BUSINESS MANAG EMENT
Transcript of BUSINESS MANAG EMENT
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OKONKWO CHARITY
PG/MBA/09/54415
AN ASSESSMENT OF THE APPLICATION OF OPERATIONS
RESEARCH TECHNIQUES IN THE DECISION MAKING
BUSINESS MANAGEMENT
BUSINESS ADMINISTRATION
BASHIR AKINKUNMI
Digitally Signed by: Content manager’s Name
DN : CN = Webmaster’s name
O= University of Nigeria, Nsukka
OU = Innovation Centre
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UNIVERSITY OF NIGERIA, ENUGU CAMPUS
FACULTY OF BUSINESS ADMINISTRATION
DEPARTMENT OF MANAGEMENT
TOPIC:
AN ASSESSMENT OF THE APPLICATION OF
OPERATIONS RESEARCH TECHNIQUES IN THE
DECISION MAKING PROCESS OF MANUFACTURING
COMPANIES
PRESENTED BY:
OKONKWO CHARITY
PG/MBA/09/54415
IN
PARTIAL FULFILLMENT OF THE REQUIREMENT
FOR THE AWARD OF THE DEGREE OF
MASTERS OF BUSINESS ADMINISTRATION
(MBA) IN BUSINESS MANAGEMENT.
JUNE, 2010
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CERTIFICATION
OKONKWO CHARITY, a postgraduate student in the
Department of Management (with Registration number
PG/MBA/09/54415) has satisfactorily completed the
requirement for the coursework and research work for the
award of the degree of Masters in Business Administration
(MBA) in Management.
The work embodied in this project is original and has not
been submitted, in part or full, for any other degree or
diploma of this or any other university.
___________________ ______________
CHIEF EZEH DATE
Supervisor
___________________ ______________
DR. EZIGBO CHARITY DATE
HOD, Management
________________________ ______________
EXTERNAL SUPERVISOR DATE
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DEDICATION
This piece of Research work is dedicated to my beloved
father, Mr. OKONKWO G, who did not have the
opportunity to fully exploit the potentials of Western
Education but did all within his powers to ensure that
others especially I do.
Thank you Special dad.
OKONKWO IFENYINWA
Researcher
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ACKNOWLEDGEMENT
In the course of this research work, numerous debts of
thanks which were too difficult to repay were incurred.
Firstly, I thank the Almighty GOD who provided the
inspiration and idea of this work.
In a very special way, I express my heart-filled gratitude to
my project supervisor, Chief Ezeh who meticulously went
through my work and provided useful and corrective
criticism. Most especially I thank him for initiating me into
the art of critical research. I also thank members of the
faculty and departmental board.
Thank you and God Bless.
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ABSTRACT
In today’s complex and aggressive business environments, it is only an effective decision making that gives organizations an edge over their competitors. Since organizations continuously make decisions, managers should ensure that it is done scientifically so as to minimize the inherent risk of errors in the subjective approach to decision making. This work seeks to appraise the application of operations research techniques in the decision making processes of manufacturing companies. This study therefore sets to identify the various operations research tools applied in decision making, the benefits of using operations research and the various limitations to its application. The target population of this study is made up of the entire top, middle and lower management staff of the selected manufacturing companies; Innoson, Anammco and Juhel Nigeria Limited. Stratified sampling method was adopted so as to give a fair representation to the selected organizations in the ratio of 3:5:2 using the proportionality formular.(Q=A/N × n/1). The study obtained its data from both primary and secondary sources. The questionnaire was the major instrument of collecting data for the research. Interviews were also conducted to complement the information from the questionnaire. Data analysis was done through the use of tabular presentation, pie and bar charts. The five (5) formulated hypothesis were also tested for acceptance or rejection using the chi-square statistical technique. The findings indicates that linear programming, Network Analysis and decision trees are some of the operations research tools used in decision making and that the benefits enjoyed as a result of applying operations research to decision making justifies the expenditure incurred in that respect. The study also recommends that the use of operations research should be encouraged and sustained in view of the numerous benefits it offers to firms and that firms should embark on aggressive training of personnel to reduce resistance to its use.
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TABLE OF CONTENTS
Title page - - - - - - - - i Certification - - - - - - - ii Dedication - - - - - - - iii Acknowledgement - - - - - - iv Abstract - - - - - - - - vii Table of Contents - - - - - - viii CHAPTER ONE: INTRODUCTION 1.1 Background of Study - - - - 1
1.2 Statement Of The Problems - - - 9
1.3 Objectives of the Study - - - - 11
1.4 Research Questions - - - - 11
1.5 Research Hypotheses - - - - 12
1.6 Significance of the Study - - 13
1.7 Scope of the Study - - - - 14
1.8 Limitation of Study - - - - 15
1.9 Historical Background Of Firms Used -
1.10 Definition of Terms - - - - 16
References - - - - - - 17
CHAPTER TWO: REVIEW OF RELATED LITERATURE
2.1 Operation Research Defined - - - 18 2.2 Evolution of Operations Research - - 19 2.3 Nature and Characteristics of operations
Research - - - - - - - 20 2.4 Procedures in Conducting Operations Research 22 2.5 Model Building in Operations Research - 26 2.6 Importance of Models in Operations Research 27 2.7 Classification Schemes of Models - - 28 2.8 Characteristics of a Good Models - - 31 2.9 Techniques of Operations Research - - 31 2.10 Decision Making in Organizations - - 40 2.11 Types and Characteristics of Managerial
Decisions - - - - - - - 45 2.12 Characteristics of the Decision Process - 46 2.13 Decision Techniques - - - - - 48 2.14 Blue Print for Decision Making - - - 50 2.15 Scope and Application of Operations Research
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in Management Decision Making - - 52 2.16 Managing the Decision Making Process - 54 2.17 Human Side of Operations Research - 55 2.18 Limitations of Operations Research - - 56
References - - - - - - 58
CHAPTER THREE: RESEARCH METHODOLOGY 3.1 Introduction - - - - - - 60 3.2 Sources of Data - - - - - 60 3.3 Population of the Study - - - - 61 3.4 Method of Sampling - - - - - 62 3.5 Research Instruments - - - - 64 3.6 Data Analysis Techniques - - - - 65 3.7 Validation of Instruments for Data Collection 66
References - - - - - - 67
CHAPTER FOUR: PRESENTATION, ANALYSIS AND DATA INTERPRETATION 4.1 Data Presentation - - - - - 69 4.2 Data Analysis - - - - - - 69 4.3 Hypotheses Testing - - - - - 96
CHAPTER FIVE: SUMMARY OF FINDINGS, CONCLUSIONS AND RECOMMENDATIONS 5.1 Summary of Findings - - - - 118 5.2 Conclusions - - - - - - 120 5.3 Recommendations - - - - - 121 BIBLIOGRAPHY APPENDIX
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CHAPTER ONE INTRODUCTION
1.1 BACKGROUND OF THE STUDY
Everyday, managers makes decisions that commit
organizational resources. These decisions determine the
survival, growth or even death of an organization. The
decision making process is not always activated when a
manager perceives a problem as most decisions are made
to ensure the stability, continuity and expansion of good
prospects and operating performance. (Akintoye and
Oluwatosin, 2006; 387).The Process of decision making
requires the analysis of alternative solutions and the
identification and selection of the alternative that offers the
best outcome.
Managers today especially in developing countries use
exclusively experience, hunches and rule of thumb in their
decision making process. This qualitative approach may be
found useful and adequate in certain circumstances but
inadequate in others. When the problem is repetitive and
the data are quantifiable, we find greater scope for the
application of the quantitative techniques to ensure
rational and logical decisions.
Okeke (1996; 1) opines that in the qualitative approach to
decision making, the manager relies on his personal
intuition or past experience in solving similar problems.
Such an Intuitive “feel” for the problem may be sufficient
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for making a decision. He however concluded that there are
problems for which more quantitative approach is
inevitable.
This quantitative approach that we mean here goes by so
many names; Management science, operations research,
Quantitative Management, Decision Sciences, Systems
Analysis etc. Although attempts have been made by some
writers to differentiate these terms, they are quite often
used interchangeably, their unifying factor or common
denominator being their utilization of the techniques of
Mathematics, Engineering, Economics, Computer Science
etc in finding solutions to organizational problems.
Operations Research is simply defined as the application of
scientific methodology in making more explicit, more
systematic and better decisions. (Litterer,
1978:171).Scientific methodology is defined as a process of
or logical approach to developing models that explain and
predict real-world behavior. (Dannenbring and starr,
1988:1).Thus operation research seeks to describe,
understand and predict the behavior of complex systems of
human beings and equipment (Stoner, 1982:186).
As the name implies, one can say that operations research
means research on operations. Filley and House (1969:10)
have noted that organizations and their component units
carry on goal-oriented activities referred to as “operations”
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and that the systematic study leading to decisions as to
which operations should be undertaken and how they
should be tackled is termed “research”. What management
scientists or operations researchers do is to observe
decision making environment, try to identify, define and
analyze problems, construct models which seek to solve
these problems, choose those inputs of data required for a
solution, find the optimal solution when it could be found
and help in the implementation of the identified
solution(Levin et al,1986:5).Operations research provides
managers with quantitative basis for decision making and
enhance their ability to make long range plans and develop
broad strategy.
Operations research is approached in a spirit that
demands that decision problems be properly defined,
analyzed and solved in a conscious, rational, logical,
systematic and scientific manner based on data, facts,
information and logic (Loomba, 1978:25).The quantitative
techniques inherent in management science are not to be
regarded as an explicit formular to be uniformly applied to
all types of situations. Rather, it is a style of management,
which demands a conscious, systematic and scientific
analysis and resolution of decision proba,1978:26-27).But
the fact that the use of quantitative data constitutes the
corner stone of operations research does not in any way
preclude the use of qualitative analysis in arriving at
optimal decisions. The quantitative approach, must build
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upon, be modified by and continually benefit from the
experiences and creative insights of managers. The final
stage in the decision making process, after all, is the
exercise of judgment and in making this judgment, the
decision taker has to take different factors-quantitative and
qualitative into account. For example, there may be sudden
change in government policy or of government itself,
change of weather, technological advancement and so on.
And this makes it very necessary for managers to involve
qualitative approaches in decision making.
1.2. STATEMENT OF THE PROBLEMS
The use of operation research tools in decision making
presents a lot of challenges to the modern day manager
irrespective of the benefits that comes with it.
Mathematical models are applicable to only specific
categories of problems since not all business related
problems are amenable to Mathematical modeling or
configuration. Issues such as motivation, leadership style,
organizational politics etc cannot be modeled. (Akintoye
and oluwatosin; 2006:336)
The insufficient number of qualified and experienced
personnel who could effectively apply these operations
research models to firm’s decision making presents
another problem. There are few professionals who have
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acquired practical exposure in the application of operations
research to decision making in firms.
Finally resistance to changes is another issue that
confronts the manager in the use of operations research in
decision making. The use of operations research often
generates resistance from employees and management
because its implementation usually introduces changes to
the known convention within the organization. This fear of
the unknown may inhibit objective implementation of the
recommendations. (Akintoye and oluwatosin; 2006, 336).
