Introduction to Operation Research (OR)

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Definition of Operations Research

"Operational research is the application of the methods of science to complex problems arising in the direction and management of large systems of men, machines, materials and money in industry, business, government and defense. The distinctive approach is to develop a scientific model of the system, incorporating measurements of factors such as chance and risk, with which to predict and compare the outcomes of alternative decision strategies and controls. The purpose is to help management, determine its policy and actions scientifically."

- Issue of the Operational Research Quarterly(London), 

the Journal of O.R society of U.K., 

September, 1962

Characteristics of Operations Research

1. Inter-disciplinary Team Approach- The O.R. team is composed of different peoples from different expertise sector.
2. O.R. is a Continuous Process- It should not stop after application of a model to one problem. continuous study, analysis & research must go on so that changes of the requirement, demand, environment(social or economical) etc can be considered.
   
3. Objective Specification is very important- Unspecified objective is like unbounded problem, feasible solution is hardly expected.
4. Increases creative ability of a decision maker- Changes of the requirement, demand, environment(social or economical) etc are  functions over the time. Changes can be minor or major. In minor changes old methodologies may be considered with minor changes in the specification but in case of major changes in the system may require to introduce new models for solving the problem. Creative management is one of the important parameter for leadership in the industry/organization.
5. It is a decision making science- It helps the management to take decision most relevant/ suitable depending on the time & space.
6. Uncover new problems for study methods- This property is always makes the sense of effectiveness on current time, without this property it is hard to survive for a long time.
7. Examine functional relationship from a system overview- Functional relationship is ultimate fact that binds different element of a system together. It is like the reason of chemical bondage among Hydrogen & Oxygen in Water. Without realizing this, enhancement of system performance is hard to achieve.
8. O.R. gives only bad answers to the problems where worse could be given, i.e. it cannot give perfect answers to the problems. Thus, O.R. improves only quality of the solution.
9. Methodological Approach- O.R. uses scientific methodologies. 
10. Replaces management by personality- Personal ability(Personality) develops & increases over the time with knowledge gathering, continuous application of the gathered knowledge, observation & analysis of the result. This is vary hard to maintain without proper structure. O.R. help us to develop personality methodically.
11. It helps to resolve conflicts, overcome uncertainty and thus reduces cost, improve profits and effect substantial economy.

Phases of Operations Research

1. Judgemental Phase
1. Determination of the operation
2. Establishment of the objectives & values related to the operation
3. Determination of the suitable measures of effectiveness
4. Formulation of the problems relative to the objectives
   
2. Research Phase
1. Operations & Data collection
2. Formulation of hypothesis & model
3. Observation & experiment to test the hypothesis on the basis of addition data
4. Analysis of the information and verification of the hypothesis using pre-  measures of effectiveness
5. Prediction of various results from hypothesis
6. Generalization of the various results and consideration of alternative methods.
3. Action Phase: Recommend or influence or apply the decision.
   

An Operations Research worker is required to

1. minimize the input value/size
2. maximize output value
3. maximize some function value

Scope of Operations Research

1. Finance, Budgeting and Investment
1. Cash flow analysis
2. Long range capital requirements
3. Investment portfolio
4. Dividend policies
5. Credit policies
6. Credit risks
7. Claim & complaint procedures 
2. Purchasing, Procurement & Exploring
1. Determining the quantity & timing of purchase of raw materials, machinery etc.
2. Rules of purchasing
3. Equipment replacement policies
4. 
   
3. Production management
1. Physical Distribution
1. Location & size of the warehouse, distribution centres and retail outlets
2. Distribution policy
2. Manufacturing & facility planning
1. Production scheduling & sequencing
2. Project scheduling,  allocation of resources
3. Number, locations & size of the factories, warehouses etc
4. determining the optimum production mix
3. Manufacturing
1. Maintenance policies & preventive maintenance.
2. Maintenance crew sizes
   
4. Marketing management
1. Product selection, timing, competitive actions
2. Advertise strategies, media selection etc
3. Stock policy
4. Sales strategy
5. Personal management
1. Requirement analysis
2. Job distribution
3. Mix of age and skills
6. Research & Development
1. Selection of area
2. Reliability and evaluation of alternative design
3. Co-ordination among multiple  projects or sub-projects
4. Determination time requirement
5. Determination of cost requirement

Methodology of Operations Research

Due to the complication involved, OR projects is broken in the following phases:

1. Problem Formulation
2. Construction of mathematical model
3. Deriving Solution
4. Testing the model
5. Control over the solution
6. Implementing Solution

Classification of Models

Classification of mathematical models can be done according to

1. Degree of Abstraction
1. Language model: abstraction is more (Commentary of  Game)
2. Concrete model: less abstraction (Globe of Earth)
2. Structure 
1. Iconic(Physical) model- Painting
2. Schematic(Analogue) model- Graphs
3. Symbolic(mathematical) model
1. Decision Variables & Parameters
2. Constraints
3. Objective Functions
3. Purpose
1. Descriptive model- Survey
2. Normative(prescriptive) mode- Linear Programming
4. Nature of Environment
1. Deterministic model- Linear Programming
2. Probabilistic model
5. Behavior characteristic
1. Static model
2. Dynamic model
6. Procedure of solution
1. Analytical model- Linear Programming
2. Simulation model- Scientific research in missile technology
3. Heuristic model- Covid-19 management

Characteristic of a Good Model

1. Considering new formulations without any significant change in the modelling.
2. Number of assumptions must be less.
3. Number of variables must be less.
4. Less time consuming for construction.
5. It should express relations & interrelations of action & reaction of cause & effect in operational situations.

Advantage of a Model

1. Provides systematic & logical approach to the problem.
2. Tools for elimination of duplication.
3. Avenues for new research.

Disadvantage of a Model

1. Only an attempt to understand the operation and should never be used as absolute in any case.
2. Validity of any model can only be verified through experiment & relevant data characteristic.

Techniques of O.R.

1. Probability
2. Decision Theory
3. Linear Programming
4. Dynamic Programming
5. Sequencing
6. Game Theory
7. Inventory Control & Management
8. Queueing Theory
9. Network Analysis (PERT/ CPM)
10. Simulation
11. Replacement Theory
12. Reliability
13. Integer Programming
14. Heuristic Programming
15. Algorithmic Programming

Limitations of O.R.

1. Magnitude of Computations.
2. Absence of Quantification.
3. Distance between managers & O.R.