A T e x t B o o k o f

O P E R A T I O N A L R E S E A R C H A N D F O O D

P L A N T M A N A G E M E N T

S U S H I L D H I T A L C E N T R A L C A M P U S O F T E C H N O L O G Y

H A T T I S A R , D H A R A N , N E P A L A P R I L 2 0 0 6

Inputs • Land • Material • Labor • Capital • Management • Information

Transformation Process

Outputs • Goods • Services

Feedback mechanism Comparison

Actual Vs Desired

Random Disturbances

Quality of output monitored

Quality of input monitored

ii

P r e f a c e

This book 'A Text Book of Operational Research and Food Plant Management' is based on the syllabus for B. Tech (Food) 4th Year. Within the scope and limitation of the syllabus, I have tried to put together information as meticulously as possible. Due care and effort is paid to customize this book into lucid simple and interesting for technical students, using simple language, common terminologies, examples of industries and Nepalese scenario. Along with text, subject matters are presented as diagram, graph, and models, making it student friendly. This book can also be useful to students of BBA and MBS.

Thanks are due to those authors whose books I have freely consulted. I am very much thankful to Rita for her support to type this manuscript.

This book is for educational purpose, and author permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Electronic version of the book is available on request.

All the views and comments about the book are most welcomed and are requested to address at sudhit2004 @yahoo.com. Sushil Dhital Central Campus of Technology Hattisar , Dharan, Nepal April 13, 2006

iii

Contents

I N T R O D U C T I O N T O O P E R A T I O N R E S E A R C H

1.1 Introduction 1 1.1.1 Techniques frequently used in OR 2 1.2. Historical development and future scope of Operation Research 4 1.2.1 Methodology of or (process of OR) 4 1.2.2 Scope of OR 6 1.3 Roles of models in OR – the need to strike a balance between simplicity and complexity 7 1.3.1 Models 7 1.3.2 Types of models 8 1.4 Role of Research in Industry and Research Administration 9

1.4.1 Research and industrial research 9 1.4.2 Industrial research 10

1.4.3 Administration of industrial research 11

L I N E A R P R O G R A M M I N G

2.1 Introduction 12 2.1.1 Component of LP Model 12 2.1.2 Construction of LP Model 13 2.2 Assumptions of Linear Programming 14 2.3 Application areas of LPP 14 2.4 Advantage of LPP 15 2.5 Graphical solution of LP problems 15 2.5.1 Graphical solution, example of a maximization model 15 2.5.2 Procedures of graphical solution 15 2.5.3 Graphical solution of LP of a minimization model 16 2.5.4 Special cases in linear programming 18 2.6 Simplex method 21 2.6.1 Solving maximization problem by simplex method 21 2.6.2 Big M method 28 2.6.3 Minimization programming 31 2.6.4 Special cases in linear programming in simplex method 33 2.7 Example worked out 38 2.8 Problems 44

N E T W O R K A N A L Y S I S

3.1 Introduction 48 3.1.1 Basic concept of Network analysis 48 3.1.2 Construction of Network 49 3.1.3 Determination of path, critical path and critical activities 50 3.2 PERT Network 50 3.3 CPM Network or CPM 51 3.4 Basic difference between PERT and CPM 53 3.5 Exercise 54

C h a p t e r

C h a p t e r

C h a p t e r

iv

Q U E U I N G T H E O R Y

4.1 Introduction 56 4.2 Definition and objectives of queuing theory 57 4.3 Problem involving queuing theory 57 4.4 Queuing system and its essential elements 58 4.4.1 Input source 59 4.4.2 Queuing process 60 4.4.3 Queuing discipline 60 4.4.4 Service process 60 4.5. Single channel queuing model 62 4.5.1 Operating characteristics of a queuing system 62 4.5.2 Assumption of single channel queuing model 62 4.5.3 Operating characteristics of a queuing system 63 4.5.4 Assumption of single channel queuing model 63 4.6 Solved examples 64 4.7 Problems 68

F I N A N C I A L M A N A G E M E N T

5.1 Concept 70 5.1.1 Purpose of investment 70 5.2 Capital 70 5.3 Sources of finance 71 5.4 Reserve and surplus 76 5.5 Financial accounting and book-keeping 76 5.5.1 Financial accounting 76 5.5.2 Book-keeping 77 5.5.2 The journal and the Ledger 78 5.6 Financial statement 78 5.6.1 Balance sheet 79 5.6.2 Income statement 80 5.7 Analysis of financial statement i.e. financial ratios 83 5.7.1 Illustrations 84 5.7.2 Summary 88 5.7.3 Solved problem 89

T I M E V A L U E O F M O N E Y

6.1 Time value of money 94 6.1.1 Compound value (future value) of money 94 6.1.2 Present value of money 96 6.1.3 Value of an annuity due 98 6.1.4 Summary of formulas 99 6.2 Capital budgeting and nature of investment decision 100 6.2.1 Types of investment decisions 101 6.2.2 Steps in capital budgeting 101 6.2.3 Project evaluation or investment evaluation criterion 102

C h a p t e r

C h a p t e r

C h a p t e r

v

I N V E N T O R Y M A N A G E M E N T

7.1 Introduction 110 7.1.1 Nature and classification of inventories 110 7.1.2 Functions of inventories: need to hold inventories 111 7.1.3 Objectives of inventory control 112 7.2 Relevant inventory cost & cost trade offs 113 7.3 Techniques of inventory management / inventory model 115 7.3.1 Basic EOQ model (EOQ model with no shortage) 115 7.3.2 EOQ model with finite replacement rate (gradual replacement model) 117 7.3.3 Quantity discount model (EOQ with price breaks model) 118 7.3.4 Probabilistic inventory model 119 7.4. Selective inventory management (ABC analysis) 121 7.5 Other terminologies associated with inventory management 123 7.6 Examples 124