1.3 OBJECTIVES OF THE STUDY
The specific objectives which the study seeks to achieve
are;
1) To determine the various operations research models
used by organizations in decision making.
2) To identify the benefits derived from applying operations
research models in decision making processes of firms.
3) To find out if the benefits derived from implementing
operations research techniques in making decisions
justifies the expenditure involved.
4) To determine the nature of the relationship existing
between the use of operations research in decision
making and the productivity levels of firms.
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5) To identify problems which manufacturing firms
encounter in the application of operations research to
decision making?
1.4 RESEARCH QUESTIONS
This research study will seek to provide answers to the
following research questions;
1) What are the various operations research models used
by organizations in making decisions?
2) What benefits do organizations derive from the
application of operations research models to decision
making?
3) Does the benefit which accrues to firms by using
operations research in decision making justify the
expenditure involved?
4) What is the nature of the relationship between the use of
operations research in decision making and the
productivity levels in firms?
5) What are the problems encountered by manufacturing
firms in applying operations research models in decision
making?
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1.5 RESEARCH HYPOTHESES
The following hypotheses would be tested for acceptance or
rejection;
1) HO1: Linear programming, Network Analysis and
Decision tree are some of the operations research
models used by firms in decision making.
Hi1: Linear programming, Network Analysis and
Decision tree are not some of the operations research
models used by firms in decision making.
2) Ho2: Cost reduction, increased productivity and efficiency
are some benefits enjoyed by firms that apply
operations research tools in decision making.
Hi2: Cost reduction, increased productivity and efficiency
are not some of the benefits enjoyed by firms that apply
operations research tools in decision making.
3) Ho3: The benefit that accrues to firms by using
operations research in decision making justifies the
expenditure incurred in implementing it.
Hi3: The benefits that accrue to firms by using
operations research in decision making do not justify
the expenditure incurred in implementing it.
4) Ho4: There is a positive linear relationship between the
use of operations research in decision making and the
productivity levels in firms.
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Hi4: There is no positive linear relationship between the
use of operations research in decision making and the
productivity levels in firms.
5) Ho5: Employee resistance, lack of commitment and
insufficient number of specialists are some limitations
encountered in using operations research in decision
making.
Hi5: Employee resistance, lack of commitment and
insufficient number of specialist are not some of the
limitations encountered in using operations research in
decision making.
1.6 SIGNIFICANCE OF THE STUDY
This study has both practical and Academic significance to
the society. The basic significance of this study is that it
focuses on a subject on which very little has actually been
written on so far.
Though manufacturing companies have existed for
decades, very few authors have really explored how
operations research models could be applied to
organizational decision making in manufacturing
companies. In this light, this study would contribute in
building a literature on operations research.
1.7 SCOPE OF THE STUDY
The study is on the appraisal of the application of
operations research models to the decision making process
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of manufacturing companies. The study is limited to
selected manufacturing companies in Enugu, south
eastern Nigeria. Manufacturing companies are scattered in
Enugu and it will be difficult to cover all of them given the
constraints involved in such exercise.
The study will therefore concentrate on the following
companies;
a) Innoson Technical and Industrial Company Limited
b) Anammco Nigeria Limited
c) Juhel Nigeria Limited
These companies were chosen because of their large
market share and most importantly the use of the scientific
method in their decision making process.
In addition to the above named organizations, the work will
make general references to all manufacturing organizations
as the need arises.
1.8 LIMITATIONS OF THE STUDY
The basic limitations to this study are those that have to
do with time, finance and the attitude of the respondents.
a) Time: The time limit for this study is very limited. This
research work is time consuming and because of the
limited time the researcher could not obtain all the
information needed for this study.
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b) Finance: Another prominent limitation to this study is
the limitation placed on finance. The budget for this
research was so huge and the researcher has not got
enough money to embark upon the study. Due to the
financial constraint, the researcher could not visit places
where information relevant to the study could be obtained.
c) Attitude of the respondents: Finally the lack of
corporation of the respondents nearly frustrated this
research effort especially as it has to do with the
companies employees. The respondents were unwilling to
supply the necessary information even when they have
been assured confidentiality and that the information
supplied would only be used for academic purposes.
In spite of these limitations, the findings of this research
will still be valid.
1.9 DEFINITION OF TERMS
a) Decisions: This is a choice or judgment that is made
by a manager after thinking about what is best to
do.(Hornby,2001;301)
b) Decision making: This is the analysis of alternative
solutions and the identification and selection of the
alternative that offers the best outcome.(Akintoye and
oluwatosin,2006;387)
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c) Models: A model is an idealized representation of a real
life situation which allows managers to analyze and
understand a system very well.
d) Operations research: This is a multi-disciplinary area
of activity that is concerned with organizational
problems, the location of optimum solutions to
problems relating to performance of men, money,
materials and machines.
e) Productivity: This has to do with the rate at which a
firm produces goods and the amount of goods
produced compared with how much time, work and
money is needed to produce them.
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1.11 HISTORICAL BACKGROUND OF FIRMS USED
INNOSON TECHNICAL AND INDUSTRIAL COMPANY
LIMITED
The company is a subsidiary of Innoson group of
companies and was incorporated in 2002 with its Head
office/factory situated at plot W/L Industrial Layout
Emene, Enugu State, Nigeria.
Full scale operations and production commenced in
October 2002. It is an Indigenous blue clip company
engaged in the manufacturing of plastic chairs, tables,
trays, plates, spoons, cups, jerry cans of different sizes
and any other allied products.
Since Inception, this company ranks as one of the biggest
plastic industry in Nigeria. It produces the highest quality
range of the plastic products of International standard and
has production of over 10,000 pieces of chairs and tables
per day. Due to the rapid demand of these products, the
company’s twelve production lines of injection moulds
have since been increased with tremendous and near
perfect production lines of international standard.
It was also established to further consolidate their leading
position in the motorcycle industry by producing the
motorcycle plastic requirement of Innoson Nigeria Limited
which is a sister company. This effort was in direct
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response to the federal government policy direction
towards encouraging private sector as the engine of growth
for the Economy. Over 600 indigenous employees and few
expatriate staff are working in the company.
The company has an Annual turnover of N3.6b. Their
foreign partners are CRETEC INDUSTRIES CO, LTD
(CHINA) whose wealth of experience is unquantifiable.
The company received the Son Quality award 2006
Industry of the year by the Nigerian union of Journalist,
Enugu State, The Economic and Social Justice award by
Amnesty International, The Best exhibiting Pavilion in
Plastic, April 2007, by Enugu Chamber of Commerce,
Industry, Mines and Agriculture, Special Merit award April
2008 by Nigerian Society of Engineers, Enugu Branch to
mention but a few.
The company is a member of Enugu Chamber of
Commerce, Industry, Mines and Agriculture, (ECCIMA),
Member Nigerian Association of Chambers of Commerce,
Industries, Mines and Agriculture (NACCIMA),
Manufacturers Association of Nigeria (MAN), member,
National Anti-Corruption Volunteer Corps (NAVC).
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2.ANAMMCO LIMITED
Anammco is the product of a joint venture between the
FGN and DAIMLER AG of Germany for the setting up of a
manufacturing plant for the Assembly of Mercedes
Vehicles using completely knocked down parts (CKD). The
Federal government had 35% of the shares, DAIMLER AG
had 40% and other Nigerian Investors consisting mainly of
state Governments of the old East Central state and few
other investors held the remaining 25% of the company
equity.
In 2007, the FGN through the Bureau for Public
Enterprises sold 24% of its shares to G.U Okeke and Sons
Ltd whilst DAIMLER AG sold 40% of its shares to
ATFREECAL Ltd a company in which the MD have shares
and is a director. Currently the major shareholders are
ATFRECAL ltd having 40.45%, the FGN through the
Bureau for Public Enterprises (BPE) having 11% and
several state governments and few private investors who
hold the remainders of the shares.
By its Memorandum of Association, ANAMMCO is
established to carry on the business of importation of CKD
sets of Mercedes Benz Commercial Vehicles and passenger
cars as well as spare parts pertaining there to and the
Assembling of same in Nigeria under license from Daimler
or from local suppliers.
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In the middle of 2006 and in accordance with the then
existent shareholders agreement between FGN and
Daimler, Daimler nominated Mr. Jacques Gelin as the MD
of Anammco. In March 2007, FGN through the Bureau for
Public Enterprises (BPE) sold 24% out of its 35% interest
in ANAMMCO to G.U. Okeke and Sons Ltd (GUO), a
company owned by Chief Godfrey Ubaka Okeke (Chief
Okeke). GUO also acquired 3% of ANAMMCO’s equity
from leventist ltd and another 0.5% from Hon. Nnamdi
Njoku, another shareholder. In order for the sale by the
FGN to GUO to be consummated, an Amendment of the
Article of Association of ANAMMCO was procured in
March 8th 2007 at a meeting of the then Board of
Directors of Anammco and the annual General Meeting.
Thereafter, via a share transfer instrument dated the 23rd
July 2007, Daimler transferred its 40% shareholding in
ANAMMCO to Alfreecal Limited.
3. JUHEL NIGERIA LTD
Juhel Nigeria Limited is located at Emene in Enugu,
capital of Enugu State, Nigeria. It is a 100% Indigenous
company Incorporated in 1987 with RC No. 104, 648 as a
wholesale pharmaceutical company. In answer to calls for
local provision of cost-effective generic products to fill the
gap left by multinational companies operating in the
country; the founder, Dr. Ifeanyi Okoye, Mni, with a
focused vision, ventured into production and the factory
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was commissioned in 1989 as the first pharmaceutical
tablet manufacturing company in old Anambra State.
Today the company is ranked as one of the fastest growing
pharmaceutical manufacturing companies in Nigeria.
The Brand and Product range of the company have since
grown in strength and include virtually all therapeutic
classes such as Antibiotics and Anti-infective,
Cardiovascular, Anti-flatulent and recently bottled mineral
water, ivy table water.
Juhel Nigeria Ltd strong management team comprises of
accomplished professionals who excelled in both their
Academic and Professional Carrier. The team leader is Dr.
Ifeanyi Okoye, Managing Director and Chief Executive
officer, a PhD holder in Pharmaceutical technology, a
member of the national institute of policy and strategic
studies, mni and a fellow of the pharmaceutical society of
Nigeria (FPSN).
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REFERENCES
Akintoye,I.R and Oluwatosin,A.R,(2006),ICAN study pack
on multidisciplinary case study, Lagos, VI publishing.
Dannenbring,D.G and starr,M.K.,(1981),Management
Science:An introduction,Tokyo,McGraw Hill book
company.
Eboh,F.E,(2002),Management Theory: Models for decision
making, Enugu, computer villa publishers.
Ewurum, U.J.F,(2007),Module on operations research,
Unpublished lecture mimeograph, Department of
Management, University of Nigeria, Enugu Campus.
Hornby, A.S, (2001),Oxford Advanced Learners Dictionary,
London, Oxford University Press,6th ed.
Levin,R.I.,Rubin,D.S and Stinson,J.P,(1986),Quantitative
Approaches to management, New York, McGraw Hill
book Company.
Loomba,N.P, (1978), Management; A Quantitative
perspective, New York, Macmillan Publishing
company Inc.
