Mathematical programming uses mathematical variables and expressions to model problems. In the formulation step of the Operations Research (OR) methodology we identify the key quantifiable decisions, restrictions and goals from the problem description, and capture their interdependencies in a mathematical programming model also known as a mathematical programme.
We can break the formulation process into 4 key steps:
For relatively simple or well understood problems the mathematical programme can often be solved to optimality (i.e., the best possible solution is identified) using algorithms such as the Revised Simplex Method, interior point methods, or branch-and-bound. However, some industrial problems would take too long to solve to optimality using these classical optimisation techniques. Often these problems are solved using heuristic methods (such as Tabu search and Simulated Annealing) which do not guarantee optimality. The best solution method for a mathematical programme is highly dependent on the type of mathematical programme being solved.
For more information about formulating and solving a mathematical programme see the topics for the specific types of mathematical programme:
-- TWikiAdminGroup - 20 Feb 2008