P R O D U C T I V I T Y M A N A G E M E N T

8.1 Introduction 126 8.1.1 Misunderstanding about productivity 126 8.1.2 Linkage between productivity and profitability 127 8.2 Productivity measurement 127

8.2.1 Measurement of output 128 8.2.2 Measurement of input 129 8.3 Types of productivity 129 8.3.1 Some important partial productivity measure 130 8.4 Various level of productivity measurement 131 8.5 Case study for productivity measurements 132 8.6 Factor affecting productivity 134 8.6.1 External factor 134 8.6.2 Internal factors 135 8.7 Productivity improvement techniques 137 8.7.1 Human ware oriented productivity improvement technique 138 8.7.2 Software oriented techniques 138 8.7.3 Hardware oriented tools and techniques 139

C O S T V O L U M E P R O F I T A N A L Y S I S

9.1 Introduction 141 9.1.1 Calculation of breakeven points 141 9.2 BEA chart 143 9.3.1 Assumption of BEA 144 9.3.2 Advantages and application of BEA 144 9.3.3 Limitations of BEA 146

C h a p t e r

C h a p t e r

C h a p t e r

vi

I N D U S T R I A L B U D G E T I N G A N D C O S T A N A L Y S I S

10.1 Introduction 147 10.1.1 Objective of budget 147

10.1.2 Advantages of budgetary control 148 10.1.3 Limitations of budgetary control system 148

10.1.4 Essentials of effective budgeting 149 10.2 Types of budget 149 10.3 Fixed and variable budget 152

10.4 Zero based budgeting (ZBB) 152

F A C I L I T Y L O C A T I O N A N D L A Y O U T P L A N N I N G

11.1 Need of facility location (factory location, plant location) 153 11.2 Factor affecting plant location 153 11.2.1 Competitive advantage between urban, rural & sub urban plant locations 155 11.3 General procedure in facility location 155 11.4 Behavioral impact in facility location 159 11.5 Factory layout concept 160 11.5.1 Objectives of layout 160 11.5.2 Principles of plant layout 160 11.5.3 Factors influencing plant layout 161 11.6 Types of layout 161 11.6.1 Process layout 161 11.6.2 Product layout 162 11.6.3 Combination layout 164 11.6.4 Fixed position layout 164 11.7 Behavioral aspects in layout designing 164 11.7.1 Behavioral aspects in process layout 164 11.7.2 Behavioral aspects in product layout 165 11.8 Comparison of basic layout 166 11.9 Methods of plant and factory layouts 166 11.10 The dynamics of layout 166 11.11 Layout procedure 168 11.12 Building for plants 170 11.12.1 Factor affecting the building design 170 11.12.2 Types of building 172 11.12.3 Types of construction 173

S I M U L A T I O N

12.1 Introduction 174 12.1.1 Definition and condition for use of simulation 174 12.1.2 Objectives of simulation model 175 12.2 Steps in building a simulation model 175 12.3 Types of simulation 176 12.4 Merits and demerits of simulation models 176 12.5 Simulation of inventory models 177 12.6 Simulation of queuing models: Monte Carlo simulation of queues 179 12.7 Exercise 181

C h a p t e r

C h a p t e r

C h a p t e r

vii

P R O D U C T D E S I G N A N D D E V E L O P M E N T

13.1 Need of new product design 183 13.2 Product design 184 13.2.1 Effect of design on cost 185 13.2.2 Character of good design 186 13.2.3 Factor affecting the product design 186 13.2.4 New product development procedure 187 13.2.5 Product life cycle 188 13.3 Tools for product development 190 13.3.1 Standardization: industrial standardization of products 190 13.3.2 Specialization 194 13.3.3 Diversification 194

P R O D U C T I O N P L A N N I N G A N D C O N T R O L L I N G

14.1 Concept of production planning and controlling 195 14.2 Objectives of production planning and controlling 197 14.3 Steps for production planning and control and function of PPC 197 14.3.1 Phases of PPC 198 14.3.2 Elements of PPC 199 14.4 Importance/ benefits/ advantage of PPC 205 14.5 Factors affecting PPC 206

M A N A G E M E N T A N D I T S F U N C T I O N S

15.1 Concept of management 207 15.1.1 Management, administration and organization 208 15.1.2 Types and function of management 208 15.2 Planning 209 15.2.1 Types of planning 210 15.2.2 Steps in planning 211 15.2.3 Relation between planning other managerial function 211 15.3 Organizing 212 15.4 Directing 213 15.4.1 Leadership 213 15.4.2 Communication 214 15.4.3 Supervision 215 15.5 Co-ordination 215 15.6 Controlling 216 15.6.1 Importance of control 217 15.6.2 The control process 217 15.6.3 Types of control 219 15.6.4 Techniques of control 220 15.7 Decision making 220 15.7.1 Decision making, a basic managerial function 222 15.7.2 Types of problems and decisions 222

C h a p t e r

C h a p t e r

C h a p t e r

viii

M A N P O W E R M A N A G E M E N T

16.1 Concept 224 16.1.1 Function of personnel management 225 16.2 Recruitment and selection 225 16.2.1 Recruitment 225 16.2.2 Selection 226 16.3 Training 228 16.3.1 Concepts 228 16.3.2 Methodology of training 229 16.3.3 Kinds or types or forms of training 229 16.4 Promotion / transfer / demotion 230 16.4.1 Promotion 230 16.4.2 Demotion 232 16.4.3 Transfer 232 16.5 Job evaluation 232 16.5.1 Concept 232 16.5.2 Objective of job evaluation 234 16.5.3 Method of job evaluation 234 16.6 Wage and salary administration 236 16.6.1 Concepts 236 16.6.2 Administrating wage and salary 237 16.6.3 Types of wage 238 16.6.4 Determination of wage/salary 238 16.6.5 Essential of sound wage plant 239 16.6.6 Method of wage payment 239

