Management science modeling techniques
Management science is basically the development and implementation of various concepts, techniques and models to help enlighten and unravel the managerial problems that are faced in an organization. Management science involves decision making and is general concerned with continuous generation of theories, concepts and models. These models are normally mathematical sometimes are also computer-based. Management science on a broader level makes use of the controllable factors and predicts the factors that are uncontrollable to reach an objective. In this essay focus will be laid on the modeling techniques applied in management science.
There are a large number of fields that are associated with management science such as simulation, forecasting, data mining, project management and so on. But the three main mathematical disciplines that are encompassed within the modeling techniques these are optimization, probability and dynamic systems. One of the basic tools used management science modeling is linear programming. Linear programming is a disciple of mathematics that is concerned with the optimization of linear objective function depending upon the linear equality and inequality constraints. It consists of an objective function that can be maximized or minimized depending upon the some constraints. Linear programming problems fall in either of three categories namely, infeasible, unbounded and optimal solution. In an Infeasible problem the result does not satisfy the constraints, unbounded solution means that there are a number of solutions that can be elicited one being and improved version of the other, and optimal solution is when there is a unique solution.
Another modeling approach for problem solving is the use of probabilistic techniques. This involves risk estimation as the statistics of probability takes into account uncontrollable events as well as risk assessment. In the probabilistic approach, the likelihood or chances of what is unknown are taken into account. Thus, conclusions can be derived by trying to fill the breach between the known and the unknown factors and there is no uncertainty about the events.
Dynamical system approach can also be followed when solving management problems. Dynamical systems include time dependent variables that may change with the passage of time.
Other than these mathematical techniques, there are also verbal, visual and computer based techniques that can be applied. Verbal models suggest that experts sit and discuss the system. This method is low cost and often less time consuming but on the contrary it could be rather biased and vague. Visual representation includes physical or iconic models. These are generally used in engineering and fields of physical science.
The basic point here is that management science should be able to support good decision making. The modeling techniques help businesses in improving their business practices and make their operations more efficient. These researches in theories and models aid the improvement of management functions. These models are aimed at assisting decision making process and help solve complex organizational problems. They provide a systematic and analytical approach to problem solving and thus, decision making.
DISTINGUISH BETWEEN MAXIMIZATION PROBLEMS AND MINIMIZATION PROBLEMS IN LINEAR PROGRAMMING
Linear programming which is also known as linear optimization is basically an optimization of the result based on a number of constraints using mathematical models. The constraints may be equality or inequality. In this essay the difference between the maximization and minimization will be described.
Linear programming can also be defined in mathematical terms as the problem of maximization and minimization of a linear function over a convex polyhedron particularized by linear and non-negativity constraints. Linear programming, also known as optimization is the process of maximizing or minimizing. The values that ensure that the mathematical function has the greatest possible numerical value are called maximization and values that ensure the mathematical expression to have the least possible numerical value is called minimization. Linear programming models have an objective function to be maximized and not minimized. (Vanderbei, 1996)
In linear programming the objective is always to maximize or to minimize some linear function of the decision variables. Decision variables are those whose values are decided in the most favorable fashion. It often appears that the real world problems are most naturally formulated as minimizations. But when it comes to mathematics it is better to work with maximization problems. The reason of this is that the real world planners tend to be pessimistic. Minimization refers to the minimization of costs where as maximization is the maximization of profits. In mathematical terms maximization is widely used equations of linear functions and is easier to formulate than minimization. However, which problem is to be solved largely depends on other variables such as the constraints and the decision variables. The goal may differ from situation to situation; some may prefer to follow the approach of profit maximization while some may tend to minimize costs. A linear programming problem can be feasible of there is some solution satisfying the constraints and if there is no solution satisfying the constraints then it is infeasible. The problem is unbounded if the maximum can be made arbitrarily large. Maximization problems in linear programming are solved by maximizing the objective function where as in solving minimization problems the problem is converted into a maximization problem
Linear programming is an optimization based on constraints and the objective functions are linear. It is called ‘programming’ because the goal of the calculations help one chose the program of action. Linear programming or optimization helps find the best result whether it may be in the form of highest profits or output (maximization) or in the form of lowest cost or waste (minimization). Linear programming serves the same purpose whether it follows the maximization of profit approach or the application of minimization of costs. Maximization can applied in industries such as manufacturing where as minimization can be used in the transportation problem where the cost of serving customers is minimized.
