Graphical and Simplex Methods of Linear Programming

Graphical and Simplex Methods of Linear Programming The graphical method is the more popular method to use because they are easy to use and understand. Working with only a few variables at a time they allow operations managers to compare projected demand to existing capacity We Have Skills To Write Papers In All Areas – Get the facts  . The graphical method is a trial and error approach that can be easily done by a manager or even a clerical staff. Since it is trial and error though, it does not necessarily generate the optimal plan. One downside of this method though is that it can only be used with two variables at the maximum.

The graphical method is broken down into the following five steps: 1) Determine the demand in each period. 2) Determine the capacity for regular time, over time, and subcontracting each period. 3) Find labor costs, hiring and labor costs, and inventory holding costs. 4) Consider company policy that may apply to the workers or to stock levels 5) Develop alternative plans and examine their total costs. When a company has a LP problem with more than two variables it turns to the simplex method.

This method can handle any number of variables as well as for certain give the optimal solution. In the simplex method we examine corner points in a methodical fashion until we arrive at the best solution which is either the highest profit or lowest cost. LP is used in a wide variety of companies in numerous applications. Airline companies use it to schedule their flights to maximize profit. Another use is for firms to figure out how much of a certain product to manufacture in order to maximize total profits.

It also is used by hospitals in order to figure out the most economic diet for patients. It is also a useful tool to figure out labor scheduling for a specific time period. Other applications include product mix planning, distribution networks, truck routing, financial portfolios, and corporate restructuring. All LP problems have four properties in common. The first, LP problems seek to maximize or minimize some quantity, usually profit or cost. The second commonality is that the presence of restrictions limits the degree to which the objective can be pursued.

A third is that there must be alternative courses of action to choose from. Lastly, the objective and constraints must be expressed in terms of linear equations or inequalities. Once the feasible region has been established there are a couple different ways to find the optimal solution. Two of them are the ISO profit solution and the corner point solution methods. The ISO method is the faster method of the two. It is where optimal solution is point in feasible region that produces the highest profit with many possible solution points in region.

Next you let objective function guide one towards optimal point in feasible region. You then plot line representing objective function on graph as a straight line. The corner point method is the simpler method but it also now involves looking at the profit of every corner point of the feasible region. It is based on the idea that an optimal solution to any problem lies at a corner point of the feasible region. To find point yielding maximum profit, one finds coordinates of each corner point and computes profit level at each point.