Operations Research — Part 1 MCQs with Explanations

A decision method is a formal (axiomatic) system, starting with a decision model, that contains at least one action axiom. Decision models are used to model a decision being made once as well as to model a repeatable decision-making approach that will be used over and over again.

Every mathematical model represents data in numerical form. Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application.

A physical model is example of a verbal model. An iconic model is an exact physical representation and may be larger or smaller than what it represents.

The qualitative approach to decision analysis relies on Experience, Judgement and Intuition. Quantitative analysis is the process of collecting and evaluating measurable and verifiable data such as revenues, market share, and wages. Quantitative analysis helps in evaluating performance, assessing financial instruments, and making predictions.

Operations Research, which is a very powerful tool for Decision – Making. Operations research is important because it is a helpful tool used to solve complex problems under uncertainty. Operations research techniques fill this void with methods that quantify issues and give business managers a better basis for making decisions.

J.F. McCloskey and F.N. Trefethen coined the term Operations Research.

H.M. Wagner defined Operations Research as scientific approach to problem solving for executive management.

C. Kitte defined Operations Research as an aid for the executive in marketing his decisions by providing him with the quantitative information based on the scientific method of analysis.

The term Operations Research was coined in the year 1940. The term "operational research" was originally used in Britain during World War II to connote scientific research done to integrate new radar technologies into Royal Air Force tactics. By 1941 the term had expanded to encompass research done to assist military officers in developing tactics and planning combat operations, whether or not technology played a critical role in the analysis.

This innovative science of Operations Research was discovered during World War II. The ambiguous term operations research (O.R.) was coined during World War II, when the British military management called upon a group of scientists together to apply a scientific approach in the study of military operations to win the battle.

Operations Research was known as an ability to win a war without really going in to a Battle field and Fighting.

Morse and Kimball (1946) defined Operations Research as scientific method of providing executive departments with a quantitative basis for decisions regarding the operations under their control. Kimbal (1946) “OR is a scientific method of providing executive department with a quantitative basis for decision regarding the operations under their control.

Operations Research has the characteristics the it is done by a team of Scientists. Operations research attempts to evaluate the effect of changes in any part of a system on the performance of the system as a whole and to search for causes of a problem that arises in one part of a system in other parts or in the interrelationships between parts. In industry, a production problem may be approached by a change in marketing policy.

There is a great scope for Economists, Administrators and Statisticians and Technicians working as a team to solve problems of defence by using the Operations Research approach.

Operations Research emphasizes on the overall approach to the system. This characteristics of Operations Research is often referred as Team Approach. Operations research (OR) is an analytical method of problem-solving and decision-making that is useful in the management of organizations. In operations research, problems are broken down into basic components and then solved in defined steps by mathematical analysis.

Operations Research cannot give perfect Answers and Solutions to problems.

Operations Research study generally involves three phases. 1.Judgment Phase. This consists of: (i) Determination of the operation (ii) establishment of the objectives and values related to the operation (iii) Determination of the suitable measures of effectiveness and (iv) formulation of the problems relative to the objectives. 2.Research Phase. This phase utilizes; (i) Operations and data collection for a better understanding of the problems, (ii) Formulation of hypothesis and model, (iii) observation and experimentation to test the hypothesis on the basis of additional data, (iv) Analysis of the available information and verification of the hypothesis using pre-established measures of effectiveness, and (v) predictions of various results from the hypothesis (vi) generalization of the various results and consideration of alternative methods. 3. Action Phase. It consists of making recommendations for the decision process by those who first posed the problems for consideration or by anyone in a position to make a decision, influencing the operation in which the problem occurred.

Allocation models involves the allocation of resources to activities in such a manner that some measure of effectiveness is optimized. Allocation models can be created to present possible asset allocation strategies for clients. Diversifying investments by asset categories can offset the fluctuations of the performance of the total portfolio. Besides offering models, OIPA supports the use of funds through allocation configuration.

Allocation problems can be solved by Linear Programming Technique and Non – Linear Programming Technique.

In Deterministic Models, everything is defined and the results are certain. Mathematical model in which outcomes are precisely determined through known relationships among states and events, without any room for random variation. In such models, a given input will always produce the same output, such as in a known chemical reaction.

