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
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 ... xn) - 'n' refers to associated quantifiable decisions to be made.
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.
The advanntages of using mathematical models are -
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
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.
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.
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
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