# Mb0048 Operations Research Solved Assignment Allama

**MB0048 : Operation Research is an aid for the executive in making his decisions by providing him the needed quantitative information, based on scientific method analysis. Discuss. ****Answer**:- The Operations Research may be regarded as a tool which is utilized to increase the effectiveness of management decisions. In fact, OR is the objective feeling of the administrator (decision-maker). Scientific method of OR is used to understand and describe the phenomena of operating system.

OR models explain these phenomena as to what changes take place under altered conditions, and control these predictions against new observations. For example, OR may suggest the best locations for factories, warehouses as well as the most economical means of transportation. In marketing, OR may help in indicating the most profitable type, use and size of advertising campaigns subject to the final limitations.

The advantages of OR study approach in business and management decision making may be classified as follows:

**1. Better Control. **The management of big concerns finds it much costly to provide continuous executive supervisions over routine decisions. An OR approach directs the executives to devote their attention to more pressing matters. For example, OR approach deals with production scheduling and inventory control.

2. **Better Co-ordination**. Some times OR has been very useful in maintaining the law and order situation out of chaos. For example, an OR based planning model becomes a vehicle for coordinating marketing decisions with the limitation imposed on manufacturing capabilities.

**3. Better System. **OR study is also initiated to analyses a particular problem of decision making such as establishing a new warehouse. Later, OR approach can be further developed into a system to be employed repeatedly. Consequently, the cost of undertaking the first application may improve the profits.

**4. Better Decisions. **OR models frequently yield actions that do improve an intuitive decision making. Sometimes, a situation may be so complicated that the human mind can never hope to assimilate all the important factors without the help of OR and computer analysis.

**QUANTITATIVE TECHNIQUES OF OR: **

A brief account of some of the important OR models providing needed quantitative information base on scientific method analysis are given below:

**1. Distribution (Allocation) Models**: Distribution models are concerned with the allotment of available resources so as to minimize cost or maximize profit subject to prescribed restrictions. Methods for solving such type of problems are known as ** mathematical programming techniques. **We distinguish between liner and non-liner programming problems on the basis of linearity and non-linearity of the objective function and/or constraints respectively. In linear programming problems, the objective function is linear and constraints are also linear inequalities/equations. Transportation and Assignment models can be viewed as special cases of linear programming. These can be solved by specially devised procedures called

*Transportation and Assignment Techniques.*In case the decision variables in a linear programming problem are restricted to either integer or zero-one value, it is known as Integer and Zero-One programming problems, respectively. The problems having multiple, conflicting and incommensurable objective functions (goals) subject to linear constraints are called linear goal programming problems. If the decision variables in a linear programming problem depend on chance, then such problems are called stochastic linear programming problems.

**2. Production/Inventory Models**: Inventory/Production Models are concerned with the determination of the optimal (economic) order quantity and ordering (production) intervals considering the factors such as—demand per unit time, cost of placing orders, costs associated with goods held up in the inventory and the cast due to shortage of goods, etc. Such models are also useful in dealing with quantity discounts and multiple products.

**3. Waiting Line (or Queuing) Models: **In queuing models an attempt is made to predict:

**(i) **How much average time will be spent by the customer in a queue?

**(ii) **What will be an average length of waiting linear or queue?

**(iii) **What will be the traffic intensity of a queuing system? etc.

The study of waiting line problems provides us methods to minimize the sum of cost of providing services and cost obtaining service which are primarily associated with the value of time spent by the customer in a queue.

**4. Markovian Models**: These models are applicable in such situation where the state of the system can be defined by some descriptive measure of numerical value and where the system moves from one state to another on probability basis. Brand-switching problems considered in marketing studies are an example of such models.

**5. Competetive Strategy Models **(Games Theory): These models are used to determine the behavior of decision-making under completion or conflict. Methods for solving such models have not been found suitable for industrial applications, mainly because they are referred to an idealistic world neglecting many essential features of reality.

**6. Net work Models: **These models are applicable in large projects involving complexities and inter-dependencies of activities. *Project Evaluation and Review Techniques (PERT) And critical Method *(CPM) are used for planning, scheduling and controlling complex project which can be characterized net-work.

**7. Job Sequencing Models: **These Models involve the selection of such a sequence of performing a series of jobs to be done on service facilities (machines) that optimize the efficiency measure of performance of the system. In other words, sequencing is conserved with such a problem in which efficiency measure depends upon the order or sequences of performing a series of jobs.

**8. Replacement Models**: The models deal with the determination of optimum replacement policy in situations that arise when some items or machinery need replacement by a new one. Individual and group replacement polices can be used in the case of such equipments that fail completely and instantaneously.

**9. Simulation Models: **Simulation is a very powerful technique for solving much complex models which cannot be solved otherwise and thus it is being extensively applied to solve to solve a variety of problems. This technique is more useful when following two types of difficulties may arise:

**(i) **The number of variables and constraint relationships may be so large that it is not computationally feasible to pursue such analysis.

**(ii) **Secondly, the model may be much away from the reality that no confidence can be placed on the computational results.

In fact, such models are solved by simulation techniques where no other method is available for its solution.

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Tags: Decision making, Integer (computer science), Inventory, Linear programming, Mathematical model, Operations research, Optimization, Scientific method

MB0048 –Operation ResearchQ1. a. Explain how and why Operation Research methods have been valuable in aidingexecutive decisions.b. Discuss the usefulness of Operation Research in decision making process and the role of computers in this field.Ans.

Churchman, Aackoff and Aruoff defined Operations Research as:

“

the application of scientificmethods, techniques and tools to operation of a system with optimum solutions to the problems

”,

where

‘optimum’

refers to the best possible alternative.The objective of Operations Research is

to provide a scientific basis to the decision-makers for solving problems involving interaction of various components of the organisation. You canachieve this by employing a team of scientists from different disciplines, to work together for finding the best possible solution in the interest of the organisation as a whole.

The solution thusobtained is known as an optimal decision.You can also define Operations Research as

“

The use of scientific methods to provide criteria for decisions regarding man, machine, and systems involving repetitive operations

”.OR

“OperationTechniques is a bunch of mathematical techniques.”

b. “Operation Research is an aid for the executive in making his decisions based onscientific methods analysis”. Discuss the above statement in brief.Ans.

“Operation Research is an aid for the executive in making his decisions based on scientificmethods analysis”.

Discussion:-

Any problem, simple or complicated, can use OR techniques to find the best possible solution.This section will explain the scope of OR by seeing its application in various fields of everydaylife.i)

In Defense Operations:

In modern warfare, the defense operations are carried out by threemajor independent components namely Air Force, Army and Navy. The activities in each of these components can be further divided in four sub-components namely: administration,intelligence, operations and training and supply. The applications of modern warfare techniquesin each of the components of military organisations require expertise knowledge in respectivefields. Furthermore, each component works to drive maximum gains from its operations andthere is always a possibility that the strategy beneficial to one component may be unfeasible for another component. Thus in

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