Okeke, O.A, (1996), Quantitative Methods for Business
Decisions, Enugu, macro Academic publishers.
Unpublished B.sc Research Project, Department of
accountancy, University of Nigeria, Enugu campus.
Unpublished PhD Thesis, Department of management,
University of Nigeria, Enugu Campus.
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CHAPTER TWO
REVIEW OF RELATED LITERATURE
2.1 OPERATIONS RESEARCH DEFINED
Although it has been argued that operations research is a
concept too difficult to define. It is specifically concerned
with man-machine operational problems and has been
defined in various ways. Gupta and Hira (2002) identified
different definitions of operations research by various
authors some of which are given below;
It is a scientific method of providing executive department
with a quantitative basis for decisions regarding the
operations under their control.(Morse and Kimball; 1982).
It is the application of scientific methods, tools and
techniques to problems involving the operation of systems
so as to provide those in control of operations with
minimum solutions to the problems. (Churchman, Ackoff
and armoff; 1979).It is a specific approach to problem
solving for executive management. (H.M.Wager; 1994).It is
the application of scientific methods to problems arising
from operations involving integrated systems of men,
machines and materials and normally utilizes the
knowledge and skill of interdisciplinary solutions.
(Oluwatosin; 2002).It is an experimental and applied
science devoted to observing, understanding and predicting
the behavior of purposeful man-machine systems; and
operations research workers and actively engaged in
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applying this knowledge to practical problems in business,
government and society.(Operations society of America;
2005).
What all these people are saying is that operations
research is the application of mathematical and statistical
methods to the problems facing businesses. This is why it
is often regarded as Management science.
2.2 EVOLUTION OF OPERATIONS RESEARCH
The origin of operations research can be traced back to
Fredrick Winslow Taylor, who in the early nineties initiated
the scientific management revolution. (Ugbam; 2001). But
modern day operations research is generally considered to
have originated during the World War 2 period when
operations research teams were formed to deal with
strategic and tactical problems faced by the military. These
teams which often consisted of people with diverse
specialties e.g. mathematicians, engineers, behavioral
scientists etc were joined together to solve a common
problem through the utilization of the scientific method.
The techniques which these teams adopted in solving their
problems proved so successful that after the war, most
firms experimented and successfully applied those
techniques that have metamorphosed to a new field of
study called “operations research”.
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Two developments that occurred during the post world war
2 periods led to the growth and use of operations research
in non-military applications. First is the continued
research on quantitative approaches to decision making
which resulted in numerous methodological developments.
Notable among this is the discovery by George Dantzig in
1947 of the simplex method for solving linear programming
problems. Coupled with this was the explosion in
computing made available through digital computers which
have enabled practitioners to use the methodological
advances to successfully solve a large variety of industrial
problems.
2.3 NATURE AND CHARACTERISTICS OF OPERATIONS
RESEARCH
Operations research which has been briefly described as
“The scientific analysis of decisions” is concerned with
assisting and advising decision makers in a wide variety of
settings in business and commerce as well as national and
local government. Operations research helps to find new
approaches to problems faced by managers and involve
analysis to clarify objectives and priorities, define
alternative courses of action and explore costs of benefits
.Management science and operations research are
sometimes viewed as distinct terms, but they are
interrelated in such a manner as to defy separation. As a
matter of fact, any attempt to draw boundaries between
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them would in practice be arbitrary because the practice of
management science in decision making is embodied in the
operations research methodology. Thus operations
research and management science are terms that are used
interchangeably to describe the discipline of applying
advanced analytical techniques to help make better
decisions and to solve problems.
The application of operations research helps determine
better ways to coordinate the growing complexity of
managing large organizations that require the effective use
of money, materials, equipment and people by applying
analytical methods from mathematics, science and
engineering.
The use of its techniques attempt to solve problems in
different ways and propose alternative solutions to
management, which then chooses the course of action that
best meets the organizational goals.
Operations research may be structured to focus on diverse
issues such as top-level strategy, planning, forecasting,
resource allocation and performance management as well
as scheduling, the design of production facilities and
systems, supply chain management, pricing,
transportation and distribution including the analysis of
large databases.
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In general terms, operations research attempts to provide a
systematical and rational approach to the fundamental
problems involved in the control of systems by making
decisions which in a sense, achieve the best result,
considering all information that has been profitably used.
This is why it may be regarded as the scientific method
employed for problem solving and decision making by the
management.(lee et al,1999).
2.4 PROCEDURES IN CONDUCTING OPERATIONS
RESEARCH
The starting of operations research is believed among
practitioners to be the recognition that the problem is
connected with the forecasting of future changes in the
operating activities of the organization in such a way that
would have positive effects in its market value. The
Application of operations research to organizational
problems usually begins with the managers in need who
describes the symptoms of a problem on hand with the
operations research analyst or team leader. This action on
the part of the user manager invites the work of the
operations research team or analyst. The first major
assignment of the analyst after the discussion with the
manager is to give a formal definition to the problem. This
definition must be simplified and clearly specified to make
it easy to be represented by a model.
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Since operations research is essentially a decision making
tool that is based on quantitative analysis, modeling is
required to construct a model that would capture the whole
essence of the problem and system being studied. For
example, if a beverage manufacturing company like
Cadbury Nigeria Plc is interested in maintaining an
economically efficient stock level for its bournvita
production, the company may be interested in the level of
cocoa powder or egg powder it should maintain to minimize
stock holding and panic purchase cost in case of stock out.
The operation research analyst studies this problem by
breaking them down into their components. Such
component may include the cost of placing order, the lead
time, storage cost, network of possible suppliers and
possible substitutes, the cost of finance for stock build up
in cocoa season, processing quality of cocoa powder.
The operations research team would then gather
information about each of the components from varieties of
sources. There may be need to hold discussions with
production engineers, purchasing department personnel,
finance department in area of storage facility and cost as
well as marketing department in ascertaining current level
of demand for bournvita which might place undue stress
on the production department if there is sudden stock out
when adequate arrangement has not been made for
replenishment. After gathering relevant data and
information, the operations research team would then
32
select the most appropriate technique to analyze the data
with the aim of arriving at optimal solution. The technique
chosen must concur with the model already specified.
The uniqueness of nearly all the techniques of operations
research is their involvement of the construction of
mathematical model that attempts to describe the method
being studied.
According to the internal information bulletin of the
institute of operation research and management science,
the use of model enables the operations research analyst to
assign values to the different components and clarify the
relationships among them. The values can then be altered
to examine what may happen to the system under different
circumstances. In carrying out an operations research
assignment, there is the general understanding that details
matter and the ability to understand the precise aspects of
the problem at hand was crucial to its solution. This is the
reason why in most cases, computer programme may need
to be developed to solve the model; this programme may
however require some modifications to accommodate some
factors which are unique to the model and the problem on
hand. The modified programme may be run for a number
of times on the model to afford the benefits of multiple
solutions that are possible under different assumed
situations.
33
The operations research team then reviews the different
solutions and come up with the one that give the optimal
result to the company. This outcome is then presented to
the management with recommendations based on the
results. In order to objectively consider all possible risk
factors that may be associated with the problem under
consideration, additional computer run to consider
different assumptions may be needed before the operation
research team present final recommendation to
management. It should be understood that operations
research does not promise a perfect or error free solution to
any management decision problems. In fact, according to
Gupta and Hira (2001), operations research can only
improve the quality of solutions but it may not be able to
give a perfect result.
Operations research provides the management with a
quantitative basis for decision making. Once management
has accepted the recommendation and approved it with or
without modification for implementation, the operations
research team will need to work with others in the
organization to ensure successful implementation of the
recommended action Based on the above, operations
research like all scientific research is therefore based on
methodology with specific procedures which can be
summarized as follows;(Gupta and Hira,2001).
34
a) Definition of problem of interest;
b) Development of a well specified statement of the
problem;
c) Construction of a model that represents and
approximates the real life solution of the system under
study;
d) Derivation of a solution from the model;
e) Testing validity of the model and the solution derived
from it;
f) Establishing controls over the solution to ensure its
workability;
g)Make recommendation to management to secure
approval for implementation of the solution.
2.5 MODEL BUILDING IN OPERATIONS RESEARCH
The operations research approach usually involves
constructing and using mathematical models. In the words
of Gupta and Hira (2002), a model as used in operations is
defined as an idealized representation of real life situation.
The need for constructing a new model in operations
research process is because it is concerned with analyzing
complex problems to work out the best means of achieving
the set goals and objectives. Models play an important role
in science and business, as illustrated by graphs,
organizational charts and industrial accounting systems.
Such models are invaluable for abstracting the essence of
the subject of inquiry, showing interrelationships and
facilitating analysis. One of the critical issues in model
35
building under operations research is the process of
assigning value to the parameters within the model. In
constructing model under operations research, the
following reveals the normal course of action;(Gupta and
Hira,2001).
1. Definition and construction of objective functions;
2. Statement of the overall means of performance to be
used;
3. Development of the procedure for deriving solutions to
the problem under consideration;
4. Validation of the procedure through series of test to
ascertain its ability to deliver optimal solution;
5. Testing of the model and improvement of its validity
in every area where such test reveal weakness;
6. Establishment of the model and the process to apply
it by developing a well documented system for applying
the model as prescribed by the management;
7. Application of the model prescribed by management
to support its decision making process.
2.5.1 Importance of Models in Operations Research
According to Akintoye and Oluwatosin (2006), operations
research tools are usually stated in mathematical formular
because;
• Mathematical models describes problems more
concisely;
36
• It aids easy understanding of the overall
structure of the problem;
• It clearly indicates the important “cause” and
“effect” relationship;
• It facilitates dealing with problem in its entirety
and considering all its relationship at the same
time;
• It facilitates the use of high powered Advanced
mathematical logic and computers in analyzing
business related problems; and
• It eases the process of the use of simulation in
analyzing and forecasting probable future
business results under variety of situations.
The objective of model according to Gupta and Hira(2002)
is to provide a means for analyzing the behavior of the
system for the purpose of improving it performance.
2.5.2 Classification Schemes of Models
Akintoye and oluwatosin (2006) were of the opinion that
models could be classified into the following schemes
a) Mathematical Models: These are established
relationships between decisions or operations variables
through simplification that adapts the use of variables.
They are usually the most abstract type since it requires
not only mathematical knowledge but also great
37
concentration to get the idea of the real life situation they
represent.
b) Descriptive Models: These explain the various
operations in non-mathematical language and try the
functional relationships and interactions between various
operations .Examples are organizational charts, pie
diagram and layout plan of a building or electric circuit
diagram of a plant which describes the features of their
respective systems.
c) Predictive Models: These tend to explain or predict the
behavior of the system. Some of the examples are
exponential smoothing of forecast model which can be used
to predict the future demand and regression analysis.
d) Deterministic Models: In deterministic models,
variables are completely defined and the outcomes are
certain at least in the state of nature assumed in these
models. They represent completely closed systems and the
results are single valued.
e) Probabilistic Models: These types of models seek to
approximate real world situation by forecasting the
likelihood of occurrence of an event and using a model
adapted under various assumed states of the world. The
input and or the output variables take the form of
probability distributions and thus represent the likelihood
38
of occurrence of an event. Thus, they represent to a
reasonable degree, the complexity of the real world and the
uncertainty prevailing it.
f) General Models: These are models that can be adopted
to provide solutions to various varieties of problems. Linear
programming model is known as a general model since it
can be used for all the functions such as product mix,
production scheduling, marketing of an organization in
which they can be specific objectives.
g) Specific Models: These are models that have specific
allocation and can not be used for general operating
problems. For example, Sales response curve or equation
as a function of advertising is applicable in the marketing
function alone. This is also true for economic order
quantity that is specifically useful only for inventory
management.
h) Static Models: These are one time decision models in
which cause and effect occurs simultaneously and time lag
between the two is zero. They are usually easy to
formulate, manipulate and solved based on different
situations and assumptions underlying the problem being
studied.
