1. IGNOU MBA Solved Assignment
MS-51 Jan June 2016
Course Code MS - 51
Course Title Operations Research
Assignment Code MS-51/TMA/SEM - I/2016
Assignment Coverage All Blocks
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Q1. Define Operations Research. Also, give a brief historical background of Operations Research.
Operations Research (O.R.), -----------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------------------. The terms management
science and analyticsare sometimes used as synonyms for operations research.
Employing techniques --------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------------------------------------- arrives at optimal or near-optimal
solutions to complex decision-making problems.
Operations research overlaps -------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------(such as profit, performance, or yield)
or minimum (such as loss, risk, or cost.)
Operations ----------------------------------------------------------------------------------------------------------------------------------------
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--------------to describe the system.
Because of the ------------------------------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------- which of these techniques are most appropriate given the nature of
the system, the goals for improvement, and constraints on time and computing power.
The major sub-disciplines ------------------------------------ research are:
Computing and -----------------------------------------------
Environment, ---------------------------------------------- resources
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Manufacturing, -----------------------------------------------------management
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Policy ----------------------------------------------sector work
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Operations ----------------------------------------------------------------------------------------------------------------------------------------
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---------------------------------------------------------------------------------------------------------------------------, because the systems
composed of human, machine, and procedures may do not have complete information.
3. Operations ----------------------------------------------------------------------------------------------------------------------------------------
----------------------- system. Thus O.R. specialists are involved in three classical aspect of science, they are as follows:
i) Determining --------------------------------------------------------------------------
ii) Analyzing the ------------------------------------------------------ appropriate models
iii) Predict ------------------------------------------------ these models
The emphasis on ---------------------------------------------------------------------------------------------------------------------------------
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---------------------, advertising policies, etc.
Historical background of Operations Research
Operation Research is a relatively new discipline. Whereas 70 years ago it would have been possible to study mathematics,
physics or engineering (for example) --------------------------------------------------------------------------------------------------------
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----------------------------------------------give a short history of O.R.
Early in 1936 the British ------------------------------------------------------------------------------------------------------------------------
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------------------------------of reliability and ranges of over 100 miles on aircraft were obtained.
It was also in 1936 that Royal ------------------------------------------------------------------------------------------------------------------
----------------------------------------------------------------------- fighter aircraft - no Hurricanes or Spitfires had come into service
- and no radar data was yet fed into its very elementary warning and control system.
It had become clear ------------------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------------------------ Kent into the effective use of such data. This early work,
attempting to integrate radar data with ground based observer data for fighter interception, was the start of OR.
1937
The first of three ---------------------------------------------------------------------------------------------------------------------------------
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---------------------through the control and display network, was not very satisfactory.
1938
In July 1938 a ------------------------------------------------------------------------------------------------------------------------------------
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------------------- drastic if necessary - had to be attempted. Some new approach was needed.
4. Accordingly, --------------------------------------------------------------------------------------------------------------------------------------
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----------------was coined as a suitable description of this new branch of applied science. The first team was selected from
amongst the scientists of the radar research group the same day.
1939
In the summer of ---------------------------------------------------------------------------------------------------------------------------------
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---------------------. Initially, they were designated the "Stanmore Research Section".
In 1941 they were redesignated the "Operational Research Section" when the term was formalised and officially accepted,
and similar sections set up at other RAF commands.
1940
On May 15th 1940, ------------------------------------------------------------------------------------------------------------------------------
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------------------------currently in France were recalled.
This is held by some to be the most strategic contribution to the course of the war made by OR (as the aircraft and pilots
saved were consequently available for the successful air defense of Britain, the Battle of Britain).
1941 onward
In 1941, an Operational -------------------------------------------------------------------------------------------------------------------------
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----------------------------- than underwater as well as being less easily detected by sonar.
Thus the Operation Research ------------------------------------------------------------------------------------------------------------------
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------------------------------------the end of the war OR spread, although it spread in different ways in the UK and USA.
In 1951 a committee on Operations Research formed by the National Research Council of USA, and the first book on
“Methods of Operations Research”, by Morse and Kimball, was published. In 1952 the Operations Research Society of
America came into being.
5. Success of Operations ---------------------------------------------------------------------------------------------------------------------------
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---------------------------countries of the world. India was one the few first countries who started using operations research.
In India, Regional Research -------------------------------------------------------------------------------------------------------------------
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----------------------------------- and Survey. In 1955, Operations Research Society of India was formed, which is one of the
first members of International Federation of Operations Research societies. Today Operations Research is a popular subject
in management institutes and schools of mathematics.