In Probabilistic Models there is risk and uncertainty. Probabailistic models incorporate random variables and probability distributions into the model of an event or phenomenon. While a deterministic model gives a single possible outcome for an event, a probabilistic model gives a probability distribution as a solution.

Iconic models represent the system as it is, but in different size. Thus Iconic models are obtained by enlarging or reducing the size of the system. In other words they are images Some common examples are photographs, drawing model airplanes, ships, engines, globes, maps etc. A toy airplane is an iconic model of a real one.

Operations Research attempts to find the best and Optimum solution to a problem. The use of computers it is possible to handle complex problems requiring large amount of calculations. The objective of the operations research models is to attempt and to locate Best or Optimal Solution.

The word Operation may be defined as some action that we apply to some problems or hypothesis. Operation means the actions and decisions made by participants and members of a business that affect the production, distribution, service, management, etc. needed for a company to function that requires the use of resources and assets.

The operations Research technique, specially used to determine the optimum strategy is simulation. Operational analysis is used in the British (and some British Commonwealth) military as an intrinsic part of capability development, management and assurance. In particular, operational analysis forms part of the Combined Operational Effectiveness and Investment Appraisals, which support British defense capability acquisition decision-making.

Models are the representation of reality. A Business Model is a representation of the reality (of a set of business activities) where the modelling exercise is to faithfully abstract the core activities into a model which is an abbreviated but accurate representation of the reality.

Symbolic Models are called mathematical models. Symbolic Modelling is a therapeutic and coaching process developed by psychotherapists Penny Tompkins and James Lawley, based on the work of counselling psychologist David Grove. Using Grove’s Clean Language, a progressive questioning technique using clients’ exact words, the facilitator works with a client’s self-generating metaphors to clarify personal beliefs, goals, and conflicts, and to bring about meaningful change. Because of its reliance on emergence and self-organisation it has been called a "post-modern oriented therapeutic approach".

Probabilistic models are also known as Stochastic Models. Stochastic modeling is a form of a financial model that is used to help make investment decisions. This type of modeling forecasts the probability of various outcomes under different conditions, using random variables.

Static Models assumes that the values of the variables do not change with time during a particular period. The static model describes the structure of a distributed parameter system, i.e. its state at a specific time instant. The intersection models relate the parameters that are to be combined in a composite field by means of their distribution models.

A Dynamic Models considers time as one of the important variable. Dynamic models are generally models that contain or depend upon an element of time, especially allowing for interactions between variables over time. A separate idea with the same name is models that are updated over time with new data. In the case of Systems Dynamics, we often have variables that are looped.

Linear Programming may be defined as a method of determining an optimum programme inter dependent activities in view of available resources. Linear programming is an optimization technique for a system of linear constraints and a linear objective function. An objective function defines the quantity to be optimized, and the goal of linear programming is to find the values of the variables that maximize or minimize the objective function.

Constraints are expressed is n the form of inequities or equations. A constraint is something that limits or controls what you can do. Their decision to abandon the trip was made because of financial constraints. Water shortages in the area will be the main constraint on development.

If there are more than one optimum solution for the decision variable the solution is alternative. An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost. A globally optimal solution is one where there are no other feasible solutions with better objective function values.

Dual of the dual is Primal. Any feasible solution to the primal linear program has a value no greater than that of any feasible solution to the dual linear program.

operations research is a multidisciplinary field with a wide variety of applications.

For analyzing the problem , decision – makers should normally study Its qualitative aspects. Qualitative data is information that is difficult to measure, count, or express in numerical terms. This type of data is used in research involving detailed, verbal descriptions of characteristics, cases, and settings.

A decision variable is a quantity that the decision-maker controls. For example, in an optimization model for labor scheduling, the number of nurses to employ during the morning shift in an emergency room may be a decision variable.

The aim is to achieve the best balance between the cost of the resources and the quality of service it provides. In practice, this aim will need to be defined for each situation and will most likely be to achieve the lowest resource cost for a desired response and work quality.

Assignment problem is one of the fundamental combinatorial optimization problems. It consists of finding, in a weighted bipartite graph, a matching of a given size, in which the sum of weights of the edges is a minimum. A common variant consists of finding a maximum-weight matching.

An optimization model Mathematically provides the best decision, Provides decision within its limited context and Helps in evaluating various alternatives constantly