Operations Research – Quantitative approach to decision making
Operations research is a system that deals with the application of advanced analytical techniques to help make better decisions. visit: assignmenthelpaus.com and get know more about Operations research and decision making.
Introduction to Operations Research
Unit objective:
Upon the completion of this unit, the learner would be able to:
 Define operations research
 Describe the significance of OR
 Explain models and their importance
 Differentiate among different categories of models
 Elucidate methodology in OR
 Identify application areas of OR models
 Describe techniques in OR
OR & Quantitative approach to decision making
Decisionmaking in todayís social and business environment has become a complex task. The uncertainty of the future and the nature of competition and social interaction greatly increase the difficulty of managerial decisionmaking. Knowledge and technology are changing rapidly, the new problems with little or no precedents these problems and provide leadership in the advancing global age, decisionmakers can not afford to make decisions by simply applying their personal experiences, guesswork or intuition, because the consequences of the wrong markets, producing the wrong products, providing inappropriate services, etc., will have major, often disastrous consequences for organizations.
Operations Research as one of the quantitative aid to decisionmaking offers the decisionmaker a method of evaluating every possible alternative (act or course of action) by using various techniques to know the potential outcomes. This is not to say, however, that management decisionmaking is simply about the application of operations research techniques.
In general, while solving a reallife problem, the decisionmaker must examine in both from quantitative as well as qualitative perspective. Information about the problem from both these perspectives needs to be brought together and assessed in the context of the problem. Based on some mixes of the two sources of information, a decision should be taken by the decisionmaker.
? Dear learner, consider a problem of an investor considering an investment in three alternatives: Stockmarket, real state and Bank Deposit. Discuss some of the quantitative and qualitative factors (information) to be considered to suggest an acceptable solution in each case? 
The evaluation of each alternative is extremely difficult or timeconsuming for two reasons: First, the amount and complexity of information that must be processed; second the number of alternative solutions could be so large that a decisionmaker simply can not evaluate all of them to select an appropriate one. For these reasons when there is a lack of qualitative information, decisionmakers increasingly turn to quantitative methods and use computers to arrive at their optimal solution to problems involving a large number of alternatives. The study of these methods and how decisionmakers use them in the decision process is the essence of the operations research approach.

History of Operations Research
It is generally agreed that operations Research came is to exist as a discipline during World War II when there was a critical need to manage scarce resources. The term ìOperations researchî was coined as a result of research on military operations during this war. Since the war involved strategic and tactical problems which were greatly complicated, to expect adequate solutions from individual or specialists in a single discipline was unrealistic. Therefore, group of individuals who collectively were considered specialists in mathematics, economics, statistics and probability theory, engineering, behavioural, and physical science were formed as a special unit within the armed forces to deal with strategic and tactical problems of various military operations. The objective was the most effective utilization of most limited military resources by the use of quantitative techniques.
After the war ended, scientists who had been active in the military OR groups made efforts to apply the operations research approach to civilian problems, related to business, industry, research and development, and even won Nobel prizes when they returned to their peacetime disciplines.
There are three important factors behind the rapid development in the use of operations research approach.
 The economic and industrial boom after World War II resulted in continuous mechanization, automation, decentralization of operations and division of management factors. This industrialization also resulted in complex managerial problems, and therefore the application of operations research to managerial decision making become
 Many operation researchers continued their research after the war. Consequently, some important advancement was made in various operations research techniques: linear programming and its solution by a method known as the simplex method, statistical quality control, dynamic programming, queuing theory and inventory theory were well developed during this
 Analytic power was made available by highspeed computers. The use of computers made it possible to apply many OR techniques for practical decision

Nature and Significance of Operations Research Assessment 1
The Operations research approach is particularly useful in balancing conflicting objectives (goals or interests), where there are many alternative courses of action
available to the decisionmakers. In a theoretical sense, the optimum decision must be one that is best for the organization as a whole. It is often called a global optimum. A decision that is best for one or more sections of the organization is usually called a suboptimum decision. The OR approach attempts to find a global optimum by analyzing interrelationships among the system components involved in the problem. In other words, operations research attempts to resolve the conflicts of interest among various sections of the organization and seeks the optimal solution which may not be acceptable to one department but is in the interest of the organization as a whole.
? Dear learner, discuss with your colleagues about how conflicting interests arise in the organization and how OR tries to balance these interests? 

