question 2Simplex method is a special algorithm that is computer based used to find optimal solutions to linear programming problems that contain thousands of constraint and decision variables.

The simplex method uses iterative algorithm to find solutions to optimization problems. The method uses or provides data on slack variables, which represent unused resources and opportunity costs or shadow costs useful in sensitivity analysis. Therefore, simplex method is an effective and efficient method that overcomes the limitations of the linear programming model to find solutions to problems of optimization by ending at an optimal solution by jumping from the feasible vertex area to the following adjacent vertex area of optimal solution.

There exist differences between simplex method and linear programming method. These differences include the following: Graphical method is applied only in solving linear programming problems with only a maximum of two variables whereas the simplex method is used for solving linear programming problems with over three variables i.e. graphical is used where constraints contain only two variables while simplex is used when constraints contain more than 2 variables. Either the simplex method introduces the concept of slack variable or shadow costs whereas the linear programming method does not mention the concept of slack variables and shadow costs.

ReferencesHillier, F. S., Mark S. H., and Gerald L. (2000). Introduction to Management Science. Burr Ridge, IL:Irwin/McGraw-Hill.