O R G A N I Z A T I O N

17.1 Organization concept 243 17.1.1 Function of organization 244 17.1.2 Principle of organization (organizational structure) 244 17.2 Types of organization 246 17.2.1 Line organization 246 17.2.2 Functional organization 247 17.2.3 Line and staff organization 248 17.2.4 Committee organization 249 17.2.5 Project organization 250 17.2.6 Matrix organization 251 17.2.7 Merit and demerit of organization types 251 17.3 Characteristics of organization executives 252

M O T I V A T I O N

18.1 Concepts 253 18.2 Approaches to motivation 254 18.3 Theories of motivation 255 18.3.1 Maslow's hierarchy of needs theory 255 18.3.2 Mc Gregor's theory X & Y 256 18.3.3 Herzberg's motivation – hygiene theory 257 18.4 Motivational techniques 258

C h a p t e r

C h a p t e r

C h a p t e r

ix

I N D U S T R I A L O W N E R S H I P

19.1 Concepts 261 19.2 Sole proprietorship (individual ownership) 262 19.2.1 Characteristics of sole proprietorship organization 262 19.2.2 Advantage of sole proprietorship enterprise 262 19.2.3 Disadvantage of SPE 263 19.3 Partnership organization 263 19.3.1 Characteristics (feature) of a partnership firm 264 19.3.2 Types of partners 264 19.3.3 Partnership deed 265 19.3.4 Mutual relationship of partners (mutual rights and obligation of partners) 266 19.3.5 Dissolution of partnership and partnership firm in Nepal 268 19.3.6 Evaluation of partnership firm (merit and demerit of partnership firm) 269 19.4 Joint stock company 270 19.4.1 Feature of joint stock company 271 19.4.2 Classification of joint stock company 271 19.4.3 Advantage and disadvantage of joint stock company 272

M A N A G E M E N T B Y O B J E C T I V E

20.1 Concepts 273 20.2 Objectives of MBO 273 20.3 Step in MBO 274 20.4 Advantage of MBO 274 20.5 Limitation of MBO 275

M A R K E T I N G M A N A G E M E N T

21.1 Concept of marketing 276 21.2 Marketing and its function 277 21.2.1 Definition 277 21.2.2 Marketing process 278 21.2.3 Marketing function 278 21.3 Marketing management and its function 279 21.3.1 Setting objectives 279 21.3.2 Planning the marketing mix 280 21.3.3 Organizing the marketing function 281 21.3.4 Controlling 282 21.4 Marketing research 283 21.4.1 Concept 283 21.4.2 Importance and marketing research 284 21.4.3 Area of marketing research 284 21.4.4 Objectives of marketing research 285 21.4.5 Marketing research process 285 21.5 Sales forecasting 285 21.5.1 Interaction about basic types of forecast 286 21.5.2 Uses of sales forecast 286 21.5.3 Basic elements of sales forecast 287 21.5.4 Methods and techniques of sales forecasting 288

C h a p t e r

C h a p t e r

C h a p t e r

x

21.6 Advertising 288 21.6.1 Merit and weakness of advertising promotion tool 288 21.6.2 Function and objective of advertisement 289 21.6.3 Media of advertising 289 21.7 Sales promotion 289 21.7.1 Objective merit demerit and kinds of sales promotion 290 21.8 Channel of distribution 291 21.8.1 Definition and types 291 21.8.2 Channel choice 292 21.9 Product packaging 293 21.10 Pricing 294 21.10.1 Price and pricing 294 21.10.2 Pricing procedure and techniques 295

M I X E D E C O N O M Y

22.1 Types of economy 297 22.2 Feature of mixed economy 298 22.3 Nepalese perspective 299 22.4 Controls in mixed economy 300

R I S K A N D F O R E C A S T I N G

23.1 Concepts 302 23.2 Economic forecasting 303 23.3 Methods of forecasting 304 23.4 Role of forecasting in business 310 23.5 Specific risk in industrial operations 311 23.6 Selection of the forecasting model 311

I N D U S T R I A L C O S T I N G

24.1 Classification of cost 313 24.2 Element of cost 315 24.3 Types of cost 315 24.4 Method (technique, process) of costing 316

Q U A L I T Y C O N T R O L

25.1 History of quality control 317 25.2 Quality: definitions 318 25.3 Quality control 318 25.3.1 Element of quality control 319 25.3.2 Methods of quality control 319 25.3.3 Function (objective) of quality control 320 25.3.4 Factors controlling quality 320 25.4 Statistical quality control 320 25.4.1 Types of control 321

C h a p t e r

C h a p t e r

C h a p t e r

C h a p t e r

xi

25.4.2 Basic principle for the construction of control chart 322 25.4.3 Construction mechanism of control chart 322 25.4.4 Control chart for mean or x chart 323 25.4.5 Control limits for range or R-chart 324 25.4.5 P-chart (fraction defective) 327 25.5 Relation of QC department with other departments 328 25.5.1 Function of QC department 328 25.5.2 Relation of QC department with general management 329 25.5.3 Relation of QC department with sales and purchasing 329 25.5.4 Relation of QC department with production 329 25.5.5 Relation of QC department with R &D 330 25.6 Problems 330

Bibliography I

Appendix – 1: Factors for Computing Central Lines and 3s Control Limits for, II X bar, S and R charts

Appendix – 2: Table of random numbers generated by Microsoft Excel 2003 III with number of variable 2, number of random number 400 between 0-100, and uniform distribution.