Q2. ABC Company is engaged in manufacturing five brands of packed snacks. It is having five
manufacturing set ups, each capable of manufacturing any of its brands one at a time. The cost to make a
brand on these set ups vary according to the following table:
S1 S2 S3 S4 S5
B1 4 6 7 5 11
B2 7 3 6 9 5
B3 8 5 4 6 9
B4 9 12 7 11 10
B5 7 5 9 8 11
Assuming five set ups are S1 ,S2, S3, S4, and S5 and five brands are B1, B2, B3, B4 and B5, find the
optimum assignment of products on these set ups resulting in the minimum cost.
Solution-
The table is as given- (--------------------------------------------------------------------------------------------------------------------------
in B4 it is 7 and in row lowest element is 5.
------- -------- ------ ---------- ----------
-------- -------- 6 ---------- 5 11
---------- ------- --------- ------- --------- 5
--------- ------ 5 --------- 6 9
7. B3 -------- ---------- ---------- 2-1= 1 -------------
B4 2-0= 2 ------------- ------------- --------- ---------
B5 --------- ---------- 4-0= 4 ----------- 6-2= 4
Thus we will ----------------------------------------
S1 S2 S3 S4 S5
B1 --------- ----------- 3 -------------- 5
B2 --------- -------------- 3 -------- -----------
B3 4 1 ------------ 1 -------
B4 ----------- ----------- -------- ------------ 1
B5 2 ---------- -------- ----------- -----------
Step 3- (i) Start from first row, examine ---------------------------------------------- with exactly one zero is found ----
--------------------- of respective columns.
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Step 4-
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Step 5-
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3. What is goal programming? State clearly its assumptions. Identify the major differences
between linear programming & goal programming.
Goal programming is a ------------------------------------------------------------------------------------------------------------------------
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------------------------------. Goal programming is used to perform three types of analysis:
1. Determine ----------------------------------------------------- of objectives.
2. Determine the ----------------------------------------------------------------- resources.
3. Providing the ---------------------------------------------------------- of resources and priorities of the goals.
Goal programming models are very ---------------------------------------------------------------------------- programs have one
objective goal programs can have several objectives. Consider the following example. ----------------------------------------------
-------------------------------------------------------------------below.
Product 1 (x1) Product 2 (x2) Available
profit per unit ----------- 12
------------------------- 3 ---- ---------
-------------- -------- 1 -------
The initial goal -----------------------------------------------------------------------------------------------------------------------------------
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-------------------goals to be achieved.
9. If the decision maker is more ------------------------------------------------------------------------------------------------------------------
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------------------------------------of incommensurability.
A major strength of ------------------------------------------------------------------------------------------------------------------------------
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------------------------, a series of connected linear programmes.
Goal programming ------------------------------------------------------------------------------------------------------------------------------
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------------------------Pareto efficient solution in an appropriate manner.
The setting of appropriate weights in the goal programming model is another area that has caused debate, with some
authors suggesting the use of the Analytic Hierarchy Process or interactive methods for this purpose.
Assumptions-
The salient feature -------------------------------------------------------------------------------------------------------------------------------
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-----------------------performs three types of analysis:
(1) It-determines --------------------------------------------- a set of goals;
(2) It -------------------------------------------------------------- given resources; and
(3) It provides the -------------------------------------------------------------------------- goal structures.
The goal programming approach to be taken should be carefully examined by the decision maker before he employs the
technique. The most important ---------------------------------------------------------------------------------------- simulation with
numerous variations of constraints and goal priorities.
Every quantitative -------------------------------------------------------------------------------------------------------------------------------
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-----------------------an effective application of goal programming - and for the matter of all mathematical techniques -, a clear
understanding of the assumptions and limitations of the technique is a prerequisite. The application of goal programming for
managerial decision analysis forces the detision maker to think of goals and constraints in terms of their importance to the
organization.
It may be mentioned in --------------------------------------------------------------------------------------------------------------------------
--------------------- are attributable to goal programming also.
10. Goal ------------------------------------------------------------------------------------------------------------------------------------------------
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------of the typical potential areas in which goal programming can be effectively applied.
Linear programming vs goal programming-
Linear ----------------------------------------------------------------------------------------------------------------------------------------------
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--------importance among these incompatible goals so that the low-order goals are considered only after the higher-order
goals are satisfied or have reached the point beyond which no further improvement are desired. If management can provide
an ordinal ranking of goals in terms of their contributions or importance to the organization and all goal constraints are in
linear relationships, the problem can be solved by goal programming.
How is an objective function to be determined and expressed in algebraic form when there exist multiple, incommensurable,
and conflicting goals? Goal programming provides an answer to- this. In 8oul programming, instead of trying to maximize or
minimize the objective criterion directly as in linear programming, deviations between goals and what can be achieved
within the given set of constraints are to be minimized.
