Operations Research Methodology

Solving an Operations Research (OR) problem is not a linear process, but the process can be broken down into five general steps:

1. Describing the problem;
2. Formulating the OR model;
3. Solving the OR model;
4. Performing some analysis of the solution;
5. Presenting the solution and analysis.

However, there are often "feedback loops" within this process. For example, after modelling and solving an OR problem, you will often want to consider the validity of your solution (often consulting with the person who provided the problem description). If your solution is invalid you may need to alter or update your formulation to incorporate your new understanding of the actual problem.

All the case studies on this TWiki (should!) follow the OR methodology. The Problem Description and Problem Formulation sections correspond to steps 1. and 2. respectively. The Computational Model section shows how some OR software was used to solve the problem, the Results section contains the solution and the analysis and the Conclusion section presents the solution and analysis.

Let's consider the five steps of the OR methodology in more detail:

1. Describing the Problem The aim of this step is to come up with a formal, rigorous model description. Usually you start an optimisation project with an abstract description of a problem and some data. Often you need to spend some time talking with the person providing the problem (usually known as the client). By talking with the client and considering the data available you can come up with a more rigorous model description required for formulation. Sometimes not all the data will be relevant or you will need to ask the client if they can provide some other data. Sometimes the limitations of the available data may significantly change your model description and subsequent formulation.
2. Formulating the OR Model The aim of this step is to translate the problem description into a valid OR model. The implementation of this step may be quite different depending on the OR model you are using. For example, if you are using linear programming to solve your problem, then formulating an OR model involves translating your problem into a linear programme. If you are using simulation to solve your problem, then formulating an OR model entails breaking down the behaviour of the system being simulated into a sequence of events and determining the random variables that "drive" the simulation.
3. Solving the OR Model The aim of this step is to solve your OR model. Just as the formulation step depended on the OR model being used, this solution step depends on your OR model. Additionally, there may be more than one solution method for a particular OR model. For example, solving a linear programme may be done using the Revised Simplex Method or an interior point method. Often, in practice, OR models may not be solved completely due to time constraints. Other algorithms may partially solve OR models (for optimisation models, these algorithms are known as heuristics and terminate with a "good" solution that is not necessarily optimal).
4. Performing analysis of the solution Often there is uncertainty in the problem description (either with the accuracy of the data provided or with the value(s) of data in the future). In this situation the robustness of our solution to the OR model can be examined using analysis. Analysis involves identifying how the solution would change under various changes to the problem data (for example, what would be the effect of a given cost increasing, or a particular machine failing?). This sort of analysis can also be useful for making tactical or strategic decisions (for example, if we invested in opening another factory, what effect would this have on our revenue?). Another important consideration in this step (and the next) is the validation of the OR model's solution. You should carefully consider what the solution means in terms of the original problem description. Make sure it makes sense to you and, more importantly, to your client. Hence, the next step, presenting the solution and analysis is very important.
5. Presenting the solution and analysis A crucial step in the optimisation process is the presentation of the solution and any analysis. The translation from an OR model's solution back into a concise and comprehensible summary is as important as the translation from the problem description into the OR model. In the case studies throughout this TWiki, we encourage the use of management summaries to present solutions and analysis from OR models. Key observations and/or decisions generated via OR must be presented in a way that is easy for the client or project stakeholders to understand. Your presentation is also a crucial first step in the implementation of any decisions generated by your OR model. If the results of your OR model and their consequences are not presented clearly and intelligently these results will never be used. This step is also your chance to suggest future work possibilities. This could include:
   • Periodic monitoring of the validity of your OR Model;
   • Further analysis of your solution, looking for other benefits for your client;
   • Identification of future OR opportunities.