C h a p t e r —

I N T R O D U C T I O N T O O P E R A T I O N

R E S E A R C H

1.1 INTRODUCTION Operation research (synonymous to operations research, operational research, quantitative method, management science, decision science and other names like system analysis or decision analysis) is a multi-disciplinary problem oriented approach used for solving complex problem. Simply, it is a Quantitative technique for managerial decision-making. Decision-making means selecting specific course of action from possible alternatives. Basically during operation or production, it is not easy to choose superlative alternative among diverse alternative, because a wrong decision may have long-term negative effect on the profitability or event sustainability of any organization. This kind of situation prevailing in management decision making are called complex situation. Any situation becomes complex when, lot of factors are affecting it or are related to it. In these situations, a subjective decision or just decisions by judgment or experience may not work well. There is a need of scientific methods to analysis of situation and obtain best course of action for decision-making. These methods basically quantitative methods when applied to the decision making in complex situations is called an operation research or operational research.

Figure 1.1: Managerial problem and Operation Research technique Techniques that are used for decision-making are varied according to the problem or situation. It means that, a type of OR technique is not applicable to all decision situations. It is the prominent role of production manager to select appropriate technique useful to him according to the encountered problem.

Problem (Managerial problem)

A

BC

D E

OR Techniques

Decision

A,B,C,D and E are factors affecting the problem

2

1.1.1 TECHNIQUES FREQUENTLY USED IN OR Some OR techniques for management decision-making are described on succeeding paragraphs. Linear Programming (LP) :It is one of the most versatile, powerful and useful techniques for making managerial decisions in the field of marketing, finance, production, personnel research and development. As most of the organization has limited or inadequate resources, therefore, the optimum use of these resources to get maximum profit or minimum cost should be the motto of organization. The sustainability or profitability of organization is largely dependent on the way of using its resources. LP is used in determining the product mix, transportation schedules, plant location, assignment of personnel and machines, media selections, investment portfolio selection, blending materials, energy, ecology (pollution) and other unlimited areas. LP used in transportation schedules is some times called as transportation problem. Similarly, LP when used in assignment of resources to activities aiming to minimize cost or maximize profit is sometimes called as assignment problems. Decision Theory/Decision Models: Decision models are related to decision-making under conditions of certainty, risk and uncertainty. Most of the business problems involve a certain degree of uncertainty about the future. The use of probability theory enables a manager to calculate the probabilities of occurrence of various events in business problem. The use of these probabilities and various decision models helps the decision maker in arriving at a suitable course of action under single stage and multistage decision processes. The decision models are extremely useful in determining the degree of uncertainty and the extent to which it may be reduced. The decision theory uses various techniques, dependent on the certainly, uncertainly or risk. Techniques applicable on the certainty conditions are linear programming, system of equation, integer programming, dynamic programming, queuing model, inventory models, capital budgeting analysis and breakeven analysis. Techniques that are used in risk conditions are EMV & EOL (Expected monitory value and expected opportunity loss), where aim is either to maximize expected pay off (monetary value) or minimize expected opportunity loss. Those courses of action that minimize EOL or maximize EMV are adequate actions. Techniques that are used in uncertainty conditions are criterion of optimism or maximization, minimum regret criterion, criterion of realism etc. Outcome state Explanation Certainty Complete and accurate knowledge of the outcome of each alternative is available. There

is only one outcome for each alternative. Risk Multiple possible outcomes of each alternative can be identified and a probability of

occurrence can be attached to each. Uncertainty Multiple outcomes for each alternative can be identified, but there is no knowledge of

probability to be attached to each. Network theory (Networking techniques): Most of the projects either carried out by public sector, private sector or governments are usually delayed significantly due to lack of proper management, their improper scheduling and controlling. Network analysis enables managers to cope with such complexities involved in projects and suggest a way to overcome them. The use of CPM and PERT which are networking techniques is extremely useful for the purpose of planning, analyzing, scheduling and controlling the progress and completion of one time and repeated projects. Some networking techniques under PERT family are:

• PERT: Project evaluation and review techniques. • PEP: Program evaluation procedure. • LCES: Least cost estimating and scheduling.

Some networking techniques under CPM family are: • CPM: Critical path method. • CPA: Critical path analysis. • MCE: Minimum cost expenditure. • NMT: Network management techniques. • CPS: Critical path scheduling

