Phases of Operation Research

OR study commonly includes the following main phases

1.      Defining the problem and collecting data

2.      Creating a mathematical model

3.      Obtaining solutions from the model

4.      Checking the model and its solutions

5.      Preparing to execute the model

6.      Final Execution or Implementation

 1. Defining the problem and collecting data

• The first job is to analyze the relevant system and formulate a well-defined statement for the problem. This comprises determining appropriate objectives, interrelationships, limitations and alternative course of action.
• The OR team generally works in an advisory capacity. The team carries out a thorough technical analysis of the problem and then provides suggestions and recommendations to the management.
• Ascertaining the appropriate objectives is a highly significant aspect of problem definition. Some of the objectives contain maintaining stable price, increasing the share in market, profits, enhancing work morale etc.
• OR team normally spends large amount of time in collecting important data.
  • To get precise understanding of problem
  • To give input for next phase.
• OR teams' takes use of Data mining methods to find large databases for interesting patterns that may direct to useful decisions.

2. Creating a mathematical model

This phase is to recreate the problem in mathematical symbols and expressions. The mathematical model of any business problem is described as the organization of equations and other related mathematical expressions. So

1.      Decision variables (x₁, x₂ ... x_n) - 'n' refers to associated quantifiable decisions to be made.

1. Objective function - It is a measure of performance (profit) which is expressed as mathematical function of decision variables. For instance P=3x₁ +5x₂ + ... + 4x_n
2. Constraints - any limitations on values that can be allocated to decision variables in terms of equations or inequalities. For instance x₁ +2x₂ ≥ 20
3. Parameters - the constant which are there in the constraints  (right hand side values)

The alternatives available for the decision problem is in the form of unknown variables

Example - Assume a company manufacturing chairs and tables with the purpose of getting optimum profit, then the decision variables are count of chairs and tables to be manufactured (say mathematically x and y). Decision variables are utilized to make the objective function and restrictions in mathematical functions.

The end product of OR model is a mathematical form associating the objective function, constraints with variables. The mathematical function is to optimize (maximize/ minimize) the magnitude of the objective function, at the same time fulfilling all the facility constraints.

The consequent solution in the form of magnitude of decision variables value of objective function is called as "optimum feasible solution".

A mathematical model of OR is arranged as

Maximize or Minimize (Objective Function)

Subject to (Constraints)

Example

Maximize Z = 45x + 80y

Subject to

5x+ 20y ≤ 400

                        10x + 15y ≤ 450

 x ≥ 0 , y ≥ 0

Here x, y are decision variables say

y = number of tables

x = number of chairs

x, y should always be nonnegative values

z= objective function

Linear Programming (LP)

It is a mathematical method which optimizes the accessible resources.

Optimization

The solution of the model gives the values of the decision variables that maximize or minimize the value of the objective function and also satisfying all the constraints of that particular system. Hence optimization can be maximization or minimization.

Example

1. Maximize the gain of the production oriented company.
2. Minimize the losses of the trading company.

The advanntages of using mathematical models are -

• Explain the problem in brief
• Makes whole structure of problem understandable
• Provide help to reveal significant cause-and-effect relationships
• Mentions clearly about what additional data are relevant for analysis
• Creates a bridge to use mathematical technique in computers to examine

3. Obtaining solutions from the model

This phase is to create a process for deriving solutions to the problem. A general theme is to strive for an optimal or best solution. The main aim of OR team is to obtain an optimal solution which minimizes the cost and time and maximizes the gains.

According to Herbert Simon "Satisficing is more widespread than optimizing in actual practice". Where satisficing = satisfactory + optimizing

According to Samuel Eilon "Optimizing is the science of the ultimate; Satisficing is the art of the feasible".

To find the solution, the OR team uses

• Heuristic procedure (which is a designed procedure and does not guarantee an optimal solution) is used to get a good suboptimal solution.
• Metaheuristics which provides both general structure and strategy guidelines for developing a precise heuristic procedure to fit in a particular kind of problem.
• Post-Optimality analysis is the analysis done after getting an optimal solution. It is also known as what-if analysis. It comprises of conducting sensitivity analysis to find out which parameters of the model are most significant in determining the solution.

4. Checking the model

After deriving the solution, it is tested and analyzed as a whole for errors if any. The process of testing and enhancing a model is to augment its validity and is generally referred as Model validation. The OR group doing this review should preferably contain at least one individual who did not contribute or participate in the formulation of model to check mistakes.

Retrospective test is a systematic approach to test the model. This test uses chronological data to reconstruct the past and then devise the model and the consequent solution. Comparing the effectiveness of this assumed performance with what actually happened signifies whether the model tends to give a noteworthy improvement over current practice.

5. Preparing to execute the model

After the ending of testing phase, the next step is to implement a well-documented system for practically implementing the model. This system will comprise the model, solution procedure and operating measures for implementation.

The system generally is computer-based. Management Information System and Databases can give up-to-date input for the model. An interactive computer based system which is called as Decision Support System is installed to assist the manager to use models and data to support their decision making as per requirement. A managerial report infers output of the model and its implications for applications.

6. Final Execution or Implementation

The end phase of an OR study is to implement the system as agreed by the management. The completion of this phase depends on the assistance of both top management and operating management.

The implementation phase include various steps

1. OR team gives a comprehensive explanation to the operating management
2. If the solution is satisfactory, then operating management will give the description to the personnel, the new guidelines.
3. The OR team supervise the functioning of the new system
4. Feedback is taken
5. Documentation

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