March 16, 2016

Optimizing the Use of Resources with Linear Programming - Review Notes

Linear programming, or LP, is one of the most powerful tools of management science. It is a mathematical technique used to allocate limited resources among competing demands in an optimal way. LP is a mathematical optimization technique.

Linear programming problems have limited resources, workers, equipment, finances or material as constraints of the problem. They have an explicit objective such as to maximize profit or minimize cost. The solution must give the maximum profit or minimum cost as the case may be.  There must be linearity and homogeneity in constraints and objective function. Another requirement  is divisibility. Normal linear programming assumes that products and resources which are represented as variable in the problem can be subdivided into fractions. If this subdivision is not possible, a modification of linear programming called integer programming is used.

The steps in the graphical linear programming optimizing process are to formulate the problem in mathematical terms, plot the constraint equations, determine the area of feasibility, plot the objective function, and finally find the optimal point.

Spreadsheets can be used to solve linear programming problems and most spreadsheets have built-in optimization routines that are very easy to use and understand. For example, Microsoft Excel has an optimization tool called Solver. 

To define an optimization model in Excel you'll follow these essential steps:

Organize the data for your problem in the spreadsheet in a logical manner.
Choose a spreadsheet cell to hold the value of each decision variable in your model.
Create a spreadsheet formula in a cell that calculates the objective function for your model.
Create a formulas in cells to calculate the left hand sides of each constraint.
Use the dialogs in Excel to tell the Solver about your decision variables, the objective, constraints, and desired bounds on constraints and variables.
Run the Solver to find the optimal solution.

To begin, click the Data tab, and in the Analysis group, click Solver.

 Note: Solver is installed by clicking the Microsoft Office Button, then Excel Options, followed by Add-Ins. In the Manage list, click Excel Add-ins, check the Solver Add-in box, and then click OK.

The Solver Parameters dialog box will appear

More detailed explanation of Excel Solver

Using Excel Solver and Solving LPP - YouTube Video


David JohnK
Has more videos on using Excel for various purposes

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Updated  16 Mar 2016, 4 Dec 2012

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