Homework SourseList and briefly explain some types of Linear programming ap
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Linear programming is a powerful quantitative tool used by operations managers and other managers to obtain optimal solutions to problems that involve restrictions or limitations, such as the available materials, budgets, and labour and machine time. These problems are referred to as constrained optimization problems. There are numerous examples of linear programming applications to such problems, including:
• Establishing locations for emergency equipment and personnel that will minimize response time
• Determining optimal schedules for airlines for planes, pilots, and ground personnel
• Developing financial plans
• Determining optimal blends of animal feed mixes
• Determining optimal diet plans
• Identifying the best set of worker–job assignments
• Developing optimal production schedules
• Developing shipping plans that will minimize shipping costs
• Identifying the optimal mix of products in a factory
Linear programming (LP) techniques consist of a sequence of steps that will lead to an optimal solution to problems, in cases where an optimum exists. There are a number of different linear programming techniques; some are special-purpose (i.e., used to find solutions for specific types of problems) and others are more general in scope. This supplement covers the two general-purpose solution techniques: graphical linear programming and computer solutions. Graphical linear programming provides a visual portrayal of many of the important concepts of linear programming. However, it is limited to problems with only two variables. In practice, computers are used to obtain solutions for problems, some of which involve a large number of variables
Linear programming models are mathematical representations of constrained optimization problems. These models have certain characteristics in common. Knowledge of these characteristics enables us to recognize problems that can be solved using linear programming. In addition, it also can help us formulate LP models. The characteristics can be grouped into two categories: components and assumptions
Four components provide the structure of a linear programming model:
1. Objective
2. Decision variables
3. Constraints
4. Parameters
Linear programming algorithms require that a single goal or objective, such as the maximization of profits, be specified. The two general types of objectives are maximization and minimization. A maximization objective might involve profits, revenues, efficiency, or rate of return. Conversely, a minimization objective might involve cost, time, distance travelled, or scrap. The objective function is a mathematical expression that can be used to determine the total profit.
In operation management, LP is used to solve a wide variety of problems such as production planning, transportation planning, labour scheduling, revenue management, productivity assessment, capacity planning.
MODEL FORMULATION An understanding of the components of linear programming models is necessary for model formulation. This helps provide organization to the process of assembling information about a problem into a model.
Graphical linear programming is a method for finding optimal solutions to twovariable problems.
The graphical method of linear programming plots the constraints on a graph and identifies an area that satisfies all of the constraints. The area is referred to as the feasible solution space. Next, the objective function is plotted and used to identify the optimal point in the feasible solution space. The coordinates of the point can sometimes be read directly from the graph, although generally an algebraic determination of the coordinates of the point is necessary. The general procedure followed in the graphical approach is:
1. Set up the objective function and the constraints in mathematical format.
2. Plot the constraints.
3. Identify the feasible solution space.
4. Plot the objective function.
5. Determine the optimum solution.
