Solving operations research problems is a collaborative endeavor in which the clients commissioning the research and the analysts work side by side. OR analysts, with their knowledge of modeling capabilities, need the practical experience and situational awareness that the client brings. Success at the stages preceding the derivation of an optimal solution to the mathematical model depends heavily on the team's creativity and experience.
Because of the "elusive" human factor, it is difficult to provide precise prescriptions for putting operations research theory into practice; in each individual case, the methodology will be unique.
In general terms, the direction of implementation can be outlined as the following high-level stages:
- Formalization of the initial problem.
- Construction of a mathematical model.
- Solving the model.
- Model validation.
- Implementation of the solution.
Formalizing the problem requires investigating the domain in which the problem has arisen or in which an optimization task needs to be solved. This is the initial stage of any research team's work. As a minimum, three fundamental elements of the problem being solved must be identified:
- a description of the feasible alternative solutions;
- identification of the objective function (or objective functions);
- identification of the system of constraints imposed on the feasible solutions.
In the classic work Introduction to Operations Research by Churchman, Ackoff, and Arnoff, six stages are described. The problem formulation stage is singled out separately. The quality of the problem formulation determines the outcome. Errors made at this stage render all subsequent efforts to construct and solve the model worthless. During problem formulation, a comprehensive analysis of the system, its goals, and possible courses of action is conducted.
Broadly speaking, the purpose of an operations research study is to determine which course of action is most effective. Consequently, a criterion of effectiveness (or a system of criteria) must be established. The participants in the study, including the decision-makers, are required to understand the following:
- which situations lend themselves to modeling;
- how to obtain the data needed to construct a model;
- when it is advisable to use models, and to do so within reasonable limits of time and cost;
- what must be done to derive benefit from the interpretation of the model and the practical implementation of the solution;
- what the limitations of the model are and to what extent the model corresponds to the actual situation.