Operation Research: Some definitions
The British/Europeans refer to “operational research”, the Americans to “Operations research” – but both are often shortened to just “OR” (which is the term we will use). Another term which is used for this field is “management science” (“MS”). The Americans sometimes combine the terms OR and MS together and say “OR/MS” or “ORMS”. Yet other terms sometimes used are “industrial engineering” (“IE”), “Decision Science” (“DSî) and ìproblem solvingî. In recent years there has been a move towards a standardization upon a single term for the field, namely the term “OR”.
Because of the wide scope of application of operations research, giving a precise definition is difficult. However, a few definitions of OR are given below.
Operations research is the application of the methods of science to complex problems in the direction and management of large systems of men, machines, materials and money in the industry, business, government and defence. 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 to analyze its policy and actions scientifically.
Operations Research Society, UK
Operations research is concerned with scientifically defining how to best design and operate manmachine systems usually requiring the allocation of scarce resources.
Operations Research Society, America
Apart from being lengthy, the definition given by ORSUK has been criticized, because it emphasizes complex problems and large systems leaving the impression that it is a highly technical approach suitable only to large organizations. The definition of ORSA contains an important reference to the allocation of scarce resources. The keywords used in the above definitions are scientific approach, scarce resources, system and model. The UK definition contains no reference to optimization, while the American definition has no reference to the word, best.
A few other definitions, which are commonly used and widely acceptable, are:
Operations research is a systematic application of quantitative methods, techniques and tools to the analysis of problems involving the operation of systems.
Operations research is essentially a collection of mathematical techniques and tools which in conjunction with the systems approach, is applied to solve practical decision problems of an economic or engineering nature.
Operations Research, in the most general sense, can be characterized as the application of scientific methods, techniques and tools, to problems involving operations of a system so as to provide those in control of the operations with optimum solutions to the problems.
Operation research seeks the determination of the optimum course of action of a decision problem under the restriction of limited resources. It is quite often associated almost exclusively with the use of mathematical techniques to model and analyze decision problems.
Operations research is the application of a scientific approach to solving management problems in order to help managers make better decisions. As implied by this and other definitions, operations research encompasses a number of mathematically oriented techniques that have either been developed within the field of management science or been adapted from other disciplines, such as natural sciences, mathematics, statistics, and engineering.
? Dear learners, would you discuss the above definitions and define OR in your words? 

Features of Operations Research Approach
From the previous discussions and various definitions of OR, important features or characteristics can be drawn. These features of the OR approach to any decision and control problems can be summarized as:

Interdisciplinary approach
Interdisciplinary teamwork is essential because while attempting to solve a complex management problem, one person may not have complete knowledge of all its aspects such as economic, social, political, psychological, engineering, etc. This means we should not expect a desirable solution to managerial problems from a single individual or discipline. Therefore, a team of individuals specializing in mathematics, statistics, computer science, psychology, etc, can be organized so that each aspect of the problem could be analyzed by particular specialists in that field.
But we shouldnít forget that certain problem situations may be analyzed even by one individual.
? Dear learner, can you mention situations which can be and can not be analyzed by a single individual? 

Methodological Approach
Operation research is the application of scientific methods, techniques and tools to problems involving the operations of systems so as to provide those in control of operations with optimum solutions to the problems.
note: A system is defined as an arrangement of components designed to achieve a particular objective(s) according to plan. The components may be either physical or conceptual or both but they share a unique relationship with each other and with the overall objective of the system.