I) Dynamic Models: They are the models for situations in
which time often plays an important role. They are used for
39
optimization of multi-stage decision problems which
requires a series of decisions with the outcome of each
depending upon the results of the previous decisions in the
series. Example is the decision to reduce dividend payment
in one year in order to use retained earnings to finance a
capital project that is considered viable.
2.5.3 Characteristics of a Good Model
A good model according to Akintoye (2006), is expected to
possess the following features;
a) It should contain few numbers of simplifying
assumptions
b) The number of relevant variables should align with
the assumption and thus should be simple, yet close
to reality.
c) It should incorporate resilience to respond to the
system environmental changes without any change in
its framework.
d) It should be adaptable to situations in which samples
can be used to predict population behavior
e) Its construction should without much strain be
economical and cost effective.
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2.6 TECHNIQUES OF OPERATIONS RESEARCH
There are various techniques usually used in operations
research. The basic ones as outlined by Akintoye and
oluwatosin(2006)includes Linear programming,
Transportation algorithm, Assignment models; Queuing
theory; Network analysis; Inventory control model; Markov
chains; Replacement analysis; Sequencing model;
Scheduling; Program evaluation and review technique;
Critical path method; Probabilistic model; Theory of games;
Dynamic programming models etc.
The basic features of some of these techniques would be
discussed below.
a) Linear Programming: This is a mathematical procedure
used for finding the maximum and minimum value of some
variables that exhibit linear relationships in terms of
objectives and constraints. It is a technique which in the
words of Duckworth (1967) can be used in a situation
where there are several products which can be made on
each several different machines and a programme is
needed to decide which product shall be made on which
machine so as to maximize output or minimize cost or to
satisfy some other criterion of efficiency. The need for
decision tool like linear programming is brought about by
the common constraints of the operating life of all business
organization.
41
b) Transportation Model: This model deals with problems
of minimizing the costs of moving goods, personnel or other
items of regular usage from one point to the other. These
points are the sources of supply to the location where they
will be used for the purpose for which they are required.
According to Omotosho (2002), it involves the movement of
specified quantity of items from sources to location at
minimum cost. It is therefore a special type of linear
programming model that avoids the use of complex simplex
algorithm by providing a more simplified approach and
calculation.
c) Assignment Model: The assignment model is a special
case of the transportation problem which is a special case
of the maximal flow problem which in turn is a special case
of the linear program. While it is possible to solve any of
these problems using the simplex algorithm, each
specialization has more efficient algorithm designed to take
advantage of its special structure.
This technique involves matching services with demand on
a one to one basis so as to achieve optimum overall
effectiveness. According to Dixon-
ogbechi(2001),assignment problems are extensions of the
transportation problems where the facilities can be viewed
as “source –nodes” and the jobs can be viewed as
“destination-nodes” where only one item is available at
42
each source and only one item is required at each
destination.
d) Queuing Theory: The queuing or waiting line theory
was developed to handle congestion on a service life-line
such as a petrol station. Since waiting line is a general
problem in everybody’s life or business organization, it has
found its applications in virtually every facet of operations
within the human society.
The common problem to be solved by a queue model is
either of provision of facilities or scheduling of arrivals or
possibly combining the two with the aim of obtaining an
optimum balance between the costs associated waiting
time and idle time.
Queuing theory therefore has wider application to business
problems. It is relevant whenever customers are involved
since customers expect a certain level of satisfaction from
services obtained while on the other hand, companies
providing services strive to keep costs at minimum level
while providing the services required by their customers.
e) Network Analysis: This technique is applied as a
powerful tool in controlling complex scheduling operations
such as the construction of bridges, maintenance of
complex plant or the marketing of a new product. In
network analysis, the major concern is the development of
43
available resources for the completion of non-repetitive
task within the minimum time. In the words of
Duckworth(1967),one of the consequences of the
realization that information is essential for control
purposes, and that the greater the information, the better
the control has been the development of network analysis
for better planning and scheduling.
In network analysis, interrelated activities in a complex
situation are represented by arrows in a diagram. The
diagram shows the logical relationship between activities
and once it has been properly drawn with due attention to
its underlying principles, it becomes relatively easy to
determine the critical path which are those sequence of
activities that significantly affect the completion period of
the project.
f)Inventory Control Model: Inventory according to
Starr(2004) are those stocks or items used to support
production(raw materials and work in progress items),
supporting activities(maintenance, repair and operating
supplies) and customer service(finished goods and spare
parts).This definition is part of the definition in the APICS
dictionary. The American production and inventory control
society (APICS) is a professional society that has played an
influential role in the inventory management area. APICS,
according to Starr (2004) has established the fact that
management of inventory is a major production and
44
operations management responsibility.
In the words of Dixon-ogbechi (2001), Inventory
management is the process of ensuring that the right
quantity and quality of materials is available when and
where needed. At the same time, it also ensures that a
capital is not tied up unduly nor there undue losses
deterioration and obsolescence.
The management of inventory is highly influenced by the
type of inventory involved and each type requires its own
unique management even though they can all be centrally
controlled or decentralized. The focus of inventory
management is to minimize the extra costs of carrying
unnecessary stock of goods in the companies’ warehouse.
The Economic order quantity (EOQ) is a classical model
which establishes an optimum level of stock a company
should order per unit of time, by balancing the cost of
holding stock against the cost of ordering new supply. This
is why the model is defined as the ordering quantity which
minimizes the balance of cost between inventory holding
costs and cost of placing new order. The economic
order quantity occurs when the total cost which is the sum
of holding cost and the ordering cost is at
minimum.(watern and head,1998).The economic order
quantity is given as;
EOQ= 2DCo
45
Cc
Where EOQ= Economic order quantity
D= Annual demand
Co= Ordering cost
Cc= carrying cost
g) Replacement Models: The necessity for replacement is
compelled by the changing condition of plant, machinery,
vehicles and other fixed assets that are subject to constant
and continuous usage over time. The effect of this usage
causes wear and tear, aging, and deterioration in operating
capacity or even obsolescence.
Replacement models are designed to assist management in
ascertaining the most appropriate time for replacing an
item of fixed assets(plants and machinery) both of high
level capital nature and such light materials as electricity
bulbs and other items that may suddenly fail in the course
of their operating lives.
In real life situation, the problem of when to replace
machines or plant is closely related to that of new
investment, though different approaches may be required
for items that exhibit outright failure which cannot be
repaired. Replacement therefore considers the optimal life
of an asset which according to Taffler (1979) is that period
of ownership from the time the asset is acquired to the
time it should be replaced by another identical asset that
46
results in least costs to the owner. There are three (3)
categories of items that are subject to replacement models.
These include;
1. Items that fail suddenly; these includes bulbs,
spare parts, components of heavy duty
machines.
2. Items that deteriorate; i.e. which wear in
efficiency and output gradually. These are the
categories of major fixed assets such as plant
and machinery, motor vehicles and office
equipment.
3. Items that depreciate gradually until totally
failed without possibility of repair eg printing
machine drum, computers mother board etc.
h). Scheduling: Scheduling is the process of assigning
tasks to a set of resources. It is an important concept in
many areas such as computing and production process. It
is a key concept in multi-tasking and multi-processing
operating system design and in real time operating system
design. It refers to the way processes are assigned priorities
in a priority queue. This assignment is carried out by
software known as the scheduler. In mathematical terms, a
scheduling problem is often solved as an optimization
problem, with the objective of maximizing a measure of
schedule quality.
47
Scheduling is important in modern production and
chemical industries, where it can have a major impact on
the productivity of a process. Common objectives in this
type of scheduling are to minimize the duration of
production or to maximize total profit for a given set of
customer demand. Modern computerized scheduling tools
greatly outperform the manual (heuristic) scheduling
methods commonly employed in the industry.
In modern times, companies often use backward or forward
scheduling to plan their human and material resources.
Backward scheduling is planning the task from the due
date to determine the start date and forward scheduling is
planning the tasks from the start date to determine the due
date.
i) Simulation: Simulation is an imitation of some real
device or state of affairs. Simulation attempts to represent
certain features of the behavior of a physical or abstract
system by the behaviour of another system.
Simulation is used in many contexts, including the
modeling of natural systems and human systems to gain
insight into the operation of these systems .In technology
and safety engineering, simulation can be used to test
some real world practical scenario. The uniqueness of this
model is that simulation using a stimulator or otherwise
48
experimenting with a fictitious situation can show the
eventual real effects of some possible conditions.
2.7 DECISION MAKING IN ORGANISATIONS
A decision is a choice made from available options or
alternatives. A decision enables a manager to exercise the
right of making a choice among competing alternatives. It
is an affirmed choice that is expected to lead to a particular
outcome. The process of decision making requires the
analysis of alternative that offers the best outcome. It is
often a misconstrued generalization that decisions are
always precipitated by problems. Most decisions are made
to ensure the stability, continuity and expansion of good
prospects and operating performance.
Decision making is the essence of a manager’s job.”
Managers makes decisions everyday and they often decide
the success or failure of the firms” (Dessler, 2001).Decision
making is therefore the process through which managers
identify organizational problems and attempt to resolve
them. Managers may not always make the right decisions,
but they can use their knowledge of appropriate decision
making process to reduce the odds.
49
2.7.1 The Veracity of Decision Making
Life is faced with a continuous task of decision making; the
same is also true for every business organization. Nearly
everything that managers do involves decision making.
This fact was captured in the analytical work of Robins and
coulter (1999) as shown below:
Planning:
What are the organizations long term objectives? What
strategies will achieve those objectives? What should the
organizations short term objectives be? How difficult
should individual goals be?
Organizing:
How many subordinates should I have to report directly?
How much centralization should there be in the
organization? How should jobs be designed? When should
the organization implement a different structure.
Leading:
How do I handle employees who appear to be low in
motivation? What is the most effective leadership style in a
given situation? How will a specific change affect workers
productivity? What is the right time to stimulate conflict?
Controlling:
What activities in the organization need to be controlled?
How should those activities be controlled? When is a
50
performance deviation significant? What kind of
management information system should be put in place?
It can be observed from the above table that much of the
decisions that managers have to make in the course of
their duties are routine in nature. Nonetheless, each
decision, if not properly made, can lead to grave
consequences. This underscores the fact that although
everybody in the organization may be involved in the
decision making process, good decision making process are
strategically important at all levels within the organization.
As pervasive as decision making is, its use and operation
in modern organization emphasizes team work. Thus, all
managers on the company’s business team have inputs in
the final decision making, though after much debate and
modification.