A Text Book of Operational Research and Food Plant Management

3

Inventory Control Models: It is known fact that about 2/3 of the investment in industries is tied up in the form of inventories. It is utmost important to release part of this locked up capital for other functions of industries. Inventory models are used to determine optimal timing and quantities of orders of resources and what quantity of a product should be stored. All organization must maintain some inventory to ensure that production and sales are not delayed. The basic or objectives of an inventory model is to ensure that production and sales are not delayed. The basic or objective of an inventory model is to ensure that production & sales are not delayed .The basis or objective of an inventory model is to minimize the variable inventory cost. These costs are of three basic types: ordering cost, holding (carrying cost) and shortage cost. Shortage costs are those related to running out of inventory. They include not being able to sell a product or service when otherwise possible and the cost of idle production time, such as having to pay people when they are not working. Keeping a large inventory of needed materials would ensure against incurring these shortage cost. Buying large quantities of required inventory in most cases will also minimize ordering cost, because the firm might receive quantity purchase discounts and perform less paper works. However these potential benefits of large inventory are offset by holding cost such as shortage expenses, handling, interest, insurance, breakage, theft and taxes. In addition management must consider the opportunity cost of tying up funds in inventory that can be used for more productive investments such as stocks, bonds or bank deposits. Several specific models have been developed to help management determine when and how much inventory to order and what stock of work in progress and finished products should be maintained. Queuing Theory: Waiting lines at any service centre are common phenomena and queuing theory is devoted to the mathematical study of waiting lines. Various alternative models have been used to describe such situations, but they basically share some common feature. A queuing problem arises when the common service rate of a facility falls short of the current flow rate of customers. If the service facility is capable of servicing the customers when he arrives, no bottle- necks will occur. But if it takes fifteen minutes to service a customers and one customer arrives every ten minutes a queue will build up and continues to build up to infinite length, if the same arrival and service rate continue. In such situation, the bottleneck is eliminated only if either arrival rate decreases or service rate increases or number of service facilities is increased. If the size of queue happens to be a large one, then at time it discourages customers and search for other alternatives. Queuing models help managers evaluate the cost of effectiveness of service system. The cost associated with the queues is called waiting time cost or waiting cost. On the other hand, if there are no queues, members of service stations may stay idle and facilities are too staying idle. Cost associated with the service or the facilities are called service cost. The objective of queuing theory is to achieve a good economic balance between waiting cost and service cost. The optimum solution is arrived at a point where the sum of the waiting and service cost is minimum. Thus the aim of queuing model is to optimize waiting cost and service cost. Queuing theory is widely used in traffic management, determining the level of service force; all traffic scheduling, hospital operation, receipt and withdrawal counters in a commercial bank. Game Theory : One of the most important variables affecting the success of an organization is its completion. Clearly, the ability to predict the action of competitors would be advantageous for any organization. Game theory is a modeling technique for assessing the impact of a decision on one's competitors. Developed by John Von Neumann and Morgenson, this is a mathematical theory applicable to completive business problems. This technique deals with situations where two or more (finite) individuals are making decisions, involving conflicting interests. However, the final decision depends upon the decision of the parties concerned. The basic assumptions made are that every competing party will adopt the policy most unfavorable to us and therefore we are required to select the best position among the worst positions. In such situations, one's favorable item is unfavorable to other. Simulation : It is a highly versatile technique of OR. It has a wide range of application in business situations. Simulations are particularly appropriate where it is difficult to build a model for the real life situation mathematically or if at all it is modeled, it is difficult to solve the model analytically. It may be noted that simulation is a manipulation of a model constructed from a formal statements of a mathematical representation. Thus, simulation is a process of designing the experiment, which will duplicate or present as nearly as possible the real situation and then watching what does happen. In business, situation actual design of some experiment might be costly. Example for finding character of aircraft, it is not needed to build it but we can simulate it i.e., the experiment is carried out by avoiding the cost of failure. The simulation models allow the modern manager to examine the probable consequences of his decision with out the risk of real life experiments.

Introduction to Operation Research

4

Instead of these seven OR techniques other techniques like Replacement theory, Reliability theory, Markovian models are also widely used. There are also some advance OR techniques like Non-linear programming, Dynamic programming, Integer programming, Goal programming, Heuristic programming, Algorithmic programming, Quadratic programming and Probabilistic programming are also developed to cope with other situations. However some of the OR techniques are very long and tedious to compute manually, thus the need of computers are recognized to solve OR problems. 1.2. HISTORICAL DEVELOPMENT AND FUTURE SCOPE OF OPERATION RESEARCH It is difficult to mark the beginning of the operations research. However, the scientific approach to management was introduced by the work of Fredenck W. Taylor in the late 19th century. The Operation Research as it exist today, was developed during second world war when the British military management called upon a group of scientists to examine the strategies of various military operations for the efficient allocation of scarce resources for the war effort. The name Operation Research came directly from the context in which it was used & developed viz. "Research on Military Operation". After the war, Operations Research was adopted by industry in managerial decision making and planning. Some of the techniques that had been applied to the complex problem of war were successfully transferred and assimilated for the use in the industrialized sector. The development of OR techniques and the use of computes are the two prime factors that have contributed to the growth and application of OR in the post-war period. In 1950s, OR was mainly used to handle management problems that were clear cut, well structured and repetitive in nature. Typically, they were of tactical and operational in nature such as inventory control, resource allocation, scheduling of construction projects etc. Since from 1960s, formal approaches have been increasingly adopted for the less well – structured planning problem as well. These problems are strategic in nature and are the ones that affect the future of the organization. The development of corporate planning models is few examples. Thus it is clear that in start OR is developed to solve military problem, then it penetrates in industries to solve tactical problems and finally it was used to solve strategic problems that are having long term effect on organization. In present conditions lots of software are developed to solve OR problem. These software are simple to operate and give accurate decision within few fractions of seconds, however, a model should be developed to be fed to software. Thus developing mathematical model is of highest importance in OR. 1.2.1 METHODOLOGY OF OR (PROCESS OF OR) The process of OR involves the following major steps in sequential order.

1. Formulation and definition of problem; 2. Construction of the model; 3. Solution of the model by various applicable techniques; 4. Testing the solution of the model; 5. Establishing the control over the solution; 6. Validation of the model; and 7. Implementation of the result.

Formulation and definition of problem Under this phase an OR expert is required to define the problem by gathering several pieces of information or data. With the help of collected information, the task of formulating the problem is carried out. In-fact, problem formulation is the most important stage of OR. Defining and formulating problem correctly is the main concern of the most of the organization. It is virtually impossible to obtain correct solution of business problem from a wrong defined ill-formulated problem. Under this phase, the OR analyst tries to express the relevant features of the problem under study in terms of mathematical model by identifying the controllable variables or decision variable as well as uncontrollable variables that are a function of external environment. Construction of mathematical model The general form of a mathematical model is E = f (xy) where f is a constant that relates between E and x, y. E is called objective function. X is controllable variable and Y uncontrollable variable. The model varies according to the decision conditions. The relation might be linear, non linear, first order, second order or so on.