DESCRIBE THE TIME SERIES METHODS OF FORECASTING
Forecasting can be defined as the estimation of something that is unknown and indefinite. Predictions are made to roughly analyze what the situation would be in the future. Forecasts are helpful in a way that through forecasting variables can be modified or altered to be prepared for the future. Forecasting can be applied in the field of supply chain management, transport planning, meteorology, technology forecasting, economic forecasting and so on. Forecasting methodologies can be categorized as, trend extrapolation, consensus methods, simulation methods, decision trees. However, this essay focuses on time series forecasting.
A time series consists of numerical data collected, observed or recorded at more or less regular intervals of time each hour, day, month, quarter or year. It produces forecasts based solely on historical values. More specifically, it is any set of data in which observations are arranged in chronological order. An Example of time series could include hourly temperature recorded at a locality for a period of years.
The analysis of a time series is a process by which a set of observations in a time series is analyzed. The observations in a time series are usually made at equally spaced points of time or they are associated with equal intervals of time.
A typical time series may be regarded as composed of four basic types of movement usually called the components of the time series. These are: secular trend, seasonal variations, cyclic fluctuations and random variations. These components are assumed to be the outcomes of distinct causes of variations. These four components are not necessarily present simultaneously in time series. Secular trend is basically a long term movement that persists for many years and indicates the general direction of the change of the observed values. This trend generally dominates other variations in the long run and covers a fairly long period of time. The seasonal variations which are mainly caused by the change in seasons are short term movements occurring in a periodic manner. These fluctuations are repeated with more or less the same intensity within a specific period of one year or less. Cyclic fluctuations are long period oscillations about the long term trend, which tend to occur in a more or less regular pattern over a period of certain number of years. Cycles have duration of anywhere form two to ten years or even a longer period. A typical cycle has the phases of prosperity, contraction, recession and then recovery or expansion. Random variations, also called irregular variations are irregular or unsystematic in nature. They occur in a completely unpredictable manner as they are caused by some unusual events such as floods, droughts etc.
The analysis of a trend component involves its measurement and elimination from observed time series data. To measure a trend which can be represented as a straight line or a curve the methods which are used are: the method of free-hand curve, the method of semi-averages, the method of moving averages, and the method of least squares.
Another aspect of time series is the process of detrending. After the determination of the trend by any method the next step in the analysis is to remove its effect from the observed time series. The variations are then analyzed and the method of analysis depends upon the measure that is applied.
Time series analysis is a very useful tool for predicting the future trends whether it may be a business life cycle, a general market trend or even the weather. There are a number of different techniques that can be used to construct a time series analysis which proves as an advantage because it enables this forecasting model to be implemented practically in a number of diverse fields. It may be applied in businesses to predict the future sales or it could be used by economists as a tool for analyzing the future of the markets. Time series forecasting helps in predicting the future and thus making decision more cautiously. These are one of the simplest methods to deploy and can be quite accurate especially over a short period of time. (Hiray, 2008)
Hiray, J (2008, feb 8). Management science modeling techniques. Retrieved September 25, 2008, from All about business and management Web site: http://businessmanagement.wordpress.com/2008/02/08/management-science-modeling-techniques/
Hiray, J (2008, feb 21). Time series methods of forecasting. Retrieved September 26, 2008, from All about business and management Web site: http://businessmanagement.wordpress.com/2008/02/21/time-series-methods-of-forecasting/
Vanderbei, R.J (1996). Linear programming: foundations and extensions.