2.7.2 The Decision Making Process
Every decision passes through eight stages which includes
the following; (Akintoye and Oluwatosin; 2006)
a) Problem diagnosis
b) Identification of decision criteria
c) Weighing of each selected criteria
d) Development o alternative courses of action
e) Analysis of alternatives based on predefined qualities
f) Selection of the most appropriate alternative
51
g) Implementation of the selected alternative
h) Monitoring of implementation to maintain focus and
achieve the desired goal successfully.
After the problem has been carefully diagnosed and proper
definition given, the next stage is identification and
specification of the decision criteria. The decision criteria
are those features and characteristics the solution must
posses some factors to be considered in determining
decision criteria to buy a product include:
a) Price durability and ruggedness.
b) Speed and safety devices.
c) Availability of reliable maintenance.
d) After sales service availability.
e) Warranties.
f) Decision for aesthetic appeal.
It is to the above non-exhaustive list that weights can be
allocated depending on the need and taste of the company.
Any criterion not specifically identified at this stage is
considered to be irrelevant to the decision on hand. It is at
this stage that the view and preferences of users must be
considered. The implementation stage is where the decision
is put to action where the people who are to implement the
decision have been involved in the process, there is the
likelihood that they will be more willing to support the
outcome if they are given directives on what to do.
52
The evaluation of decision result is the final stage of the
decision process. This is where the decision is put to
action. It is the stage at which the outcome of the
implementation of the alternatives is carried out. The
rationale is to know whether the alternative chosen is able
to accomplish the desired result.
2.7.3 Types and Characteristics of Managerial
Decisions
Decisions in business environments can be classified into
two main categories: programmed and non programmed
decision.
Programmed decision are those that are suitable for
structured problems in which the goals of the decision
maker is clear, the problem is familiar and information
about the problem is easily desired and completed. Thus,
in many cases of programmed decision, procedures usually
rely wholly on precedent. These types of decision are highly
responsive to quantitative techniques in providing required
solutions.
Non-programmed decisions are those decisions that are
adaptive to unstructured problems. These are problems
that have no repetitive pattern and on which past data are
not available nor can they be modeled for quantitative
analysis. Such decision therefore, relies heavy on intuition
53
and judgment or focus of the company’s strategic outlook
for growth, expansion and survival.
The basic features of programmed and non programmed
decisions are shown below in table2.1 below for imperative
analysis.
Table 2.1: Programmed Vs Non-Programmed Decisions
Programmed Non-programmed
Type of
decision
Programmable;
Routine; Generic;
Computational.
Non-Programmable;
unique;
Innovative
Nature of
decision
Procedural;
Predictable; Well
Defined Information
and decision criteria
Novel; Unstructured;
Incomplete Channels
of information;
Unknown criteria
Decision
making
strategy
Reliance on Rules
and Computations
Reliance on Principles,
Judgment, Creative
problem solving
process
Decision
making
technique
Management
science, Capital
budgeting,
Computerized
solutions, rules
Judgment, Intuition,
Creativity
Source: Dessler, G. (2001),Management: Leading people
and organizations in the 21st century, London, Pretence
hall, p.99.
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2.7.4 Characteristics of the Decision Process
Whatever type of problem a manager confronts; the actions
will be influenced by the major assumptions underlying the
required decision. They are two types of decision process,
namely; rational and bounded rationality.
A rational decision making process will operate where the
following assumptions subsists;
a) The existence of perfect information
b) Clearly defined problem not dampened by ambiguous
symptoms
c) Clearly identified criteria that could be objectively
weighted upon specified preferences.
d) Knowledge of all possible alternatives that can be
accurately assessed against each criterion.
e) Existence of clear goals and preferences which are
stable over time.
f) Sufficient creative ability exists in the manager with
which he evaluates the alternatives and selects the
most attractive one.
g) There is the existence of a unique chance-The
alternative that will yield the maximum payoff.
Bounded rationality decision making process thrives on the
assumptions that perfect rationality is not usually met in
real business operations. The decision adjusts rationality
assumptions to approximate the variations in real life
55
situation. Thus in bounded rationality, the decision maker
constructs models that extract the essential features from
problems without capturing all the possible complexities.
Given the limitation and constraints imposed by the
organizational problems, the decision maker thus tend to
behave rationally within the parameter of the simple
model. The result of this behavior is that of obtaining
satisfactory solution that is “good enough” rather than a
maximizing one that is the goal of bounded rationality.
2.8 DECISION TECHNIQUES
There are numerous decision techniques which manager
use. They are classified under the following sub-topics;
2.8.1 Qualitative Techniques
a) T-Chart: This is an orderly graphic representation of
alternative features or points involved in a decision. In one
form, it can be a list of positive and negative attributes
surrounding a particular choice. Drawing up this chart
ensures that both the positive and negative aspects of each
direction or decision will be taken into account.
b) Group Brainstorming: This is a way of generating
radical ideas in a group. During the brainstorming process,
there is no criticism of ideas as free rein is given to people’s
creativity. Group brainstorming can be very effective as it
56
uses the experience and creativity of all members of the
group. Therefore, it tends to develop ideas in more depths
than individual brainstorming.
c) PEST Analysis: In the words of Manktelow (2004), PEST
analysis is a simple but important and widely used tool
that helps decision makers to understand the big picture of
the political, economic, socio-cultural and technological
environment that they are operating in. PEST is used by
business leaders worldwide to develop the strategic
direction of their business.
d) Delphi Technique: This is a technique that was
pioneered by Rand Corporation in the United States in
1950 to assess the timing and likelihood of new technology.
This technique which has gained wider recognition and
application is based on panel consensus method but
incorporate basic features which enable it to overcome the
adverse effects of group pressure. It is based on the simple
premise that shared knowledge where properly coordinated
and anonymity maintained can enhance the quality of
decision making
2.8.2 Statistical Decision Theory Techniques
These techniques are used to solve problems for which
information is incomplete or uncertain. Because
incomplete information is inadequate as inputs for decision
57
making, the decision maker requires a tool to assist in
bridging the gap of the missing information. Dessler (2001)
identified three degrees of uncertainty which managers face
in making a decision namely-certainty, uncertainty and
risk. Certainty is the condition of knowing in advance the
outcome of a decision. Uncertainty is the absence of
information about a particular area, while risk is the
chance that a particular outcome will or will not occur.
Many business decisions are usually made in an
environment of risk or uncertainty and it is for this type of
decision that statistical theory decisions was developed.
Statistical decision theory considers the existence of
alternative outcomes and the probabilities of their
occurring.
2.9 BLUE PRINT FOR DECISION MAKING
Hull (2001) presents the following blue print of decision
making excellence;
a) Timeliness: Every decision has an appropriate time
frame within which if taken and implemented will yield
the expected result and outside the period, will result
in sheer waste.
b) Isolation: Decision is an act of making strategic and
right choice among the most likely and equally
attractive alternative.
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c). Integrate the three methods of decision making: There
are three basic approaches in problem solving and
decision making. They are Intuition, Experience and
analysis. They should be used together.
d) Proper documentation of decision steps: A brief and
clear documentation of the procedures employed in a
decision making process is important.
e) Immediate action: When all the necessary steps have
been taken, the decision maker should be bold enough to
act immediately. In every situation requiring immediate
action, the right decision is the first outcome, its
subordinate is the wrong decision; but to do nothing is
complete failure.
f) Openness and humility: Every good decision currently
uses all the available and relevant data timely. It is better
for a manager who is in doubt of the level of information
required or the true meaning of a term to be open and
humbly ask for further explanation from someone who
understands, even if that person is a subordinate.
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2.10 SCOPE AND APPLICATION OF OPERATIONS
RESEARCH IN MANAGEMENT DECISION MAKING
Duckworth (1965) defines operations research as the study
of administrative systems pursued in the scientific manner
in which systems in physics, chemistry and biology are
studied in natural sciences The objective of the study
according to the author is to gain understanding of these
systems so that they can be more readily controlled. The
only way of bridging the operating systems of modern
organizations is through informed decision making that
produce quality goods and manage or expand distribution
channels such that the company gains competitive edge
over its rivals in the market place. Operations research
involves utilizing big minds to work on small problems.
Organizations face problems today from growing domestic
and international competition and must work to make their
operations as effective as possible. As a result, businesses
will increasingly rely on operations research techniques to
optimize profits by improving productivity and reducing
costs. As new technology is introduced into the market
place, operations research is needed to determine how to
utilize the technology in the best way.
Operations research is a problem solving and Decision
making science. It is a kit of scientific and programmable
rules providing the management with a quantitative basis
60
for decisions regarding operations under its control. Some
of the areas where operations research techniques can be
scientifically applied include the following functional areas;
a)Production and facility planning
-Project scheduling and resource allocation
-Replacement policy
-Programming of repairs and maintenance of plants
-Forecasting inventory requirements
b)Marketing
-management of distribution channels
-Product selection and timing
-selection of the most effective advertising media
- Forecasting customer demand
c)Finance
-capital requirements, cash flow analysis
-credit policies, credit risks etc
-determination of optimum replacement policy
d)personnel
-Job allocation policies and assignment of jobs
-Training and retraining for specific assignment
-selection of personnel based on skill assessment
-determination of retirement age that optimize skill
adaptation and utilization.
According to Gupta and Hira (2001), the objective of
operations research is to provide a scientific basis to the
61
managers of an organization for solving problems involving
interaction of the components of the system by employing a
systems approach by a team of scientists drawn from
different disciplines, for finding a solution which is in the
best interest of the organization as a whole.
2.11 MANAGING THE DECISION MAKING PROCESS
The following guidelines will assist decision makers in
managing the decision making process; (Akintoye and
Oluwatosin;2006;404).
a) Recognize that it is impossible for managers to make
optimum decisions and orient their actions to
making the best decision possible.
b) To make the best decision possible, learn to use
intuition and judgment to uncover acceptable
alternatives and choose between them.
c) Constantly monitor changes in organizational
performance and in the environmental forces to
discover if there are any opportunities and threats
that need to be addressed.
d) Create a set of clearly defined criteria to frame
opportunities and threats and apply these criteria
consistently.
e) Encourage managers at all levels to make problem
solving a major part of their jobs and to generate as
many feasible alternatives as possible.
62
f) Be aware of the role peoples preferences and interests
play in generating alternative courses of action and
learn how to manage coalitions to promote effective
decision making.
g) Once the alternative course of action have been
chosen, take steps to implement the decision. Request
periodic updates on the situation from the managers
responsible for implementing the chosen alternative.
2.17 HUMAN SIDE OF OPERATIONS RESEARCH
Successful Implementation of operations research projects
demands interpersonal skills on the part of the operations
research managers. Apart from the entire mathematical
model that operations research is assumed to be made up
of, it is important to emphasize the human side of
operations research if the project is to have organizational
success. A very important part of operations research is
concerned with talking to people about a problem, getting
them to describe the objectives and constraints. This
requires a lot of inter-personal skills which embraces the
following; (Australian Society of operations Research;
2005).
a) Establishing the right, friendly but business-like
atmosphere in which to conduct your discussion.
b) Communicating clearly, the purpose of your
investigation.