A Text Book of Operational Research and Food Plant Management

5

Deriving solution from the model Once the mathematical model is formulated, the next step is to determine the value of decision variables that optimize the given objective function. Various techniques are used to derive the solution. Testing solution of model Since a model is only a partial and simplified representation or reality, the results are to be tested against the real world experience in order to establish the model's credibility. Several simplified assumptions or simplifying assumptions are made during model building. These assumptions can be relaxed one by one to see the reaction of model result to such relaxation. Similarly, some variables need to be included or some need to be excluded to get appropriate results. However model distortion through simplification intentional or otherwise has to be properly assessed with the help of previous experience, judgment, actual test data and similar devices. Establishing control over the solution Once the model and its solution are acceptable, the analyst tries to incorporate necessary controls in to the model, so that it is adoptable to changing environment. In a dynamic business world, some variables become outdated, new parameters emerge and structural relationships among these variables may also change. Hence OR analyst or the decision maker has to take sufficient care of these changing situations. Validation of model Validating a model requires determining, if the model can reliably predict the actual system's performance. A common approach for testing the validity of a model is to compare its performance with past data available for the actual system. Implementing the solution This is the last and most important phase of OR where an operationally feasible solution obtained it is put in to practice. After the solution has been implemented, the analyst observes the response of the solution to the changes made. Finally no system is even completely static and it is always necessary to monitor the environment within which a system operates to ensure that changing conditions do not render a solution inappropriate. It is important to ensure that any solution implemented is continuously reviewed and (if necessary) updated and modified in the light of changing environment. The methodology of OR process and its interaction with management is shown in following figure 1.2.

Figure 1.2: Methodology of OR

Real world situation (Problem identification)

Formulation and construction of model (Including input data acquisition)

Model output (Decisions, predictions and other useful data)

Compare output with management experience, judgment and infusion.

Model is implemented

Revision required

Introduction to Operation Research

6

1.2.3 SCOPE OF OR OR started from a little military decision making techniques in II world war, has now gained acceptance as a fundamental managerial tools. Its scope is unlimited and used in wide areas from design, development, production, finance, administration and lots of other areas. Some of the areas of management where operation research are applied or could be applied are listed below. 1. Finance, Budgeting and Investment. – Cash flow analysis, long range capital requirement, investment portfolios, dividend policies etc. – Credit policies, credit risks and delinquent account producers etc. – Claim and complaints of producers. 2. Purchasing, Procurement and Exploration. – Determining the quantity and timing of purchase of raw material, machinery etc. – Rules for buying and supplies under varying prices. – Bidding policies. – Equipment replacement policies. – Determination of quantities and timing of purchase. – Strategies for exploration and exploitation of new material sources. 3. Production management. (A) Project planning. – Location and size of warehouse, distribution centers, retail outlets etc. – Distribution policy. (B) Manufacturing and facility planning. – Production scheduling and sequencing. – Project scheduling and allocation of resources. – Selection and location of factories, warehouses. – Determining the optimal production mix.

– Maintenance of policies and preventative maintenance. – Maintenance of crew sizes

– Scheduling and sequencing the production run by proper allocation of machines. 4. Marketing Management. – Product selection, timing, competitive actions. – Advertising strategy and choice of different media of advertising. – Number of salesman, frequency of calling of accounts etc. – Effectiveness of market research. – Size of stock to meet the future demand. 5. Personnel management. – Recruitment policies and assignment of job. – Selection of suitable personal with due consideration of age and skills etc. – Establishing equitable bonus system. 6. Research and Developments. – Determination of areas of concentration of research and development. – Reliability and evaluation of alternative design. – Control of development projects. – Co-ordination of multiple research projects. – Determination of time and cost requirements. From all above areas of applications, one may conclude that OR can be widely used in taking timely management decisions and also as a corrective measure. The application of this tool involves certain data and not merely a personality of decision maker and hence we can say "OR has replaced management by personality".

A Text Book of Operational Research and Food Plant Management

7

1.3 ROLES OF MODELS IN OR – THE NEED TO STRIKE A BALANCE BETWEEN SIMPLICITY AND COMPLEXITY

1.3.1. MODELS As preceding topics, the first step in OR methodology is the formulation of problem. This stage is very hard task compared to other process. The starting point for formulation of problem is the deep study of actual situation to find out what is happening and what was supposed to happen. Thus is a framework between actual situation and ideal situation is made. Assume that the problem is a lower sales volume. This is the objective of the problem to maximize the sales. However the lower sales might be due to various tangible and intangible factors. The seasonal fluctuation might occur, it may be due to huge competition or competitor's do-die strategy, or it is due to sales force problem or due to machine factor, promotion factor etc. so on. However, increasing or decreasing one affecting factor may not give the adequate result, e.g. if sales force is increased, the sales volume may raise, but at the cost of higher expenses. Hence, it is needed to be specific in formulation of a problem. A biased subjective or personalized formulation may give wrong result. During this formulation, the effect of variables in objective function should be determined in simple manner. A vague formulation with larger number of controversial variable may give inadequate results. After setting the problem, the modeling plays an important part. Modeling refers to the idea of constructing a model from a given problem and deriving the solution from it for the problem under consideration. Mathematically, a model is the mathematical representation of problem formulated. The representation might be in equation form, table form, matrix form etc. As stated above, E = f(X,Y) is a mathematical model for the formulation, optimize E, where x are controllable variable and y uncontrollable variable. The objective E can be related to the variables x and y by a function f. i.e. f is the function. It is further to be pointed out that the controllable and uncontrollable variables are not universally characterized variables. Depending upon a problem, different variables may come up and their natures are also varied depending upon the problem. Controllable variable are those that can be manipulated by management, the uncontrollable variables are those that cannot be controlled by management with in the problem defined. Hence, during verification/validation of problem formulated after setting the result from model, the needed variables are added or non-needed variables are excluded. This is a continuous process, and a good manager is always alert about the effect of variables on this decision obtained from OR techniques. That means he should balance between simplicity and complexity of variables. A simple problem is to find out the product mix of A and B that fulfills the minimum requirement vitamin A and vitamin B and also minimizes the product cost of mix is derived below. This derivation is called problem formulation. The formulated problem from analyzing the ingredient composition, cost of ingredient is as follows: - Food X contains 6 units of vitamin A per gram and 7-unit vitamin B per gram and cost 12 paisa per gram. Food X contains 8 units of vitamin A per gm, 12 units of vitamin B per gm and cost 20 paisa per gm. The daily requirement of vitamin A and vitamin B are 100 and 120 units respectively. The manager wants to find out product mix that fulfill the given requirement and minimize the product cost. The above problem can be tabulated as follows:

r a m e t e r s r o d u c t X r o d u c t Y D a i l y r e q u i r e m

e n t

t a m i n . A 6 / g m 8 / g m 1 0 0 u n i t s

t a m i n . B 7 / g m 1 2 / g m 1 2 0 u n i t s

s t 1 2 / g m 2 0 / g m

Minimise C =12x + 20y Subject to. 6x + 8y ≥ 100 7x + 12y ≥ 120 X, Y ≥ 0 This problem can be solved by OR techniques called linear programming.

Introduction to Operation Research

8

1.3.2 TYPES OF MODELS There are various types of OR models among them, the most used model in OR is mathematical model that will be discussed in detailed in succeeding topics. Some common OR models are:

• Symbolic models (Schematic models); • Physical models (Iconic models); • Analog models; and • Mathematical models.

Symbolic models (Schematic models) These models include all forms of diagram, drawings, graphs and charts, most of which are designed to deal with specific type of problems. By presenting significant factors and interrelationships in pictorial form, schematic models are also to indicate problems in a manner that facilitates analysis. A bar chart, for example can be used effectively as a summary presentation of company's monthly production forecast. The schematic models shows more clearly than words or numbers if it is used adequately. Common schematic models and their uses are shown below. Schematic models Problem Area. Flow process chart Plant layout; process analysis Operator charts; activity chart Labor simplification Break- even charts Operator analysis and planning QC chart like x, p, c chart Inspection and QC Gantt chart Production scheduling Block diagrams Multiple use Organization chart Organization planning Iconic or Physical model: An icon is an image or likeness of something. Thus iconic models are scaled physical operating replicas of a product or operation. They are extremely helpful tools in analyzing certain problems since they make possible a thorough, actual operational observation of the forces present. The range of management problem areas where these models can be used effectively is extremely narrow; however these are very useful in engineering and science. In engineering "mock ups" or pilot models are widely used for R and D purpose. The final design is generally based on the data of these pilot plants. These iconic models can be simulated to actual performance of a product like airplane for testing purpose. This avoids the tremendous expenses of designing full-scale experimental model and reduction of failure cost. Analog models: Analog models are quite similar to iconic models however they are not replicas of problem situation. Rather they are small physical systems that have characteristics similar to those of the problem. The aim is to find out the effect of interaction of system elements. e.g.. hydraulic system can be used as analog model for electrical, traffic and economic system. Mathematical models: The major advantage of mathematical models stems from the precision of mathematics. These models permit a clear, unambiguous statement of the relationships that exist among the variable in a problem. An equation such as a = b + l, means the same thing to anyone who reads it. Further more it defines a direct and unique relationship between 'a' the dependent variable and 'b' the independent variable, namely that 'a' is always greater than 'b'. Thus, if 'b' is known 'a' is always known. Because of the clarity and simplicity of expression in mathematical model, complex relationships between large numbers of variables can be defined. Thus, mathematical model has wide applicable in present situations. There are three basic types of mathematical model.

a. Deterministic model (non probabilistic or exact model) b. Probabilistic model c. Hybrid model.

Deterministic model (Not probabilistic or exact model) In deterministic models, the variables and their relationships are stated exactly, condition of certainty exists with definite relationships between variables. The results obtained with the same data are always same. Let us discuss the break-even analysis condition. The sales revenue is given by

A Text Book of Operational Research and Food Plant Management

9

R = P. V , Where, R = revenue , P = unit price , V = number of units (volume) The total cost is given by : Tc = Fc + V. Cv , Where, Tc = Total cost , Fc = Fixed cost , Cv = Variable cost per unit In break-even point Tc = R i.e. Fc + V.Cv = PV or V = Fc/(P-Cv) where, V = Vbe (Break even volume) and P-Cv = Contribution margin

Probabilistic models Probabilistic models come in to use when there is uncertainty about variables or about their relationships. Bco3' of these uncertainties, probabilistic model do not yield the same answer each time. Since, the variables or relationships change, the result must change. Decision analysis, Markov process and Queuing theory use probability i.e. they are probabilistic models.

Hybrid Models These models use both probabilistic and non-probabilistic concepts like PERT-CPM, inventory, simulation etc. The models are summarized as follows in figure 1.3

Figure 1.3: Types of OR models OR Models

Symbolic Mathematical Physical Analog Probabilistic Non probabilistic Hybrid Decision analysis Linear programming PERT – CPM Markov process Transportation Dynamic programming Queuing theory Assignment Simulation.

