PHASES OF AN OR STUDY

In this section, we will discuss the essential steps in solving real-world problems, using OR methodology. These steps are as follows:

- Defining the problem
- Developing a model
- Obtaining input data
- Solving the model
- Testing and analysing the solution,
- Implementing the results

Every OR study does not follow the exact steps shown in the above figure, but many -!ies follow these general guidelines. Moreover, it is to be remembered that one step does not e to be completely finished before the next is started.

Briefly above results are:

Step I: Defining the Problem

It is often found that the real-world problems are described in very broad terms. It is very essary to convert them into well-defined and manageable OR problems. By problem defination, we mean to gather the following necessary information concerning the problem:

- Recognition that a problem exists
- Determining its magnitude
- Defining it precisely
- Noting what symptoms are

Often, what is described as a problem (e.g., excessive costs) may only be a symptom of a problem (e.g., improve inventroory levels. It is sometimes difficult to distinguish between specified and relevant restrictions identified. It helps to focus attention on what the problem is. Since this step affects the outcome of the whole process a careful consideration. Many OR studies fail simply because the problem is poorly defined.

In brief, this step concerns with developing a clear concise statement of the problem under study.

Step 2: Developing the Model

Our next step is to develop a model. We have already discussed various types of models.

The task of modeling is one of the most delicate. All mathematical models consist of three basic components:

**Decision (controllable variable or simply variable) variables.****Uncontrollable variables****Result variables**

Decision (controllable) variables describe elements in the problem for which a choice must be made. These are manipulate-able and controlled by the decision-maker. They are also called independent (decision) variables or simply unknown variables and are denoted by Xl. X2. X3 . ... or by x, y, z, ... , etc. The aim of OR models is to find the best values for these variables.

Uncontrollable (environmental) Variables In any decision situation there are factors that affect the result (output) variables and are not under the control of the decision maker. They are also independent variables since they affect the result variables. Some examples of uncontrollable variables are inflation rate, regulations, demand for service, etc. The values of such variables may be known with certainty or unknown. If the values are known, the un-controlable variables are referred to as parameters or coefficients of the model. A moder in. which all the rariables are known and cannot vary is called a deterministic model. On the other hand, a model in which the values of these variables are not known with certainty is called a probabilistic tochastic) model.

The result variables tell us how well the system performs or attains its goals. Some of the e common result variables that are used in organisations to measure effectiveness, such as equations or inequalities. The mathematical model may include two major parts:

**Objective function****Constraints**

The Objective function describes the goal of the problem and may be stated as:

Maximise v = a1X1 + a2X2

here v symbolises the total revenue, XI and X2 are the decision variables, and al and a2 are the controllable variables; may be the price of these two variables. The objective (or goal) is to miniimise the revenue, such an objective is usually limited by constraints. It can also be to minimize cost.

The constraints express the limitation imposed on managerial systems due to regulations, computation, scarcity of resources, or other uncontrollable variables. For example, a marketing constraint might be expressed by 2Xl + 3X2

__<__10. That is, the total quantity of the two roducts that can be sold is 10 or less, or simply cannot be more than 10.

Step 3: Obtaining Input Data

Once the model has been developed, the next step is to obtain the (input) data that are to used in the model. Data collection is a critical part of an OR study, and therefore must be ckled with care and diligence. Data can be collected from several sources:

- From organisation records and documents.
- From interviews with employees or other persons related to the organisation and the study at hand.
- From research studies and journals.

The data collected must be tested before using In a model. The data may be defective as a result of observational errors, calibration errors, interpolation/extrapolation of data and result in accurate estimation of parameters. As the complexity of a model changes. the required data may also change

Step 4: Solving the Model

After constructing the requIred model and collecting the necessary input data, we are ready now to solve the model. A solution to a model means to determine an optimal (best) ution for the model. In other words, find the values of the decision variables that maximize, the revenue without violating the constraints, or mmimize the cost incurred.

In order to solve an OR model, we use an algorithm. An algorithm is a series of rules or procedures that is used in a step-by-step manner to find the best solution for the given problem. In this book, we will describe several algorithms to solve various types of problems manually or using computers.

Step 5: Testing and Analysing the Solution

After the solution has been obtained, it should be completely tested. Since accuracy of the solution depends on the accuracy of the input data and the model, it requires testing. Inaccurate data will lead to an incorrect solution. It is said that garbage-in, garbage-out. The following are some ways to test input data and the model:

If the original data were collected using interviews, it may be reasonable to use direct or sampling methods .

If the data coilected were found to be accurate but the results are inconsistent with the problem at hand, the model may not be appropriate. The model can be rechecked to make sure it is logical and represents the real system. It may be already known or can be easily obtained. If the solution to the test problem is satisfactory then the model can be used for solving larger problems. If the testing and validation procedures identify errors, the model may be reconstructed or more accurate input data may have to be recollected.

Since the model is an approximation of reality, the sensitivity of the solution to changes in the model and input data is a Very important part of analysing the results. This part of analysis is called sensitivity analysis. The purpose of sensitivity analysis is to determine the effect of changes in the independent variables on the values of dependent variabley. This analysis is not only applied in order to investigate the influence of unwanted errors in the data used, but also of intentional changes.

Step 6: Implementing the Results

In simple words, implementation can be defined as putting a solution to work. Implementation is the most rewarding aspect of an OR project, but it can also be difficult. There is no golden rule of implementation, but experience has shown that certain conditions, such as those given below, foster a situation that facilitates implementation:

- Support from top management in the organisation.
- Availability of accurate and adequate data.
- A vailability of sufficient time to analyse a real problem with a sophisticated approach.
- Provision of accurate and timely information to the decision maker.

It is rightly said that a model which secures a moderate theoretical benefit and is implemented is better than a model which ranks very high on obtaining theoretical advantage but cannot be implemented. If the results of a model are not implemented, the whole exercise will go waste. Once all the above steps are completed, it does not necessarily mean that OR process is completed. The model results and decisions based on the results provide feedback to the original model. The original model can be modified to different conditions and decisions that might occur in the future. The results may indicate that a different problem exists that had not been thought of

reviously, thus the original model is altered or restructured. As such, the OR process is ontinuous rather than simply consisting of one solution to one problem. Finally, it is necessary that an adequate number of OR personnel should be available in the organization, because OR in ice is a team effort, requiring close cooper.ation among decision makers and other parties.