Wholistic Approach or Systems Orientation
While arriving at a decision, an operation research team examines the relative importance of all conflicting and multiple objectives and the validity of claims of various departments of the organization from the perspective of the whole organization.

Objectivistic Approach
The OR approach seeks to obtain an optimal solution to the problem under analysis. For this, a measure of desirability (or effectiveness) is defined, based on objective(s) of the organization. A measure of desirability so defined is then used to compare alternative courses of action with respect to their outcomes.
 Decision Making ñ OR increases the effectiveness of management decisions. It is the decision science which helps management to make better decisions. So the major premise of OR is decision making, irrespective of the situation
 Use of Computers: OR often requires a computer to solve the complex mathematical model or to perform a large number of computations that are
 Human factors: In deriving quantitative solution, we do not consider human factors which doubtlessly play a great role in the problems. So the study of the OR is incomplete without a study of human
Operations research, though young, is a recognized and established discipline in the field of business administration. The application of management science techniques is widespread, and they have been frequently credited with increasing efficiency and productivity of business firms.
Activity
1. Operations research is an aid for the executive in making his/her decisions by providing the needed quantitative information, based on scientific method analysis. Discuss.
2. Discuss the significance and scope of OR in modern management and Ethiopian context?
3. Quantitative techniques complement the experience and judgment of an executive in decision making. They do not and can not replace it. Discuss. 

Models and Modeling in Operations Research Assessment 1
Both simple and complex systems can easily be studied by concentrating on some portion or key features instead of concentrating on every detail of it. This approximation or abstraction, maintaining only the essential elements of the system, which may be constructed in various forms by establishing relationships among specified variables and parameters of the system, is called a model. In general, models attempt to describe the essence of a situation or activity by abstracting from reality so that the decisionmaker can study the relationship among relevant variables in isolation.
Models do not, and cannot, represent every aspect of reality because of the innumerable and changing characteristics of the reallife problems to be represented. Instead, they are a limited approximation of reality. For example, to study the flow of materials through a factory, a scaled diagram on paper showing the factory floor, the position of equipment, tools, and workers can be constructed. It would not be necessary to give such details as the colour of machines, the height of the workers, or the temperature of the building. For a model to be effective, it must be representative of those aspects of reality that are being investigated and have a major impact on the decision situation.
? Dear learner, can you mention some of the limitations of models? 
A model is constructed to analyze and understand the given system for the purpose of improving its performance. The reliability of the solution obtained from a model depends on the validity of the model in representing the system under study. A model allows the opportunity to examine the behavioural changes of a system without disturbing the ongoing operations.
Note: The key to model building lies in abstracting only the relevant variables that affect the criteria of the measures of performance of the given system and expressing the relationship in a suitable form. But oversimplification of a problem can lead to a poor decision. Model enrichment is accomplished through the process of changing constants into variables, adding variables, relaxing linear and other assumptions, and including randomness.

Classification of OR Model
As we discussed earlier, the OR model is an abstract representation of an existing problem situation. It can be in the form of a graph or chart, but most frequently an OR model consists of a set of mathematical relationships. These mathematical relationships are made up of numbers and symbols.
There are many ways to classify models:

Classification based on the structure
 Physical Models
These models provide a physical appearance of the real object under study either reduced in size or scaled up. Physical models are useful only in design problems because they are easy to observe, build, and describe. Since these models can not be manipulated and are not very useful for prediction, problems such as portfolio analysis selection, media selection, production scheduling, etc cannot be analyzed by physical models.
 Symbolic models
These models use symbols (letters, numbers) and functions to represent variables and their relationships to describe the properties of the system.

