Organizational Research

7/28/2019 Organizational Research

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OPERATIONS RESEARCH

(OR)


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Objective

Operations Research is the science of decisionmaking and the art of decision modelling. It is a set

of quantitative tools used by the managers to take

decisions and formulate their business strategies.

The basic objective of this course is to provide anunderstanding of the important techniques used in

decision making. A certain level of mathematical

hands-on expertise will be required to ensure

understanding of the tools in operations research.


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Course Evaluation

The learning pace in this class is going to be fast andheavy. The following proportions will be used to estimate

your learning from the course:

Project 20%

Mid Term - 30%

End Term - 50%

Although there may be valid reasons for not attending

class, the participant is still responsible for the material

covered in the class.


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Academic Integrity..

A student is expected to know what

constitutes academic integrity (please go

through students manual) to avoidcommitting an academic offence, and to take

responsibility for his/her actions. Any kind of

academic dishonesty (e.g., plagiarism,cheating) will be dealt very seriously.


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Grading Pattern

Range

of

Marks

0-

30

30-

35

35-

40

40-

45

45-

50

50-

60

60-

70

70-

80

80-

100

Grades F D D+ C C+ B B+ A A+


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Operations Research

Operations Research (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. The resultwas called Operations Research.


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Operations Research

OR is the discipline of applying advanced

analytical methods to help make better

decisions.


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Operations Research Optimization is everywhere

Firms want to maximize value to shareholders

People want to make the best investment decisions

People want to get the highest quality at the lowest

price.

It is modeling business situations.

The goal of the model is `insight, not numbers.


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OR Approach

Understanding and describing the system

Building a model of the real-life system

Using the model as a basis for predicting

future situations.


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Phases of OR study

Definition of the problem

Construction of the model

Solution of the model

Validation of the model

Implementation of the final results.


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Goal of Operations ResearchThe goal of operations research is to find values for n

decision variables X = (x1, x2, , xn). The decisionmaker must choose values for the variables so that he isin a position to optimize his objective which mayinclude

Maximize profit Maximize utilization of equipment

Minimize cost

Minimize raw materials or resources

Minimize traveling timeetc. etc.


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Basic OR Models-Allocation Models - Markov Chain Models

Linear Programming Models - Queuing Models

Integer Linear Programming models - Simulation Models

Transportation Problem - Replacement Models

Assignment Problems

Goal Programming

- Dynamic Programming Models- Sequencing Models

- Decision Analysis Models

- Network Models

- Inventory Models

- Game Theory Models


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Linear programming

George B. Dantzig (1947) published

Programming in Linear Structure

Kontorovich (1939) was published in 1959.

Koopmans coined the term Linear

Programming (1948).


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Problem Formulation

Step 1. Formulate the Objective Function: Determinethe quantity to be optimized and express it as amathematical function. Doing so serves to define theinput variables.

Step 2. Formulate the Constraints: Identify all stipulatedrequirements, restrictions and limitations, and expressthem mathematically.

Step 3. Express any hidden conditions. Such conditions

are not stipulated explicitly in the problem but areapparent from the physical situation being modeled.Examples: non-negativity, Integerrequirements.


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ProblemAn automobile manufacturer makes automobiles and

trucks in a factory that is divided into two shops. Shop A

which perform the basic assembly operation must work 5

man days on each truck but only 2 man days on each

automobile. Shop B which perform finishing operationsmust work 3 man days for each automobile or truck that it

produces. Because of men and machine limitations shop

A has 180 man days per week available while shop B has

135 man days per week. If the manufacturer makes aprofit of Rs. 300 on each truck and Rs. 250 on each

automobile; how many of each should be produced to

maximize his profit?


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E l 2 Bl di


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Example 2. Blending..

The manager of an oil refinery must decide on the optimum mixof two possible blending processes of which the input and

output production runs as follows:

The maximum amount available of crudes A and B are 250units and 200 units respectively. Market demand shows atleast 150 units of gasoline X and 130 units of gasoline Ymust be produced. The profit per production run fromprocess 1 and process 2 are Rs. 5 and Rs. 7 respectively.Formulate the problem to maximize profit.

Input Output

Crude A Crude B Gasoline X Gasoline Y

1 6 4 6 9

2 5 6 5 5

Hard Dri ers Inc man fact res comp ter hard dri es


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Hard Drivers Inc. manufactures computer hard drives.Because demand has seasonal variations it is difficult toschedule production to keep costs to a minimum. Next year,management estimates that the demand for a 10-GB hard

drive will be 50,000 units in the first quarter followed by100,000, 50,000 and 200,000 in the second, third and fourthquarters. Because the companys production capacity is125,000 units per quarter, during the slow seasons thecompany must produce extra hard drives and store them in

inventory to help meet demand during the high seasons,particularly during the fourth quarter because Christmassales makes the highest sales quarter of the year. The

production cost of a hard drive is Rs. 25 per unit andcompany policy is to charge an inventory holding cost ofRs. 1 per hard drive per quarter for each unit in inventory atthe beginning of a quarter. Assume the company starts offthe first quarter with 10,000 units in inventory and wishes toend the last quarter with 20,000 units in inventory. Formulate

a linear programming to determine how many hard drives should beproduced in each quarter in order to minimize total cost.


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Portfolio Selection Problem..

International City Trust (ICT) invests in large cap stocks, corporatebonds, precious metal stocks, mortgage-backed securities, and

construction loans. ICT has Rs. 5 million available for immediate

investment and wishes to maximize the interest earned on the

investments over the next year.

To encourage a diversified portfolio, the board of directors has

placed several limits on the amount that can be committed to any

one type of investment: (i) no more than 25% of the total amount

invested may be in any single type investments, (ii) at least 30%

of the funds invested must be in precious mode, (iii) at least 45%invested in large cap stocks and corporate bonds, and (iv) the

average risk score of the total investment must be 2 or less.


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For each type of investment, the following table shows

the expected return over the next year as well as a score

that indicates the risk associated with the investmentInvestment Int. earned Risk Score

Large Cap Stocks 19% 1.7

Corporate Bonds 10% 1.2

Gold Stocks 18% 3.7

Platinum Stocks 12% 2.4

Mortgage Securities 8% 2

Construction Loans 15% 2.9


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Example(HR)The MTNL wants to know the minimum number of operators

required to meet the daily requirement of the Jamshedpur

telephone exchange:

Time of day Minimum no. of operators required

02000600 2

06001000 8

1000-1400 10

1400-1800 5

1800-2200 4

2200-0200 1

An operator is on duty continuously for eight hours from the

time of the duty commences. Formulate the LP model of the

problem.


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Flair Furniture CompanyThe flair furniture company produces inexpensive tables and

chairs. The production process for each is similar in that bothrequire a certain number of hours of carpentry work and a

certain number of labor hours in the painting and varnishing

department. Each table takes 4 hours of carpentry and 2 hours

of painting and varnishing shop. Each chair requires 3 hours of

carpentry and 1 hour of painting and varnishing. During the

current production period, 240 hours of carpentry time

available and 100 hours of painting and varnishing time

available. Each table sold with a profit of Rs. 7; each chair

produced is sold for a Rs. 5 profit.

Flair Furnitures problem is to determine the best possible

combination of tables and chairs to manufacture in order to

reach the maximum profit. The firm would like this production

mix situation formulated as an LP problem.


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Documents

Organizational Research