Linear Programming Concept Paper
Linear Programming Concept Paper
There are two types of linear programming:
1.Linear Programming- involves no more than 2 variables, linear programming problems can be structured to minimize costs as well as maximize profits. Due to the increasing complexity of business organizations, the role of the management executive as a decision maker is becoming more and more difficult. Linear programming is a useful technique to solve such problems.
The necessary condition is that the data must be expressed in quantitative terms in the form of linear equations and inequalities. The general nature of the business problems in which linear programming can be effectively used are multifaceted. They include purchasing, transportation, job assignments, production scheduling and mixing. Linear programming provides a method of maximizing or minimizing a first degree function subject to certain environmental restrictions or constraints which are usually in the form of equations and inequalities.
2.Simplex method- is an algorithm for solving linear programming with any number of variables. Most real-world linear programming problems have more than two variables and thus are too complex for graphical solution. A procedure called the simplex method may be used to find the optimal solution to such problems. The simplex method is actually an algorithm (or a set of instructions) with which we examine corner points in a methodical fashion until we arrive at the best solution—highest profit or lowest cost. Computer programs (such as Excel OM and POM for Windows) and Excel spreadsheets are available to solve linear programming problems via the simplex method. (Operations Management, 10th Edition. Pearson Learning Solutions p. 704).
A few examples of problems in which LP has been successfully applied in operations management are: 1. Scheduling school buses to minimize the total distance traveled when carrying students 2. Allocating police patrol units to high crime areas to minimize response time to 911 calls 3. Scheduling tellers at banks so that needs are met during each hour of the day while minimizing the total cost of labor 4. Selecting the product mix in a factory to make best use of machine- and labor-hours available while maximizing the
firm’s profit 5. Picking blends of raw materials in feed mills to produce finished feed combinations at minimum cost (Operations Management, 10th Edition. Pearson Learning Solutions p. 690).
All LP problems have four requirements: an objective, constraints, alternatives, and linearity: 1.LP problems seek to maximize or minimize some quantity (usually profit or cost). We refer to this property as the objective function of an LP problem. The major objective of a typical firm is to maximize dollar profits in the long run. In the case of a trucking or airline distribution system, the objective might be to minimize shipping costs.
Objective function- A mathematical expression in linear programming that maximizes or minimizes some quantity (often profit or cost, but any goal may be used). 2.The presence of restrictions, or constraints, limits the degree to which we can pursue our objective. For example, deciding how many units of each product in a firm’s product line to manufacture a quantity (the objective function) subject to limited resources (the constraints).
Constraints- Restrictions that limit the degree to which a manager can pursue an objective. 3. There must be alternative courses of action to choose from. For example, if a company produces three different products, management may use LP to decide how to allocate among them its limited production resources (of labor, machinery, and so on). If there were no alternatives to select from, we would not need LP. 4. The objective and constraints in linear programming problems must be expressed in terms of linear equations or inequalities.(Operations Management, 10th Edition. Pearson Learning Solutions p. 691). ISO Profit Solution Method- An approach to solving a linear programming minimization problem graphically. Once the feasible region has been established, several approaches can be taken in solving for the optimal solution. The fastest one to apply is called the iso-profit line method Corner-Point Solution Method A second approach to solving linear programming problems employs the corner-point method. This technique is simpler in concept than the iso-profit line approach, but it involves looking at the profit at every corner point of the
feasible region.(Operations Management, 10th Edition. Pearson Learning Solutions p. 695).