Classification based on function or purpose
Models based on the purpose of their utility include:
 Descriptive models
Descriptive models simply describe some aspects of a situation, based on observation, survey, questionnaire results or other available data of a situation and do not recommend anything. Example: Organizational chart, plant layout diagram, etc.
 Predictive Models
These models indicate ìIf this occurs, then that followî. They relate dependent and independent variables and permit trying out ìwhat ifî questions. In other words, these models are used to predict outcomes due to a given set of alternatives for the problem. These models do not have an objective function as a part of the model to evaluate decision alternatives.
For example, S = a + bA +cI is a model that describes how the sales (S) of a product changes in advertising expenditures (A) and disposable personal income (I). Here, a, b, and c are parameters whose values must be estimated.
 Normative (Optimization) models
These models provide the ìbestî or ìOptimalî solution to problems subject to certain limitations on the use of resources. These models provide recommended courses of action. For example, in mathematical programming, models are formulated for optimizing the given
the objective function, subject to restrictions on resources in the context of the problem under consideration and nonnegativity of variables. These models are also called prescriptive models because they prescribe what the decisionmaker ought to do.

Classification Based on Time Reference
 Static Models
Static models represent a system at some specified time and do not account for changes over time. For example, an inventory model can be developed and solved to determine an economic order quantity for the next period assuming that the demand in planning period would remain the same as that for today.
 Dynamic models
In dynamic models, time is considered as one of the variables and allows the impact of changes due to change in time. Thus, sequences of interrelated decisions over a period of time are made to select the optimal course of action to optimize the given objective. Dynamic programming is an example of a dynamic model.

Classification based on Degree of certainty
 Deterministic Models
If all the parameters, constants and functional relationships are assumed to be known with certainty when the decision is made, the model is said to be deterministic. Thus, in such a case, the outcome associated with a particular course of action is known. That is, for a specific set of input values, there is a uniquely, determining output which represents the solution of the model under consideration of certainty. The results of the models assume a single value. Linear programming models are examples of deterministic models.
 Probabilistic (Stochastic) models
Models in which at least one parameter or decision variable is a random variable are called probabilistic (or stochastic). Since at least one decision variable is random, a dependant variable which is the function of the independent variable(s) will also be random. This means consequences or pays off due to certain changes in the independent variable can not be produced with certainty. However, it is possible to predict a pattern of values of both the variables by their probability distribution. Insurance against the risk of fire, accidents, sickness, etc are examples where the pattern of events is studied in the form of a probability distribution.

Classification Based on Method of solution or Quantification
 Heuristic Model
These models employ some sets of rules which, though perhaps not optimal, do facilitate solutions of problems when applied in a consistent manner.
 Analytical Models
These models have a specific mathematical structure and thus can be solved by known analytical or mathematical techniques. Any optimization model (which requires maximization or minimization of an objective function) is an analytical model.
 Simulation Models
These models have a mathematical structure but are not solved by applying mathematical techniques to get a solution. Instead, a simulation model is essentially computerassisted experimentation on a mathematical structure of a reallife problem in order to describe and evaluate its behaviour under certain assumptions over a period of time.
Simulation models are more flexible than mathematical ones and therefore, can be used to represent a complex system which otherwise can not be represented mathematically. These models do not provide a general solution like those of mathematical Models.
? Dear learner, do you think that the above classification of models is mutually exclusive? Support your response with evidence. 

Advantage of Models
Models, in general, are used as an aid for analyzing complex problems. However, a model can also serve other purposes as:
 A model provides economy in the representation of the realities of the system. That is, models, help decisionmakers to visualize a system so that he/she can understand the systemís structure or operation in a better any. For example, it easier to represent a factory layout on paper than to construct it. It is cheaper to try out modifications of such systems by rearrangement on
 The problem can be viewed in its entirety, with all the components being considered simultaneously.
 Models serve as aids to transmit ideas and visualization among people in the organization. For example, process chart can help the management to communicate about better work methods to
 A model allows us to analyze and experiment in a complex situation to a degree that would be impossible in the actual system and its environment. For example, the experimental firing of the satellite may be costly and require years of
 Models simplify the investigation considerably and provide a powerful and flexible for predicting the future state of the processor