63
c) Listening carefully and attentively, to appreciate the
correct emphasis of what the other person is saying
and things which were implied but not said directly.
d) Judgment in being able to establish the truth when
you get conflicting accounts of the same “facts” from
different sources; thus ,avoiding jumping to
premature or one-sided conclusions.
e) Willingness to learn the technicalities of fields entirely
new to enhance, so that you can understand what is
really happening.
f) Ability to accept and deal with inputs that are vague,
uncertain or unquantifiable.
g) Sensitivity to the feelings of people who may be
resistant to changes brought about by operations
research or feels threatened by your investigations
and recommendations.
h) Helping to build consensus among a diverse group of
people as to the basis for effective implementation.
2.13 LIMITATIONS OF OPERATIONS RESEARCH
Operations research has among its many limitations, the
following;
a) Mathematical modeling delimits the scope of
operations research as many factors such as leadership
style, organizational politics and peer group pressure are
emotional factors which influence and affect the
performance of business enterprises are not all responsive
to Quantitative measurement. Thus, the significant
64
reliance of operations research on mathematical models
which do not consider these qualitative factors makes its
models to fail in Negating real life business operations.
b) Mathematical models are applicable to only specific
categories of problems since not all business related
problems are amenable to mathematical modeling or
configuration.
c) It often generates resistance from the employees
because its implementation usually introduces changes to
the known conventions within the organization.
d) Management may by itself resist the changes its
implementation can engender due to conventional thinking
and fear of the unknown. This resistance may inhibit
objective implementation of the recommendations.
e) Young enthusiasts of operations research often
forget that it is meant for men and not otherwise, thus
their actions usually lack human approach in the
implementation of recommended solution hence they
normally experience resistance or frustration.
Gupta and Hira (2000), stress that in the
implementation stage, the decisions cannot be governed by
quantitative considerations alone. It must take into
account the delicacies of human relationships. That is in
65
addition to being a pure scientist, one has to be tactful and
learn the art of getting the decisions implemented. This art
can be achieved by experience as well as by getting training
in the social sciences as particularly psychology.
66
REFERENCES
Akintoye I.R and Oluwatosin R.A, (2006), ICAN Study Pack
on Multi-disciplinary Case Study, VI Publishers, Lagos.
Akintoye,I.R, (2005), Decisions, Concepts and Management,
Lagos, Glorious Hope publishers.
Australian society for operations research Inc {ASOR} (
2005), Careers in Operations Research, Melbourne,
Australia.
Dessler, G. (2001), Management: Leading People and
organization in the 21st century, London, Upper saddle
River, Pretentice hall.
Dixon-Ogbechi,N.B., (2001), Decision Theory in Business
with Q/A, Lagos, Philglad Nigeria Limited.
Duckworth, W.E., (1962), A Guide to Operations Research,
London, Methuen and company Limited.
Gupta K.P. and Hira, D.S (2002), Operations Research,
Ram Nagar, New Delhi, S. Chand and Company.
Gupta C.B. and Gupta V,(1996), An Introduction to
Statistical Methods (9thed), New Delhi, Vickas
Publishing.
Hill, S. (2001), Making Excellent Decisions in Financial
times, Handbook of Management, New York, London,
Prentice Hall publishers.
ICAN (2006), Management Information Systems Study
Pack, VI Publishers, Lagos.
Omotosho, Y.M. (2002), Operations Research Project,
Ibadan, yosodo Book Publishers.
67
Robbins, S.P and Coulter, M. (1999) , Management (6th
ed),Upper Saddle River, Prentice Hall.
Starr,M.K., (2004), Productions and Operations
Management, Cincinnati, Ohio, Atomic dog
Publishing.
Taffler,J.R,(1979), Using Operations Research: A Practical
Introduction to Quantitative Methods in Management,
Englewood Cliffs, Prentice Hall International.
Ugbam, O.C, (2001),Quantitative Techniques: An
Introductory Text, Enugu, Chirol Ventures Limited.
68
CHAPTER THREE
RESEARCH METHODOLOGY
3.1 INTRODUCTION
The aim of this chapter is to discuss the methods and
procedures adopted by the researcher in carrying out the
research work. This chapter consists of the area of the
study, sources of data, population and sample size,
description of research instrument, data analysis
techniques and the validity and reliability of data.
3.2 SOURCES OF DATA
The study relied heavily on data from two broad sources
namely the primary and secondary data.
a)Primary Sources
Ewurum (1995), states that primary sources are obtained
first by the person conducting the research. They are
created through first hand research, experiments or using
such tools as questionnaire or survey.
The above assertion is true of this study. The primary
sources used in this study are those collected from
respondents through the designed questionnaire,
observations and interviews conducted.
69
b) Secondary Sources
Secondary data are facts that the researcher collected from
already existing sources. The secondary data came from
both internal and external sources. The internal sources
included information from books, journals, newsletters,
periodicals, seminar/workshops papers while the external
sources included information from textbooks, newspapers,
magazines, encyclopedia etc.
3.3 POPULATION OF THE STUDY
A population has been described as a make-up of specific
conceivable traits, events, elements, people, subjects or
observation, which relate to the situation of interest in the
study to be conducted. (Sannie and Segilola, 2006;65).The
population for this study consist of all manufacturing
organizations in Enugu state. However, it would not be
possible to use the entire population due to obvious
limitations. Three (3) manufacturing organizations in
Enugu were selected.
The target population for this study consist of the entire
top, middle and lower management staff of the selected
organizations; Innoson Technical and Industrial Limited,
Anammco Nigeria Limited and Juhel Nigeria Limited.
70
According to information obtained from the selected
Manufacturing organizations concerning their population
we have;
Innoson - 360
Anammco - 600
Juhel - 240
Total 1200
The Population for this study is one thousand, two
hundred (1,200).
3.4 METHOD OF SAMPLING
Sampling according to Sannie and Segilola (2006;67) is the
process of determining the proportion of subjects, elements
or members drawn from a population through quantitative
means. The sampling procedure was carefully chosen to
arrive at our sampling size.
In calculating the sample size, the researcher applied the
statistical formular for selecting from a finite population as
formulated by Yamane (1964;280).
The formular is stated thus,
71
n= N 1 + N (e) 2
where n= Sample size
N= Population size
e= Error limit
1= constant
Based on the population of 1200 and a desired error level
of 5%, the sample size for this study was obtained as;
N = 1200
1+1200(0.05)2
= 1200
1+1200(0.0025)
= 1200
4.0
n = 300
Based upon the size of the firms studied, the researcher
decided to use the stratified sampling method so as to give
a fair representation to the designated organizations in the
ratio of 3:5:2 using the proportionality formular to allocate
this sample size. The formular is given as
72
Q = A/N × n/1
Where Q=Number of questionnaire allocate to each
segment A=Population of each segment
N=Total population of all segments
n=Estimated sample size
Innoson = 360 × 300 = 90
1200
Anammco = 600 × 300 = 150
1200
Juhel = 240 × 90 = 60
1200
The above stratified sampling method adopted gave a fair
representation to the designated companies in the ratio of
3:5:2.
3.5 ADMINISTRATION OF QUESTIONAIRE
In the Administration of the Questionnaire, 90 copies were
Administered to the staff of Innoson Technical and
Industrial Limited, 150 copies to the staff of Anammco Ltd
and 60 copies of the questionnaire Administered to the
staff of Juhel Nigeria Limited.
73
A total of 210 responses to the questionnaire were duly
completed and returned to the Researcher. 63 of these
respondents were from the staff of Innoson technical and
Industrial Company, 105 from Anammco Nigeria Limited
while 42 were from members of staff of Juhel Nigeria
Limited.
The summarized data in table 3.1 indicates the number of
Questionnaires issued to each class of the respondents and
how they were returned.
Table 3.1. Questionnaire Issued and Returned
Respondents Issued Returned Total Percentage
Returned
Innoson Ltd 90 63 180 21%
Anammco Ltd 150 105 300 35%
Juhel Nig. Ltd 60 42 120 14%
Total 300 210 600 70%
Source: Field Survey, 2010.
From the table above, 70% of the Questionnaires Issued
were duly competed and returned.
74
3.6 DESCRIPTION OF RESEARCH
INSTRUMENTS
The Instruments used in the collection of data for this
research include the use of questionnaire, Interviews and
observation.
The questionnaire consists of two parts. Part 1 is the
respondents’ personal data and Part 2 contains the
research Questions. The questionnaire contains a total of
23 questions.
Oral Interview was conducted with senior staff of the
selected organisations. The Interview gives an on the spot
response from the respondents. It provides complimentary
data to the questionnaire.
3.7 DATA ANALYSIS TECHNIQUES
The data generated from the study were analyzed using
appropriate statistical tools such as tables and simple
percentages. The hypotheses were also tested using the
chi-square statistical technique. This includes hypothesis
1,2,3,4 and 5.
The chi-square is used to measure the agreement or
discrepancy between observed and expected frequencies.
(Eboh;1988).
75
To calculate the chi-square, the formular below will be
applied.
X2= ∑(of – ef)2
ef
where ∑=Summation
of = observed frequencies
ef = expected frequencies
X2 = Chi-square
The degree of freedom;
It is the assumption of a certain level of confidence or error
margin. The degree of freedom which is significant in the
use of chi-square is presented in the form;
d.f=(R-1)(C-1)
Where R = Number of rows
C = Number of columns
Decision rule in the use of chi-square(x2)
If the computed or calculated value of the test statistics(x12)
is less than or equal to the critical value (x02), accept the
null hypotheses. However, if the computed or observed
value is greater than or equal to the chi-square critical
76
value, the null hypotheses should be rejected, thus
accepting the alternate hypotheses.
Mathematically, it is stated thus,
Reject Ho, if x12 ≥ xo2
Accept Ho, if x12 ≤ xo2
3.8 VALIDITY OF THE RESEARCH INSTRUMENT
Data collected should be tested or validated to ensure that
they are authentic. To ensure that the research
instruments applied in the work are valid, the researcher
ensured that the instruments measure the concepts they
are supposed to measure. The questionnaire was properly
structured and a pre-test was conducted on every question
contained in the questionnaire to ensure that they are
valid. Also the design of the questionnaire was made easy
for the respondents to tick their preferred choice from the
options provided. Response validity was obtained by re -
contacting the individuals whose responses appear
unusual or inconsistent.
3.9 RELIABILITY OF DATA
A Reliability test was also conducted on the instrument to
determine how consistent the responses are. Reliability is
defined as the degree to which similar outcomes are
77
produced by a measuring instrument when used in
different situations.(Onwumere,2009;68).
The Researcher utilized the test/retest method of
Reliability testing where the questionnaire was
administered at two different times to the same group of
respondents. A time lag of 3 weeks was allowed to ensure
that the respondents do not have their earlier responses in
memory.
A correlation of the two sets of observations was conducted
and it reveals a high degree of association which indicates
that the measure is very reliable.
78
REFERENCES
Eboe, F.E, (1988), Social and Economic Research Principles
and Methods, Lagos, Academic Publications and
Development Resources Limited.
Ezejielue et al, (1990), Basic Principles in Managing
Research Project, Onitsha, Africana Feb Publishers
limited.
Onodugo,V.A,(2004),Mimeograph on Research Methodology,
Department of Management, University of Nigeria,
Enugu Campus.