In goal programming, the -----------------------------------------------------------------------------------------------------------------------
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-------------------------------------------------------, based on the relative importance or priority assigned to them.
The solution --------------------------------------------------------------------------------------------------------------------------------------
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----------------involving multiple, conflicting goals according to the manager's priority structure.
4. A company has determined from its analysis of production and accounting data that, for a part
number KC-438, the annual demand is equal to 10,000 units, the cost to purchase the item is Rs
36 per order, and the holding cost is Rs 2/unit/year.
(a) What should the economic order quantity be?
(b) What is the number of days’ supply per optimum order? (Assume 300 working days in a year)
12. Q5. “Game theory provides a systematic quantitative approach for analyzing competitive
situations in which the competitors make use of logical process and techniques in order to
determine an optimal strategy for winning”. Comment.
Many a decision is taken in a competitive situation in which the outcome depends not on that decision alone but
rather on the -------------------------------------------------------------------------------------------------------------------------------------
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-----------------to solve. Other methods, of which war games are long-established examples -----------------------------------------
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-------------------------------------------------------------------------------------------------------------the issues in many decision=
making processes.
Game theory -------------------------------------------------------------------------------------------------------------------------------------
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-----------------situations.
The parallels between ---------------------------------------------------------------------------------------------------------------------------
-------------------------------------------------- moves in sequence. After observing the move made by the first player, the second
player makes a counter move. Then the first player, having observed the first two moves, makes the third move and so on.
Compare this to the ------------------------------------------------------------------------------------------------------------------------------
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------------------------well as anticipating competitive responses when making decisions.
First, game theory provides a ------------------------------------------------------------------------------------------------------------------
------------------------------------------------------------- players in a game (consumers, sellers, input providers, governments,
foreign organisations, etc.), their possible actions and reactions to the actions of other players, and the payoffs or rewards
implicit in the game.
Game theory models ----------------------------------------------------------------------------------------------------------------------------
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--------------------------players.
In order for game --------------------------------------------------------------------------------------------------------------------------------
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----------------------situations.
Because game theory can -----------------------------------------------------------------------------------------------------------------------
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-------------------------------strategic situation.
In what types of business situations can game theory be applied? Click on the linkhere to find out.
The nature of the solution(s) in game theory also motivates businesses to analyse how the structure of the game can be
altered so that a different (and perhaps a more favourable) game can be played. Because of its systematic approach, game
theory allows businesses to examine the consequences of actions that they may not have considered.
It is worth noting here ---------------------------------------------------------------------------------------------------------------------------
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---------------------------with fixed rules, the rules of business are continuously in flux. They may be formulated by law, by
tradition or by accident. Often, however, players have an influence on how rules are decided.
Because game theory can be -------------------------------------------------------------------------------------------------------------------
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----------------------------------- Each firm's decisions in the market depend on the specific assumptions it makes about how its
rivals make pricing and output decisions.
In addition, there are other situations in which there is one buyer and one seller. Microeconomics without game theory does
not adequately address these matters.
Consider a market in which --------------------------------------------------------------------------------------------------------------------
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----------------------------------assume that the firms are price takers.
The players in a game are those ---------------------------------------------------------------------------------------------------------------
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---------------------------------------and is referred to as chance.
When modelling a game, -----------------------------------------------------------------------------------------------------------------------
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14. ------------------------------------------------------------------------------------------------------------------------------------------------------
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-------------------------------strategies and the outcome of the game.
Take, for example, the -------------------------------------------------------------------------------------------------------------------------
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-----------------------------industry would also account for the interests of the two governments (or, more precisely, one
government and one confederation of governments). In addition, labour unions, shareholders, suppliers and others in the
United States and the European Union can also have a vested interest in influencing aircraft production.
At the outset, a very comprehensive introduction to the theory of games has been provided with a clear conceptual
framework and -----------------------------------------------------------------------------------------------------------------------------------
----------------------------------------------------------------------- We have also mentioned that saddle point occurs in the case of
pure strategies adopted by both the -players. Examples have worked out to illustrate the method.
Mixed strategies have been covered as situations where the saddle points do not exist. The concept is well brought out
through an example. The ------------------------------------------------------------------------------------------ has been derived so as
to enable you to use the formul4s for a given problem.
The principle of ---------------------------------------------------------------------------- has been dealt with through an example.
2xn game has been the next --------------------------------------------------------------------------------------------------------------------
--------------------------------------------------------------- of 2x2 sub-games within which lies the solution of the larger game. One
numerical example has been worked out to bring the essence.
Exploiting the opponent's mistake -------------------------------------------------------------------------------------------------------------
---------------------------------------------------------------------------------------------------------------------- through an example.
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