The methodology of Operations Research
For effective use of OR techniques, it is essential to follow some steps that are helpful for decisionmakers to make a better solution. The flow diagram representing the methodology of OR is shown as:
Step 1. Observation and defining a problem
The first step in the OR process is the identification of a problem that exists is a system (organization). The system must be continuously and closely observed so that problems can be identified as soon as they occur or anticipated. Problems are not always the results of crisis, but instead, frequently involve an anticipatory or planning situation. Once it has been determined that a problem exists, the problem must be clearly and concisely defined. Because improperly defining a problem can easily result in no solution or an inappropriate solution. Since the existence of a problem implies that the objectives of the firm are not being met in some way, the goals (objectives of the organization) must also be clearly defined.
? Dear learner, can you identify an individual(s) who are responsible to identify problems and problems they face while they identify these problems? 
Step 2. Formulating a model
Model formulation involves an analysis of the system under study, determining the objective of the decisionmaker, and alternative course of action, etc, so as to understand and describe, in precise terms, the problem that an organization faces.
The major steps which have to be taken into consideration for formulating the model are:
 Problem Components.
The first component of the problem to be defined is the decisionmaker who is not satisfied with the existing state of affairs. The interaction with the decisionmaker will help the OR specialist in knowing his/her objectives. That is, either he/she has already obtained some solution of the problem and wants to retain it, or he wants to improve it to a higher degree. If the decisionmaker has conflicting multiple objectives, he/she may be advised to rank the objectives in the order of preference; overlapping objectives maybe
 Decision environment
It is desirable to know about the resources such as managers, employees equipment, etc which are required to carry out the policies of the organization considering the social and ecological environment in which the organization functions. Knowledge of such factors will help in modifying the initial set of decisionmakerís objectives.
 Alternative courses of Action
The problem arises only when there are several courses of action available for a solution. An exhaustive list of course of action can be prepared in the process of going through the above steps of formulating the problem. Courses of action which are not feasible with respect to objectives and resources may be ruled out.
 Measure of effectiveness
A certain measure of effectiveness or performance is required in order to evaluate the merit of several courses of action. The performance or effectiveness can be measured in different units such as birr (net profits), percentage (share of market desired), time dimension (service or waiting time).
 Collecting Data and Constructing a Mathematical Model
After the problem is clearly defined and understood, the next step is to collect the required data and then formulate a mathematical model. Model construction consists of hypothesizing relationships between variables subject to and not subject to control by decisionmaker. Certain basic components required in every decision problem model are:
 Controllable (decision) Variables – These are the issues or factors in the problem whose values are to be determined (in the form of numerical values) by solving the model. The possible values assigned to these variables are called decision alternatives (strategies or courses of actions). Example, in LPP the number of units produced is a decision variable.
 Uncontrollable variable. These are the factors whose numerical value depends upon the external environment prevailing around the organization. The values of these variables are not under the control of the decisionmaker and are also termed as the state of nature.
 Objective
It is a representation of (i) the criterion that expresses the decisionmakerís manner of evaluating the desirability of alternative values of decision variables, and (ii) how that criterion is to be optimized (minimized or maximized. A stated objective helps to focus attention on what the problem actually is.
 Constraints or Limitations
These are the restrictions on the values of the decision variables. These restrictions can arise due to limited resources such as space, money, manpower, material, etc. The constraints may be in the form of equations or inequalities.
 Functional relationships
In a decision problem, the decision variables in the objective function and in the constraints are connected by a specific functional relationship. A general decision problem model might take the form:
Optimize (Max or Min) Z = f(x) Subject to the constraints:
gi(x) (≤, = ≥ ) bi; i = 1,2,Ö..m and x ≥ 0
Where, x = a vector of decision variables (x_{1}, x_{2}, x_{3}, x_{n})
f(x) = Criterion or objective function to be optimized gi(x) = the ith constraint
bi = fixed amount of the ith resource
