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Types of mathematical models – Simulation techniques, decision theory, replacement models, heuristi

Simulation is a representation of reality (problem, system etc.) through the use of a model or other device which will react in the same manner as reality under a given set of conditions. Simulation is a very powerful tool and is used for problems which fail to be solved by the direct analysis. Once the simulation model is designed, it takes a little time to run a simulation on a computer. Decision theory: Decision theory plays an important role in helping managers make better decisions. Since, in the world people live, the course of future events cannot be predicted with absolute certainty, probabilities are associated with those events. Decision theory covers three categories of decision making under certainty, risk and uncertainty.

Replacement models: Replacement problems are generally two types involving the replacement of items that deteriorate with time and those that do not deteriorate but suddenly fail. The first category includes items like vehicles, machines, equipments, uniforms etc. The problem consists of finding the optimum time for a replacement so that the sum of the cost of new equipment, the cost of maintaining efficiency on the old and the cost of loss of efficiency is minimized. These problems can be solved by calculus and dynamic programming. The second category includes items like electric bulbs, tubes, tires etc. The problem, here, is about finding which items to replace and whether or not to replace them in a group and, if so, when. The objective is to minimize the sum of the cost of the item, cost of replacing the item and the cost associated with failure of items. These problems can be solved by statistical sampling and probability theory. Heuristic models: The heuristic models use rules of thumb or intuitive rules and guidelines (generally under computer control) to explore the most likely paths and to make educated guesses in arriving at a problem’s solution. Thus, checking all the alternatives, so as to obtain the optimum one, is not required. Heuristic models seem to be quite promising for future OR work. They bridge the gap between strictly analytical formulations and the operating principles which managers are habitual of using. Combined methods: A production control problem, for example, normally consists of a combination of inventory, allocation and queuing models. The usual method of solving such combined models consists of solving them one at a time in some logical sequence. However, operations research combines those models and constructs some type of master model, which takes into account the interaction of individual models.

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