Graphical and Simplex Methods of Linear Programming

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Topics: Optimization
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. 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

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