A model is referred to as a linear model if all functional relationships among decision variables X_{1}, X_{2}, X_{n} in f(x) and g(x) are of a linear form. But if one or more of the relationships are non ñ linear, the model is said to be a nonlinear model
 Parameters These are constants in functional relationships. Parameters can be deterministic or probabilistic in
? Dear learner, take the case of the furniture manufacturing unit at Adama University. Identify and define the unstructured problem of the unit and construct a real OR model for the unit? 
Step 3.Solving the Mathematical Model
This involves obtaining the numerical values of decision variables. Obtaining these values depends on the specific form or type, of mathematical models. Solving the model requires the use of various mathematical tools and numerical procedures. In general, there are two categories of methods used for solving an OR model.
 Optimization model. These models yield the best value for the decision variables both for unconstrained and constrained problems. In constrained problems, these values simultaneously satisfy all of the constraints and provide optimal or acceptable value for the objective function or measure of effectiveness. The solution so obtained is called the optimal solution to the
 Heuristic Model. These methods yield values of the variables that satisfy all the constraints, but not necessarily provide the optimal solution. However, these values provide an acceptable value of the objective
Heuristic Methods are sometimes described as ìrules of thumbî which work. These methods are used when obtaining an optimal solution is either very time consuming or the model is complex.
Difficulties in problemsolving
Some times difficulties in problemsolving arise due to lack of an appropriate methodology for it and psychological perceptions on the part of the problem solver. The major difficulties in problemsolving:
Step 4. Validating (Testing) the solution
After solving the mathematical model, it is important to review the solution carefully to see that values make sense and that the resulting decisions can be implemented. Some of the reasons for validating the solution are:
 The mathematical model may not have enumerated all the limitations of the problem under
 A certain aspect of the problem may have been overlooked, omitted or simplified,
 The data may have been incorrect estimated or recorded, perhaps when entered into the
Step 5. Implementing the solution
The decisionmaker has not only to identify good decision alternatives but also to select alternatives that are capable of being implemented. It is important to ensure that any solution implemented is continually reviewed and updated in light of a changing environment.
Step 6. Modifying the Model
For a mathematical model to be useful, the degree to which it actually represents the system or problem being modelled must be established. If during validation, the solution cannot be implemented, one needs to (a) identify the constraint that was omitted during the original problem formulation or (b) finds if some of the original constraints were incorrect and need to be modified. In all such cases, one must return to the model formulation step and carefully make the appropriate modifications to represent more accurately the given problem. A model must be applicable for a reasonable time period and should be updated from time to time, taking into consideration the past, present, and future aspects of the problem.
Step 7. Establishing control over the solution
The dynamic environment and changes within the environment can have significant implications regarding the continuing validity of models and their solutions. Thus, a control procedure has to be established for detecting significant changes in decision variables of the problem so that suitable adjustments can be made in the solution without having to build a model every time a significant change occurs.
 Features of OR solution
A solution that works but is quite expensive compared to the potential savings from its application should not be considered successful. Also, a solution that is well within the budget but which does not accomplish the objective is not successful either. The following are features of a good solution:
 Technically appropriate. The solution should work technically; meet the constraints and operate in the problem
 The solution must be useful for a reasonable period of time under the conditions for which it was designed.
 Economically viable. The economic value should be more than what it costs to develop and should be seen as a wise investment in hiring OR
 Behaviorally appropriate. The solution should be behaviorally appropriate and must remain valid for a reasonable period of time within the
 Basic Operations Research Models
There is no unique set of problems which can be solved by using OR models or techniques. Some OR models or techniques include:
Allocation Models
Allocation models are used to allocate resources to activate in such a way that some measure of effectiveness (objective function) is optimized. Mathematical programming is the broad term of OR techniques used to solve allocation problems.
If the measure of effectiveness such as profit, cost, etc., is represented as a linear function of several variables and if limitations of resources (constraints) can be expressed as a system of