Sannie, M.B.A and Segilola, B.T.Y, (2006), ICAN Study Pack
on Business Communication and Research
Methodology, Lagos, VI Publishers Limited.
Yamane, T, (1964), Statistics: An Introductory Analysis,
New York, Harper and Row
79
CHAPTER FOUR
PRESENTATION AND ANALYSIS OF DATA
4.1 DATA PRESENTATION
This chapter deals essentially with the Analysis of data
collected through the distributed questionnaire. Data
generated from the study were analyzed using appropriate
statistical tools such as tables, percentages, pie chart and
bar charts. From the analysis of questionnaire distributed
and returned, it is pertinent to recall that out of the 300
copies of the questionnaire distributed, 210 representing
about 70% were returned while 90 representing 30% were
not returned.
Figure 4.1: pie chart for questionnaire returned
and unreturned
Returned Unreturned
80
4.2 DATA PRESENTATION AND ANALYSIS
In this section, the researcher analyzed in a tabular form
the responses on the questions asked relating to the
respondents and those generated from the objectives of the
study.
PART A: PERSONAL DATA
Table 4.2.1: Frequency Distribution of Respondents by
Gender
Response
s
No of Respondents
Tota
l
Percentag
e
Innoso
n
Anammc
o
Juhe
l
Male 54 81
27
162
77%
Female 9 24
15
48
23%
Total 63 105
42
210
100%
Source: Field Survey, 2010.
81
Table 4.2.2: Section where employees are employed
Responses Total Response Percentage
Innoson Anammco Juhel Total
Production 18 30 12 60 28.6%
Marketing 9 12 3 24 11.4%
Administration 15 18 12 45 21.4%
Personnel 6 18 3 27 12.8%
Others 15 27 12 54 25.7%
Total 63 105 42 210 100%
Source: Field Survey, 2010.
.
Table 4.2.3: Educational Qualification of respondents
Responses Total Response Percentage
Innoson Anammco Juhel Total
FSLC/WAEC/NECO 12 14 7 33 15.7%
OND/HND 18 39 10 67 31.9%
B.SC 15 21 14 50 23.8%
M.Sc/MBA/Ph.D 12 20 4 36 17.1%
Professional
qualification
3 4 7 14 6.7%
Others 3 7 - 10 4.7%
Total 63 105 42 210 100%
Source: Field Survey, 2010.
The Analysis of the above tables confirms that majority of
the respondents are male as they accounted for about 77%
of the respondents. The tables also reveal that production
82
staffs are the majority of the respondents as they
accounted for about 28.6% of total respondents. The rest
are in Marketing, administration and Personnel. Also the
tables revealed that the majority of the respondents i.e.
31.9% had diploma, 17% had higher degrees, and 23.8%
had university degree while about 15.7% had not more
than O’ level Certificates.
PART B: RESEARCH DATA
Table 4.2.4 below represents the primary data gotten
through the questionnaire administered for analyzing the
various operations research techniques used in decision
making in the selected organizations. Questions 5,6,7,8
and 9 were designed to validate or disprove the above
objective. The responses obtained from the five questions
were presented in the table.
83
TABLE 4.2.4: Responses on the various operations
research techniques used in decision making.
S/N
Description Agree Strongly
Agree Disagree Strongly
Disagree Total
5 Linear programming, Assignment model, Queuing theory and Network analysis are some of the operations research techniques
used in decision making.
50
65
60
35
210
6 Linear programming is a mathematical technique used for finding the optimal values of some variables that exhibit linear relationship in terms of objectives and constraints.
65
40
45
60
210
7 The assignment model involves matching services with demand on a one to one basis so as to achieve optimum overall effectiveness.
74
36
50
50
210
8 The common problem to be solved by a Queuing model is the provision of facilities or scheduling of arrivals to obtain an optimum balance between
waiting time and idle time.
60
70
45
35
210
9 Network analysis is concerned with the development of resources for the completion of non-repetitive tasks within the minimum time.
53
63
51
43
210
Total 566 (54%) 483 (46%) 1050
Source: Field Survey, 2010.
84
From table 4.2.4 above, it can be observed that 566
respondents representing 54% answered in the
“Agreement” category, while 483 respondents representing
46% answered in the category of “Disagreement”.
Table 4.2.5 below represents the primary data gotten
through the questionnaire administered for analyzing the
benefits of using operations research techniques in
decision making in the selected organizations. Questions
10,11,12,13 and 14 were designed to validate or disprove
the above objective. The responses obtained from the five
questions were presented in the table.
85
TABLE 4.2.5: Responses on the benefits of using
operations research techniques used in decision
making.
S/N
Description Agree Strongly Agree
Disagre
Strongly Disagree
Total
10
Operations research aids easy understanding of the overall structure of a business problem.
73
59
45
33
210
11
The use of operations research in decision making helps to clearly indicate the important “cause” and “effect” relationship.
67
63
45
35
210
12
Operations research models facilitates dealing with problem in its entirety and considering all its relationship at the same time.
57
55
53
45
210
13
Operations research facilitates the use of high powered advanced
mathematical logic and computers in analyzing business problems.
53
67
50
40
210
14
Operations research eases the process of the use of simulation in analyzing and forecasting probable future business results
under variety of situations.
70
60
50
30
210
Total 624 (59.4%) 426 (40.6%) 1050
Source: Field Survey, 2010. From table 4.2.5 above, it can be observed that 624
respondents representing 59.4% answered in the
“Agreement” category, while 426 respondents representing
40.6% answered in the category of “Disagreement”.
86
Table 4.2.6 below represents the primary data gotten
through the
questionnaire administered for analyzing the cost-benefits
of using operations research techniques in decision making
in the selected organizations. Questions 15,16 and 17 were
designed to validate or disprove the above objective. The
responses obtained from the three questions were
presented in the table
TABLE 4.2.6: Responses on the cost- benefit analysis of
using operations research techniques used in decision
making.
Source: Field Survey, 2010
Source: Field Survey, 2010.
S/N Description
Agree Strongly Agree
Disagree Strongly Disagree
Total
15 The benefits of using operations
research in decision making do not justify the expenditure incurred.
53
65
45
47
210
16 The benefits of using operations research in decision
making justifies the expenditure incurred.
57
65
50
38
210
17 The cost incurred in implementing operations research models in decision making equates the benefits derived.
60
55
45
50
210
Total 329 (52.2%) 301 (47.8%) 630
87
From table 4.2.6 above, it can be observed that 329
respondents representing 52.2% answered in the
“Agreement” category, while 301 respondents representing
47.8% answered in the category of “Disagreement”.
Table 4.2.7 below represents the primary data gotten
through the questionnaire administered for analyzing the
relationship between the use of operations research in
decision making and the productivity level in the selected
organizations. Questions18 and 19 were designed to
validate or disprove the above objective. The responses
obtained from the five questions were presented in the
table.
TABLE 4.2.7: Responses on the relationship between
the use of operations research techniques in decision
making and productivity.
S/N
Description
Agree Strongly Agree
Disagree Strongly Disagree
Total
18 The nature of the relationship between the use of
operations research models in decision making and productivity is positive.
70
50
50
40
210
19 The nature of the relationship between the use of operations research models in decision making and productivity is negative.
60
50
40
60
210
Total 230 (54.7%) 190 (45.3%) 420
Source: Field Survey, 2010.
88
From table 4.2.7 above, it can be observed that 230
respondents representing 54.7% answered in the
“Agreement” category, while 190 respondents representing
45.3% answered in the category of “Disagreement”.
Table 4.2.8 below represents the primary data gotten
through the questionnaire administered for analyzing the
problems encountered in using operations research
techniques in decision making in the selected
organizations. Questions 20,21,22, and 24 were designed
to validate or disprove the above objective. The responses
obtained from the five questions were presented in the
table.
TABLE 4.2.8: Responses on the problems of using
operations research techniques in decision making.
S/N
Description
Agree Strongly Agree
Disagree Strongly Disagree
Total
20 Mathematical models are applicable to only specific categories of problems since not all business related problems are amenable to mathematical modeling.
65
70
45
30
210
21 The use of operations research often generates resistance from the
67
65
39
39
210
89
employees because its implementation introduces changes to known convention within the organization.
22 The action of managers usually lacks human approach in the implementation of operations research.
54
66
43
47
210
23 The reliance of operations research on mathematical models which do not consider qualitative factors makes the model to fail in negating real life business operations.
57
65
53
35
210
Total 509 (60.6%) 331 (39.4%) 840
Source: Field Survey, 2010. From table 4.2.8 above, it can be observed that 509
respondents representing 60.6% answered in the
“Agreement” category, while 331 respondents representing
39.4% answered in the category of “Disagreement”.
4.3 HYPOTHESIS TESTING PROCEDURES
In this section, the five (5) hypothesis which were earlier
formulated in chapter one will be tested accordingly so as
to achieve the objectives of the study. Each of the
formulated hypotheses would be tested using the chi-
square statistical technique.
Hypothesis 1
Degree of freedom (d.f):
The degree of freedom is d.f (R-1) (c-1)
Where C = No of Column
90
R = No of Row
d.f = (5-1) x (2 – 1)
= 4 x 1
= 4.
Computation of Critical Value
X2
Decision Rule: The decision rule is stated as
Reject Ho: If X2 (calculated) > 9.49
Accept Ho: If X2 (calculated) < 9.49
Computation of Data for Validation of Hypothesis 1
Table 4.3.1: Contingency table for Hypothesis 1
S/N
Description Agree Disagree
Row Total
5 Linear programming, Assignment model, Queuing theory and Network analysis are some of the operations research techniques used in decision making.
115
95
210
6 Linear programming is a mathematical technique used for finding the optimal values of some variables that exhibit linear relationship in terms of objectives and constraints.
105
105
210
7 The assignment model involves matching services with demand on a
4, 0.05 = 9.49 (from X2 tables)
91
one to one basis so as to achieve optimum overall effectiveness.
110 100 210
8 The common problem to be solved by a Queuing model is the provision of facilities or scheduling of arrivals to obtain an optimum balance between waiting time and idle time.
130
80
210
9 Network analysis is concerned with the development of resources for the completion of non-repetitive tasks within the minimum time.
116
94
210
Column Total 576 474 1050
Source: Field Survey, 2010
Computation of Calculated chi square value
Of Ef of-ef (of-ef)2 (of-ef)2/ef
115 115.2 (0.2) 0.04 0.00035
95 94.8 0.2 0.04 0.00042
105 115.2 (10.2) 104.04 0.90313
105 94.8 10.2 104.04 1.09747
110 115.2 (5.2) 27.04 0.23472
100 94.8 5.2 27.04 0.28523
130 115.2 14.8 219.04 1.90139
92
Decision: The test Statistics has faller into the Acceptance
or Non Rejection region since the calculated chi-square
value of 6.74557 is less than the critical value of 9.49
obtained from tables.In accordance with the decision rule
stated earlier, we accept the Null (H0) hypothesis which
states that Linear programming, Network analysis and
decision trees are some of the operations research tools
used by manufacturing companies in decision making.
