1

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

27

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”.

28

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

29

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.

40

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.

54

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.

58

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.

59

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.

98

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

100

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.

102

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

104

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.

106

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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