linear inequalities or equalities, the allocation problem is classified as linear programming problems.
But, if the objective function of any or all constraints can not be expressed as a system of linear equalities or inequalities, the allocation problem is classified as a nonlinear programming problem.
When the solution values or decision variables for the problem are restricted to being integer values, the problem is classified as an integer programming. The problem having multiple, conflicting and incommensurable objective function (goals) subject to linear constraints is called goal programming. If decision variables in the linear programming problem depend on chance, such a problem is called a stochastic programming problem.
If resources such as workers, machines or salesmen can be assigned to perform a certain number of activities such as jobs or territories on one to one basis so as to minimize total time, cost or distance involved in performing a given activity, such problems are classified as assignment problems. Conversely, if the resources can be used for more than one activity, the allocation problem is classified as a transportation problem.
Inventory Model
Inventory Models deal with the problem of determination of how much to order at a point in time and when to place an order. The main objective is to minimize the sum of three conflicting inventory costs: the Cost of holding or carrying extra inventory, the cost of shortage or delay in delivery of items when it is needed, a cost of ordering or setup.
Competitive (Game Theory) Model
These models are used to characterize the behaviour of two or more opponents (called players) who compete for the achievement of conflicting goals.
Network Models
These models are applied to the management (planning, controlling and scheduling) of large scale projects. PERT/CPM Techniques help in identifying potential trouble spots in a project through the identification of the critical path. These techniques improve project coordination and enable the efficient use of resources. Network methods are also used to determine timecost tradeoff, resource allocation and updating of activity time.
Decision analysis Model
These models deal with the selection of an optimal course faction given the possible payoffs and their associated probabilities of occurrence. These models are broadly applied to problems involving decision making under risk and uncertainty.
 Operations Research Techniques
OR techniques can be loosely classified into five categories
there is the structure of Operations Research Assessment 1 Homework Answers
Source: Taylor, 1990, Introduction to Management Science, 3^{rd} edition, Brown Publisher
Linear Mathematical Programming Techniques refer to a predetermined set mathematical solution steps used to solve a problem, while probabilistic techniques are techniques with model parameters that are not known with certainty. Inventory models are specifically designed for the analysis of inventory problems frequently encountered by business firms. On the other hand, network techniques consist of models that are represented as diagrams rather than strictly mathematical relationship. As such, these models offer a pictorial representation of a system.
Other linear and nonlinear Techniques deal with calculusbased models.
Note: This classification is loose as many of the techniques cross over between classifications. Example, Network, inventory models can be either deterministic or probabilistic.
Summary
· Management science is the application of a scientific approach to solving management problems in order to help managers make better decisions. · Management science encompasses a logical, systematic approach to problemsolving, which closely parallels what is known as the scientific method for attacking problems and includes generally recognized ordered set of steps including Observation, the definition of problems, model construction, model solution, solution testing, implementation of solution results. · A management science model is an abstract representation of an existing problem situation. ï Management science techniques roughly can be categorized as Linear mathematical programming, probabilistic techniques, inventory techniques, and network techniques, other linear and nonlinear techniques. 
O Activity
1. Discuss what the management science approach to problemsolving encompasses? 2. Explain what a model is and how it is used in management science? 3. The ultimate test of a manager who uses management science techniques is the ability to transfer knowledge in this material into the business world. What does it mean? 4. Suppose you are being interviewed by the manager of the commercial firm for a job in a research department which deals with the application of quantitative techniques. Explain the scope and purpose of quantitative technique and its usefulness to the firm. Give some examples of the applications of quantitative techniques in the industry. 5. Management science is an ongoing process. Why do you think is the reason? 6. Distinguish between model results that recommend a decision and model results that are descriptive. 
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