Hypothesis 2
Degree of freedom (d.f):
The degree of freedom is obtained as
d-f. = (R-1) (C-1)
where R = Number of Rows
C = Number of Columns
d.f = (5-1) (2-1)
= 4 x1
= 4
80 94.8 (14.8) 219.04 2.31055
116 115.2 0.8 0.64 0.00556
94 94.8 (0.8) 0.64 0.00675
Total ∑∑∑∑ (of-ef)2/ef
6.74557
93
Computation of critical value
2
= 9.49 (from x2 tables). 4,0.05
Decision Rule:
The Decision rule is stated thus;
Reject H0, if 2 (calculated) > 9.49
Accept H0, if 2 (calculated) < 9.49
Computation of Data for Validation of Hypothesis 2
Table 4.3.2: Contingency table for Hypothesis 2
S/N
Description Agree Disagree Row Total
10 Operations research aids easy understanding of the overall structure of a business problem.
132
78
210
11 The use of operations research in decision making helps to clearly indicate the important “cause” and “effect” relationship.
130
80
210
12 Operations research models facilitate dealing with problem in its entirety and considering all
112
98
210
94
its relationship at the same time.
13 Operations research facilitates the use of high powered advanced mathematical logic and computers in analyzing business problems.
120
90
210
14 Operations research eases the process of the use of simulation in analyzing and forecasting probable future business results under variety of situations.
130
80
210
Column Total 624 426 1050
Source: Field Survey, 2010. Computation of Calculated chi square value
Of ef of-ef (of-ef)2 (of-ef)2/ef
132 124.8 7.2 51.84 0.41538
78 85.2 (7.2) 51.84 0.60845
130 124.8 5.2 27.04 0.22167
80 85.2 (5.2) 27.04 0.31737
112 124.8 (12.8) 163.84 1.31282
98 85.2 12.8 163.84 1.92300
95
120 124.8 (4.8) 23.04 0.18462
90 85.2 4.8 23.04 0.27042
130 124.8 5.2 27.04 0.22167
80 85.2 (5.2) 27.04 0.31737
Total ∑∑∑∑ (of-ef)2/ef
5.7928
Decision: The test Statistics has fallen into the Non
Rejection region since the calculated chi-square value of
5.7928 generated is less than the critical value of 9.49
obtained from tables. In accordance with the earlier
stated decision rule, we accept the Null (H0) hypothesis
which states that cost reduction, increased productivity
and efficiency in operations are some of the benefits of
using operations Research techniques in the decision
making process of organization.
Hypothesis 3
Degree of freedom (d.f):
The degree of freedom is obtained as
d-f. = (R-1) (C-1)
where R = Number of Rows
C = Number of Columns
d.f = (3-1) (2-1)
= 2 x1
= 2
96
Computation of critical value
2 = 5.99 (from x2 tables).
2,0.05
Decision Rule:
The Decision rule is stated thus;
Reject H0, if 2 (calculated) > 5.99
Accept H0, if 2 (calculated) > 5.99
Computation of Data for Validation of Hypothesis 3
Table 4.3.3: Contingency table for Hypothesis 3
S/N
Description Agree
Disagree
Row Total
15
The benefits of using operations research in decision making do not justify the expenditure incurred.
118
92
210
16
The benefits of using operations research in decision making justify the expenditure incurred.
122
88
210
17
The cost incurred in implementing operations research models in
115
85
210
97
decision making equates the benefits derived.
Total 329 301 630
Source: Field Survey, 2010. Computation of Calculated chi square value
Of Ef of-ef (of-ef)2 (of-ef)2/ef
118 110 8 64 0.5818
92 100 (8) 64 0.6400
122 110 12 144 1.3091
88 100 (12) 144 1.4400
115 110 5 25 0.2273
95 100 (5) 25 0.2500
Total ∑∑∑∑ (of-ef)2/ef
4.448
Decision: The test Statistics has fallen into the Non
Rejection region since the calculated chi-square value of
4.448 generated is less than the critical value of 5.99
obtained from tables. In accordance with the decision rule
which was earlier stated, we would accept the Null (H0)
hypothesis which states that the benefits of using
operations research tools in decision making justify the
expenditure incurred in its implementation.
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Hypothesis 4:
Degree of freedom:
The degree of freedom is obtained as
d-f. = (R-1) (C-1)
where R = Number of Rows
C = Number of Columns
d.f = (2-1) (2-1)
= 1 x1
= 1
Computation of critical value
2 = 3.84 (from chi square tables).
1, 0.05
Decision Rule:
The Decision rule is stated thus;
Reject H0, if 2 (calculated) > 3.84
Accept H0, if 2 (calculated) < 3.84
Computation of Data for validation of hypothesis 4
Table 4.3.7: Contingency table for Hypothesis 4
S/N Description Agree Disagree Row Total
18 The nature of the relationship between the use of operations research models in decision making and productivity is positive.
120
90
210
19 The nature of the relationship between the use of operations research models in decision making and productivity is
110
100
210
99
negative.
Column Total 230 190 420
Source: Field Survey, 2010.
Computation of Calculated Chi Square Value
Of Ef of-ef (of-ef)2 (of-ef)2/ef
120 115 5 25 0.2174
90 95 (5) 25 0.2632
110 115 (5) 25 0.2174
100 95 5 25 0.2632
Total ∑∑∑∑ (of-ef)2/ef
0.9612
Decision: The test Statistics has faller into the Non
Rejection region since the calculated chi-square value of
0.9612 generated is less than the critical value of 3.84
obtained from tables.In compliance with our decision rule,
we would accept the Null (Hi) hypothesis which states that
there is a direct positive relationship between the use of
operations research in decision making and the
productivity level in firms.
Hypothesis 5:
Degree of freedom (d.f):
The degree of freedom is obtained as
d-f. = (R-1) (C-1)
where R = Number of Rows
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C = Number of Columns
d.f = (4-1) (2-1)
= 3 x1
= 3
Computation of critical value
2
= 7.82 (from chi square tables).
3,0.05
Decision Rule:
The Decision rule is stated thus;
Reject H0, if 2 (calculated) > 7.82
Accept H0, if 2 (calculated) > 7.82
Computation of Data for Validation of Hypothesis 5
Table 4.3.8: Contingency table for Hypothesis 5.
S/N Description Agree Disagree Row Total
20 Mathematical models are applicable to only specific categories of problems since not all business related problems are amenable to mathematical modeling.
135
75
210
21 The use of operations research often generates resistance from the employees because its implementation introduces changes to known convention within the organization.
132
78
210
101
22 The action of managers usually lacks human approach in the implementation of operations research.
120
90
210
23 The reliance of operations research on mathematical models which do not consider qualitative factors makes the model to fail in negating real life business operations.
125
85
210
Column Total 509 331 840
Source: Field Survey, 2010. Computation of Calculated chi square value
of Ef of-ef (of-ef)2 (of-ef)2/ef
135 127 8 64 0.5039
75 83 (8) 64 0.7711
132 127 5 25 0.1969
78 83 (5) 25 0.3012
120 127 (7) 49 0.3858
90 83 7 49 0.5904
125 127 (2) 4 0.0315
85 83 2 4 0.0.482
Total ∑∑∑∑ (of-ef)2/ef 2.829
Decision: The test Statistics fell into the Acceptance or the
Non-Rejection Region since the calculated chi-square value
of 2.829 is less than the critical value of 7.82 obtained
from the chi-square tables. We therefore Accept the Null
hypothesis which states that employee resistance, lack of
commitment and insufficient number of specialists are
some of the problems which are encountered in the use of
operations resources techniques in the decision making
process of our firms.
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CHAPTER FIVE
SUMMARY OF FINDINGS, CONCLUSIONS AND
RECOMMENDATIONS
5.1 INTRODUCTION
This chapter summarizes the various research results
which emerged from the study. The results were aligned
with the various objectives and hypotheses set out earlier
in chapter one of the project. Relevant conclusions were
103
also drawn and recommendations made from the findings
of the research.
5.2 SUMMARY OF FINDINGS
The major findings of the study were summarized below.
That the companies understand what operations research
techniques are and use them extensively in their decision
making process. Among the most popular techniques
which are used include linear programming, network
Analysis and decision trees. This was confirmed by the
testing of hypothesis one.
That there are numerous benefits which accrue to
organizations by applying operations research techniques
in decision making process of firms. These benefits were
found to be in the form of Increased Productivity and
revenue, Cost reduction and efficiency in operations. Test
of hypothesis two confirmed this.
That the Amount spent on the implementation of
operations research techniques in decision making is
considered insignificant considering the benefits which are
derived by using operations research in decision making.
So, the benefit of using operations research in decision
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making more than justifies the expenditure involved. The
results of the testing of hypothesis three confirmed this.
The study also revealed that there has been an increase in
the productivity level of the firms studied and that this
increase in productivity was found to be as a result of the
application of operations research models in decision
making. This therefore, shows that there is a direct positive
relationship or correlation between the application of
operations research models in decision making and the
productivity levels in firms. Hypothesis four proves this to
be correct.
Finally, it was observed that there are some factors which
hinder, mitigate or limit the application of operations
research models in the decision making processes of firms.
Among these difficulties or problems to the use of
operations research includes employee resistance, lack of
commitment and insufficient number of qualified personnel
who can implement operations research in decision
making. Test of hypothesis five confirmed this.
5.2 CONCLUSIONS
This study has delved into the modern technique of using
operations research techniques in the decision making
processes of manufacturing firms. The basic conclusions
which were arrived at the end of the study were the
105
exposition of the various techniques of operations research
which were applied in decision making. The various
benefits which the firms enjoy as a result of using
operations research in decision making were also
highlighted.
Furthermore, we were also led to the conclusion that a
direct positive relationship exist between the productivity of
firms and the use of operations research in making
decisions. A comparison was also carried out between the
cost and benefit of using operations research. The result
indicates that the use of operations research is cost
effective as the expenditure incurred was justified by the
benefits derived in this regard.
In spite of the numerous benefits of using operations
research in decision making, it was also noted that there
are still some challenges or obstacles hindering the
effective use of operations research in decision making.
Unless these obstacles are properly managed we might not
reap all the benefits of using operations research
techniques in decision making.
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5.3 RECOMMENDATION
Based upon the findings of this research work, the
following recommendations were made;
Presently only Linear programming, Network analysis and
Decision tree are widely used by firms in decision making.
It is thereby recommended that firms should explore the
use of other modern techniques of operations research so
as to improve decision making.
In view of the numerous benefits of applying operations
research to decision making, the firms should encourage
the continual use of operations research so as to continue
to enjoy those benefits.
The budget for operations research should be increased so
that the scope of application of operations research could
be enlarged. This is necessary since the use of operations
research is cost effective as the firms would enjoy the
economies of large scale operations.
For organizations to still remain in business, it needs to be
very productive. And since the use of operations research
leads to increased productivity, it is therefore
recommended that those companies who are yet to start
implementing operations research in their decision making
should do so as to enjoy increased productivity.
107
Lastly, it is recommended that the companies should
embark on aggressive training of personnel so as to
appreciate the usefulness of operations research thereby
reducing resistance from employees and management. Also
the use of operations research should be regulated to
manage some of its hindrances and this is why this
research is advocating for the establishment of the
institute of operations research (chartered) to regulate the
profession.
108
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