OPERATIONS RESEARCHCHAPTER 01 - INTRODUCTION

DEFINITIONS UK: Operational Research is the application of the methods of science

to complex problems arising in the direction and management of large systems of men, machines, materials, and money in industry, business, government, and defense. The distinctive approach is to develop a scientific model of the system incorporating measurements of factors such as chance and risk, with which to predict and compare the outcomes of alternative decisions, strategies, or controls. The purpose is to help management determine its policy and actions scientifically.

USA: Operational Research is concerned with scientifically deciding how to best design and operate man-machine systems, usually under conditions requiring the allocation of scarce or limited resources.

APPLICATIONS Military:

Radar deployment policies. Antiaircraft fire control. Fleet convoy sizing. Detection of enemy submarines. Military offensive and defensive plans.

Finance and economy: Oil companies (prices and logistics) Traffic control and vehicle routing Health planning Travel and tourism Government planning Computers and Technology

MODELING IN ORReal

System Model

Real Conclusions

Model Conclusions

Formulation

Interpretation

Deduction

Validation

PRINCIPLES OF MODELING Do not build a complicated model when a simple one will suffice. Beware of molding the problem to fit the technique. The deduction phase of modeling must be conducted rigorously. Models should be validated before implementation. A model should never be taken too literally. A model should neither be pressed to do, nor criticized for failing to do,

that for which it was never intended. Some of the primary benefits of modeling are associated with the

process of developing the model. A model cannot be any better than the information that goes into it. Models cannot replace decision makers.

TYPES OF OR Linear Programming: a typical mathematical program consists of a

single objective function, representing either a profit to be maximized or a cost to be minimized, and a set of constraints that circumscribe the decision variables.

Integer Programming: is concerned with optimization problems in which some of the variables are required to take on discrete values.

Dynamic Programming: it describes a process in terms of states, decisions, transitions and returns.

Nonlinear Programming: is the process of solving an optimization problem defined by a system of equalities and inequalities, collectively termed constraints, over a set of unknown real variables, along with an objective function to be maximized or minimized, where some of the constraints or the objective function are nonlinear.

TYPES OF OR Simulation: is a very general technique for estimating statistical

measures of complex systems. A system is modeled as if the random variables were known. Then values for the variables are drawn randomly from their known probability distributions. Each replication gives one observation of the system response. By simulating a system in this fashion for many replications and recording the responses.

Network Flow Programming: describes a type of model that is a special case of the more general linear program. The class of network flow programs includes such problems as the transportation problem, the assignment problem, the shortest path problem, the maximum flow problem, the pure minimum cost flow problem, and the generalized minimum cost flow problem.

PHASES OF OR STUDY Definition of the problem:

Describe the goal or objective of the study. Identify the decision alternatives. Recognize the limitations, restrictions, and requirement of the system.

Construction of the model: Choose the best appropriate model in accordance with the nature of the system.

Solution of the model: concerning the behavior of the solution due to the changes of the system

parameters. Validation of the model:

Compare the solution with historic data and determine the predictability of the model.

Implementation of the final results: Control and monitor the execution of the solution.