Advantages and Disadvantages of Linear ProgrammingThe model formulation is crucial in decisionmaking because it captures the core of the business choice problem. The process of transforming verbal descriptions and numerical data into mathematical formulations that accurately reflect the relationships between decisionmaking elements, objectives, and resourceuse constraints is known as formulation. Linear programming (L.P.) is a specific kind of technique used for economically allocating "scarce" or "limited" resources, like labour, material, machine, time, warehouse space, capital, energy, etc., to several competing activities, like goods, services, jobs, new equipment, projects, etc. based on a given optimality criterion. Resources that are limited in availability throughout the planning stage are referred to as scarce resources. The decisionmaker must know all these assumptions and attributes before using linear programming to solve a realworld choice issue. "linear" refers to a model's variables' linear relationships. As a result, every change in one variable will always result in a proportionate change in the other. For instance, double the investment in a certain project will be twice the return rate. Programming is the mathematical modelling and solution of problems involving the economic allocation of scarce resources by selecting a particular course of action or strategy from a range of possible options to reach the desired goal. Structure Of Linear ProgrammingGeneral Structure of L.P. ModelThree elements make up the L.P. model's overall structure. In decisionmaking processes and factors determining the objective function's superior value, we must examine various possibilities (courses of action). Of course, we wouldn't require L.P. if there were no options. The characteristics of the objective function and the accessibility of resources serve as the basis for evaluating various options. For this, we engage in several tasks, often indicated by x1, x2,... x.n. The amount to which each of these tasks is accomplished is reflected in the value of those activities. For instance, while manufacturing a product mix, the management may utilize L.P. to determine how many units of each product to produce with the help of its limited resources, such as labour, equipment, funds, and materials. Because the decision maker has power over them, these actions are sometimes referred to as decision variables. These choice factors, which are frequently connected in terms of finite resources, call for concurrent solutions. Every choice variable is nonnegative, controllable, and continuous. Specifically, x1>0, x2>0,....xn>0 The main purpose is: Each L.P. problem's objective function represents the objective mathematically in terms of a measurable quantity, such as profit, cost, revenue, distance, etc. It is shown as follows in its simplest form: Optimize (Maximize or Minimize) (Maximize or Minimize) Z equals c1x1 plus c2..X2... cn …xn Where Z is the performance measure variable and x1, x2,..., xn are functions of it. Quantities c1, c2...cn are parameters that show how much a unit of each variable x1, x2..., xn contributes to the performance measure Z. The graphical approach or simplex method determines the best value of the given objective function. The limitations: The degree to which a purpose may be fulfilled is always subject to specific restrictions (or constraints) on the utilization of resources, such as labour, machinery, raw materials, space, money, etc. Such limitations must be represented as linear equalities or inequalities in the decision variables, and an L.P. model's solution must adhere to these restrictions. When the objective function and the restrictions can be written as linear mathematical functions, the linear programming approach is a way to select the best option from a list of viable options. Linear Programming Application AreasIn commerce, industry, and several other industries, linear programming is the most often employed decisionmaking method. Several of the major application domains for linear programming will be covered in this section. 1. Farming applications These programmes come under the management and agriculture economics areas. At the same time, the latter is focused on the issues facing a specific farm, and the former deals with the agricultural economy of a country or area. Interregional rivalry and the best distribution of crop output are topics covered in the study of agricultural economics. Under restrictions on local land resources and overall demand, a linear programming model can be used to specify efficient production patterns. In agricultural planning, linear programming may allocate scarce resources, such as land, labour, water, and working capital, to maximize net revenue. 2. Applications in the Military Choosing an air weapon system against an adversary to keep them pinned down while reducing the amount of aviation fuel needed is an issue in military applications. The community defence against disaster problem, whose solution determines the number of defence units that should be used in a specific attack to provide the required level of protection at the least expensive cost, are variations of the transportation problem that maximize the total tonnage of bombs dropped on a set of targets. 3. Production Control
4. Financial Administration
5. Marketing Administration
6. Personnel Administration
Other areas where linear programming is used include administration, education, fleet management, contracting out work, running hospitals, and capital budgeting. Advantages of Linear ProgrammingThe advantages of linear programming include the following:
Disadvantages of Linear Programming
Linear Programming ObjectiveThe realvalued function whose value must be either maximized or minimized by the restrictions set out on the specified linear programming issue across a collection of potential solutions is the objective function in linear programming problems. It is simply a mathematical phrase that expresses the goal of the task and may be scaled up or down. The goal function has the mathematical formula z = ax + by. You may determine whether you need to maximize or decrease the objective function based on the problem's objective. It frequently indicates expense or profit. What Does an Objective Function for Linear Programming Entail?The objective function in linear programming issues is the realvalued function whose value must be either maximized or minimized under the constraints stated on the specific linear programming issue across various viable solutions. It is only a mathematical expression of the task's objective and may be scaled up or down. Z = ax + by is the equation for the goal function. Depending on the goal of the challenge, you could decide whether you need to maximize or reduce the objective function. It typically denotes a cost or gain. The most popular type of mathematical optimization can very well be linear programming, and several computer tools are available to solve linear programming issues.
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