Unit 4 – Systems Engineering Tools Deterministic Operations Research, Linear Programming Source: Introduction to Operations Research, 9th edition, Frederick S. Hillier, McGraw-Hill 1 1. What is Operations Research (OR) 2
What is Operations Research? • It is an application of scientific methods, techniques and tools to the analysis and solution. • It is a Process • It assists Decision Makers • It has a set of Tools • It is applicable in many Situations 3 What is Operations Research? Operations The activities carried out in an organization. Research The process of observation and testing characterized by the scientific method including situation, problem statement, model construction, validation, experimentation, candidate solutions. Model An abstract representation of reality. Mathematical, physical, narrative, set of rules in computer program. 4
What is Operations Research? It is a Systems Approach Include broad implications of decisions for the organization at each stage in analysis. Both quantitative and qualitative factors are considered. It finds Optimal Solution A solution to the model that optimizes (maximizes or minimizes) some measure of merit over all feasible solutions. It involves a Team A group of individuals bringing various skills and viewpoints to a problem. It includes many different OR Techniques A collection of general mathematical models, analytical procedures, and algorithms. 5 History of OR OR started just before World War II in Britain with the establishment of teams of scientists to study the strategic and tactical problems involved in military operations. The objective was to find the most effective utilization of limited military resources by the use of quantitative techniques. 6
History of OR Although scientists had (plainly) been involved in the hardware side of warfare (designing better planes, bombs, tanks, etc) scientific analysis of the operational use of military resources had never taken place in a systematic fashion before the Second World War. Military personnel were simply not trained to undertake such analysis. 7 History of OR These early OR workers came from many different disciplines, one group consisted of a physicist, two physiologists, two mathematical physicists and a surveyor. What such people brought to their work were "scientifically trained" minds, used to querying assumptions, logic, exploring hypotheses, devising experiments, collecting data, analysing numbers, etc. Many too were of high intellectual calibre (at least four wartime OR personnel were later to win Nobel prizes when they returned to their peacetime disciplines). 8
History of OR Following the end of the war, OR took a different course in the UK as opposed to in the USA. In the UK (as mentioned above) many of the distinguished OR workers returned to their original peacetime disciplines. As such OR did not spread particularly well, except for a few isolated industries (iron/steel and coal). In the USA OR spread to the universities so that systematic training in OR began. 9 History of OR You should be clear that the growth of OR since it began (and especially in the last 30 years) is, to a large extent, the result of the increasing power and widespread availability of computers . Most (though not all) OR involves carrying out a large number of numeric calculations. Without computers this would simply not be possible. 10
History of OR Manufacturers used operations research to make products more efficiently , schedule equipment maintenance, and control inventory and distribution. And success in these areas led to expansion into strategic and financial planning … and into such diverse areas as criminal justice, education, meteorology, and communications. 11 Future of OR A number of major social and economic trends are increasing the need for operations researchers . In today’s global marketplace, enterprizes must compete more effectively for their share of profits than ever before. And public and non-profit agencies must compete for ever-scarcer funding dollars. 12
Future of OR This means that all of us must become more productive . Volume must be increased. Consumers’ demands for better products and services must be met. Manufacturing and distribution must be faster . Products and people must be available just in time. 13 Objectives of Operations Research • Improve the quality in decision making. • Identify the optimum solution. • Integrating the system. • Improve the objectivity of analysis. • Minimize the cost and maximize the profit. • Improve the productivity. • Success in competitions and market leadership. 14
Applications of Operations Research • National plans & budgets. • Defense services operations. • Government developments & public sector units. • Industrial establishment & private sector units. • R & D and engineering division. • Public works department. • Business management. • Agriculture and Irrigation projects. • Education & Training. • Transportation and Communication. 15 Definitions • Operations Research (OR) is the study of mathematical models for complex organizational systems. • Optimization is a branch of OR which uses mathematical techniques such as linear and nonlinear programming to derive values for system variables that will optimize performance. • OR professionals aim to provide a rational basis for decision making by seeking to understand and structure complex situations and to use this understanding to predict system behavior and improve system performance. 16
The Process: Recognize the Situation • Manufacturing Situation – Planning – Design – Scheduling – Dealing with Defects – Dealing with Variability – Dealing with Inventory – … Example : Internal nursing staff not happy with their schedules; hospital using too many external nurses. 17 Formulate the Problem Formulate the Problem Situation Problem Statement • Define the Objective • Determine variables • Select measures • Identify constraints Example : Maximize individual nurse preferences subject to demand requirements, or minimize nurse dissatisfaction costs. 18
Gather Data • Production volume • Scheduling Situation • Fixed cost • Variable cost • Time Data • Labor • …. Example : Gather information about nurse profiles, work schedule, pay structure, overhead, demand requirement, supply, etc. 19 Construct a Model Formulate the Problem Situation Problem Statement Data Construct • Math. Programming Model a Model • Stochastic Model • Statistical Model Model • Simulation Model Example : Define relationships between individual nurse assignments and preference violations; define tradeoffs between the use of internal and external nursing resources. 20
Definitions • Model: A schematic description of a system, theory, or phenomenon that accounts for its known or inferred properties and may be used for further study of its characteristics. • System: A functionally related group of elements, for example: – The human body regarded as a functional physiological unit. – An organism as a whole, especially with regard to its vital processes or functions. – A group of interacting mechanical or electrical components. – A network of structures and channels, as for communication, travel, or distribution. – A network of related computer software, hardware, and data transmission devices. 21 Models of Operations Research Models of OR By nature of By structure environment Physical Analogue Mathematical Deterministic Probabilistic model model model Model Model 22
Models • Linear Programming – Typically, 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. The objective function and constraints all are linear functions of the decision variables. – Software has been developed that is capable of solving problems containing millions of variables and tens of thousands of constraints. • Network Flow Programming – A special case of the more general linear program. Includes such problems as the transportation problem, the assignment problem, the shortest path problem, the maximum flow problem, and the minimum cost flow problem. – Very efficient algorithms exist which are many times more efficient than linear programming in the utilization of computer time and space resources. 23 Models • Integer Programming – Some of the variables are required to take on discrete values. • Nonlinear Programming – The objective and/or any constraint is nonlinear. – In general, much more difficult to solve than linear. – Most (if not all) real world applications require a nonlinear model. In order to make the problems tractable, we often approximate using linear functions. 24
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