# Modeling Techniques in Management Science

Management science is the science for managing and involves decision making. It utilizes what is controllable, and tries to predict what is uncontrollable in order to archive a specific objective. Science is a continuous search; it is a continuing generation of theories, models, concepts, and categories. Management science uses analytical methods to solve problems in areas such as production and operations, inventory management, and scheduling. Typical management science approach is to build a model for the problem being studied, such a model is often a mathematical model. Practical problems are often unstructured and lack clarification in definition of problem which makes mathematical modeling a challenge. Therefore modeling of a problem is important phase in problem solving technique. Once model is built, algorithms are used to solve problem. Various techniques are devised to model problem and solve it for possible solutions.

Linear programming is one of the widely used modeling techniques. Linear programming problems consist of an objective function (also know as cost function) which has to be minimized or maximized subject to a certain number of constraints. The objective function consists of a certain number of variables. The constraints are linear inequalities of the variables used in the objective function. This technique is closely related to linear algebra and uses inequalities in the problem statement rather than equalities. A linear programming problem can fall in three categories: infeasible, unbounded and an optimal solution. In an infeasible problem values of decision variables do not satisfy constraint condition. A problem is unbounded if the constraints do not sufficiently restrain the objective function so that for any given feasible solution, another feasible solution can be found that makes further improvement to the objective function. In an optimal solution, the objective function has a unique maximum or minimum value. Linear programming problems can be solved using graphical analysis method. Sensitive analysis is extension to solution found in linear programming to find out effect of parameter changes on the optimal solution. The parameters are called coefficients and can be quantity or value used in objective function. In linear programming results are rounded to get reasonable output, however rounded solution might not be feasible and many not give an optimal solution. Therefore, Integer programming model is used with fractional values. Linear programming is also use to solve transportation, transshipment, and assigning problems. Linear programming is widely used in production planning and scheduling. It is very well used in airline industry for aircraft and crew scheduling.

Probabilistic techniques are another class of modeling approach for problem solving. It is based on application of statistics for probability of uncontrollable events as well as risk assessment of decision. In this technique risk means uncertainty for which the probability of distribution is know. Therefore risk assessment involves study of the outcomes of decisions along with their probabilities. Probability assessment tries to fill gap between what is know and what need to be know for an optimal solution. Therefore, probabilistic models are used to prevent events happening due to adverse uncertainty. Decision analysis and queuing systems are example of probabilistic techniques. The modeling technique use to solve physical problems such as transportation or flow of commodities is Network modeling. Network problems are an abstract representation of processes and activities for a give problem and illustrated by using network branches and nodes. This technique uses most cost effective way to transport the goods, to determine maximum/minimum possible flow from source to destination and to find shortest critical path in large projects.

The management science modeling process helps businesses to improve their operations through the use of scientific methods and the development of specialized techniques. It is the process of researching for an optimal solution to the existing problem. Management science modeling process provides systematic, analytical and general approaches to the problem solving for decision-making, regardless of the nature of the system, product, or service. Management science modeling process is the application of scientific methods to complex organizational problems. Models are aimed at assisting the decision-maker in decision-making process. Management science modeling process is one of the innovative decision making tool of the twentieth century.

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