Operations Research Chapter one

Introduction Operations Research is an Art and Science World War 2 George Dantzig [Linear Programming], First Computer (Father of computer) It had its early roots in World War II and is flourishing in business and industry with the aid of computer Primary applications areas of Operations Research include forecasting, production scheduling, inventory control, capital budgeting, and transportation.

What is Operations Research? The activities carried out in an organization.  Research The process of observation and testing characterized by the scientific method. Situation, problem statement, model construction, validation, experimentation, candidate solutions.  Operations Research is a quantitative approach to decision making based on the scientific method of problem solving.

What is Operations Research? Operations Research is the scientific approach to execute decision making, which consists of: The art of mathematical modeling of complex situations The science of the development of solution techniques used to solve these models The ability to effectively communicate the results to the decision maker

Definition of OR OR professionals aim to provide rational bases for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. Much of this work is done using analytical and numerical techniques to develop and manipulate mathematical and computer models of organizational systems composed of people, machines, and procedures.

Terminology The British/Europeans refer to “Operational Research", the Americans to “Operations Research" - but both are often shortened to just "OR". Another term used for this field is “Management Science" ("MS"). In U.S. OR and MS are combined together to form "OR/MS" or "ORMS". Yet other terms sometimes used are “Industrial Engineering" ("IE") and “Decision Science" ("DS").

Operations Research Models Linear Programming • Nonlinear Programming

Linear Programming: Model Formulation and Graphical Solution Chapter 2 Linear Programming: Model Formulation and Graphical Solution

Linear Programming Objectives of business firms frequently include maximizing profit or minimizing costs. Linear programming is an analysis technique in which linear algebraic relationships represent a firm’s decisions given a business objective and resource constraints. Steps in application: Identify problem as solvable by linear programming. Formulate a mathematical model of the unstructured problem. Solve the model.

Model Components and Formulation Decision variables - mathematical symbols that does not have a specific value representing controllable inputs. Objective function - a linear mathematical relationship describing an goal of the firm, in terms of decision variables, that is maximized or minimized Examples : Maximize profit Minimize cost Minimize distance Minimize time Constraints - restrictions placed on the firm by the operating environment stated in linear relationships of the decision variables. Parameters - numerical coefficients and constants used in the objective function and constraint equations. The objective and constraints must be definable by linear mathematical functional relationships

Graphical Solution of Linear Programming Models Graphical solution is limited to linear programming models containing only two decision variables (can be used with three variables but only with great difficulty). Graphical methods provide visualization of how a solution for a linear programming problem is obtained.

Step of Graphical method Drawing the two axis Plot the constraints as equations Determine the feasible solution points Optimal solution with objective function

Identification of Optimal Solution

Optimal solution coordinates

solution at all corner pointe

Optimal solution with objective function