1.4 ROLE OF RESEARCH IN INDUSTRY AND RESEARCH ADMINISTRATION 1.4.1 RESEARCH AND INDUSTRIAL RESEARCH

Research is a common item referring to "Search for Knowledge". This type of research for sake of knowledge with or without consideration of commercial possibilities is called as "Fundamental" or "Pure" research. Pure research deals with basic sciences e.g. “Why the grass is green?” Basic research is aimed at the discovery or explanation of fundamental laws and phenomena of nature, whether physical or organic. These types of basic research are generally conducted by government, universities and generally require long time frame, more laboratory analysis and or more money. The information obtained from basic research can be transferred to places or organization, where it can be adopted for specific application e.g. for industrial application. This transfer of information needs further more research or work called "Applied research". Applied research is directed at some specific industrial problem. This applied research can be viewed as an outgrowth or outcomes of pure research. Example; Do point worked on "What results on synthesis of long chain polymer?” He found the new polymer called "Nylon" with different properties than the original polymer. This development of Nylon was pure research. Once Nylon was developed, the applied researches were carried out for the utilization of this new polymer. From the result, now nylon is a widely used plastic material. Lots of pure research were applied for the production of antibiotics, synthesis of nutrients, vitamins etc. in areas of microbiology. The finding of carbon and hydrogen has elaborated arena of applied chemistry. The fission and fusion of atoms and radioactivity has now become more versatile area of applied research. Regarding operation research, this is also a type of applied research. As we know, various OR scientists had carried out pure research to develop various methodology of OR, which are further used and elaborated for using at decision-making.

Introduction to Operation Research

10

1.4.2. INDUSTRIAL RESEARCH The major areas of industrial research are as follows: Marketing research : The chief aim of market research is to test consumer acceptance of products, to develop data for manufacturing schedules and prices and to provide a source of new ideas for development. Unlike the past, when in small shops custom made goods were produced through intimate contacts of producers and customer; modern industry is separated from consumer by complicated organizations, contract marketing, contract production and global marketing. The change from intimate producer-consumer contact to wide separation of produces and consumers has been likened to a broken circular chain in which marketing research supplies the missing link.

A. Relationship, which exist between manufacturer and customer under condition of one-man shop.

B. In the large modern business institutions, the producer has become separated from the

customer, and the intimate relationship no longer exists.

C. Marketing research supplies the missing link to the broken chain and thus rejoins the producer

and customer.

Material research :Research in material is linked with the product development, since the discovery and improvements of material frequently lead to a new products and lower cost on existing products. For example, introduction of laminates has changed the overall packaging technology. The production of palm- based oil has changed the overall oil industry from Soya based to palm based etc. Product research: The important of product research to the continuing prosperity of the enterprise has already been stated. It embraces the stimulation of new product concepts to fill the needs of customers and prospective customers. Similarly, it also stimulates the new use of existing products. With these activities, the new area of by-product utilization has emerged as powerful applied research area in these days. The concepts of reduce, reuse and recycle has boosted a product research to new area. Equipment and process research :To manufacture product, it is necessary to develop the process that are adequate to produce it in the quantity and quality designed by manufacture and customer. Frequently a product can be made on a small-scale pilot plant in research laboratory, where as the manufacture of that product or commercialization of the product is not as easy as pilot plant manufacture. It is then the function of process research to develop the method of manufacturing it on the scale desired. Similarly, certain standards of quality may be set up for the product, which may not be easily adhered to in large-scale production. Here again the research study is required to develop methods of maintaining quality in production manufacture. Research pertaining to industrial process is usually directed towards the development of methods of manufacture, tools and equipment as well as handing devices that tend to increase productivity. The replacement

Manufacturer Customer

Customer

Dealer

Sales Production

Research Engineering

Marketing Research

Customer

Dealer

Sales Production

Research Engineering

A Text Book of Operational Research and Food Plant Management

11

of human skill and heavy labor by mechanical device to better the operating efficiency and the development of methods and mechanism for increasing the safety of processes are both fertile fields for further study.

1.4.3. ADMINISTRATION OF INDUSTRIAL RESEARCH Research conducted within the enterprise may be of two types:

(a) Findings of the employee, suggestions of employee or suggestions from inventors. (b) Finding or suggestion from the functionalized research and development (R & D) department.

These both approaches are vital to the enterprise. If the first alone is used, it is likely to be hit and trial procedure. Sole reliance on the second may lead to the negligence of the real value, which can be found in the experience, interest, and ideas of employees. A coordinated dual approach encourages employees to offer suggestions through the "Suggestion box". These suggestions from experienced worker may be very helpful to carryout further R & D works. On the other hand, experienced supervisors or foreman or related team may also be involved with R & D department for sharing information, ideas of products, process or material. These may be sometime very helpful and economic for R & D purpose. The above-discussed methodology is fundamental of Japanese manufacturing systems. The administration of industrial research can be discussed further more under headings.

– Organization of industrial research. – Operating procedures. – Human resources (Personal)

Organization of industrial research : In small companies a manager (relevant) could be selected to carryout research. He is provided with technicians and other required facility to carryout research. However, if the organization is large, there need to set up separate research department to carryout research activities. As we know research itself is very vague and needs experts from different fashion. e.g.. Physics, Chemistry, Mathematics, Food-Technology, Engineering, Microbiology etc. So, organization needs to allocate these experts and when necessary during research work. Operating procedures : The research procedures are necessary to carryout research effectively. It eliminates the duplication of work and thus reduces the cost. Each project must have a clear- cut path to follow from conceptions of idea to the launching of product on the production line. Definite stopping points for the renewal of projects progress should be determined previously. The overall budget of research departments may be based on a percentage of sales or probable financial returns. It means some budgetary procedures should be constructed. It is natural to expect that not all research projects will turn out profitably. Some encounter difficulties and to be abandoned, other prove to be economically unsound or other to be unfit at present condition. So a suitable procedure for testing usefulness of project on determined interval is necessary i.e. if it is found unfit initially. The project is terminated avoiding future investment in unsuccessful project i.e. progress report and reviewing the report is necessary.

Personal procedures : The personnel to carry out research should be research ability, creativity and in-depth knowledge of subject matter. Since it is an applied research, the cost or expenses awareness is necessary. Other important is time awareness, production of products before competitors produce them, portion industry to enjoy monopoly market. The personnel all involved should be able to work in team for one goal. Multiple interests may lead to ambiguity of work and may not give appropriate findings.

Introduction to Operation Research