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Linear programming (LP) is a powerful tool that operations managers use in order to determine how to best allocate their scarce resources (Keyes 2007) in a line, which provides the shortest connection between the points. It is a mathematical technique for planning and making the necessary decisions to allocate resources, which concerned with the maximization or minimization of a linear objective function or the value of the objective and the constraints on that function to guarantee the optimal solution. There are special software designed to solve large and complex LP problems.

Example for use of linear programming; If OM needs to compare between virtual and original producer. If virtual producers is better than the original producer by either making more output with the same input or making the same output with less input then the original producer is inefficient. The procedure of finding the best virtual producer can be formulated as a linear program. Analyzing the efficiency of n producers is then a set of n linear programming problems.

The objective function is function associated with an optimization problem which determines how good a solution is, for instance, the total cost of edges in a solution to a traveling salesman problem.
There are requirement of LP problem, which must identifies. LP problems seek to maximize or minimize some quantity in other word minimise cost and maximise profit and presence of restrictions, which limits the degree to which we can pursue our objective. There must be alternative courses of action to choose from provided by the objective function and constraints. The objective and constraints in linear programming problems must be express in terms of linear equations (Keyes 2007); in which each term is either, a constant or a product of a constant times the first power of a variable.
There are three types of constraints, the upper limits where the amount used is less/equal the amount of a resource, the lower limits where the amount used is more/equal the amount of the resource and the equalities where the amount used is equal to the amount of the resource (Heizer 2005, appendix B). The constraints more important than the objective function in a linear programming model because in order for operation mangers to achieve the improvement of the optimal solution by finding a way to reduce the binding constraints. Reduction of the binding constraints will deteriorate the objective the function value.


Reference:

• Jessica Keyes, 2007: Project Management and Linear Programming
• Dantzig, George B., 1997 Linear Programming: Introduction.
• Jay Heizer, Barry Render 2005: Operations Management 8-e