Operations research (OR) pertains to the process of gathering statistical information about different types of operations and the nature of their output. Operations research is a subset of statistical studies on industrial production, consumption, service and pricing. It is used in all areas of human action such as manufacturing, economic, business, operation design, planning, supply chain management and environmental assessment. The main objective of operations research is to quantify the results of operations in terms of productivity, quality and cost. It is a statistical approach that deals with analysis of theoretical economic theories.
Operations Research Statistics (ORS) has four main statistical methods: the graphical method, the linear method, the random sample or binomial tree and binomial trend. The graphical method concentrates on estimating trends, random variables or time series values and is quite useful for comparing estimates from different models. It is an efficient way of representing the data and can be applied directly to the model without having to complicate the models. It is more appropriate for forecasting purposes and it is less subject to sampling error. For example, all data used in a research study may not be accurate for a particular time period because of small evidence interval.
The graphical OR model is based on mathematical formulations that allow for the assumption of a normal distribution of data distribution and its interval distribution. It uses a mathematical model called a polynomial or logistic equation to fit data from different types of economic models. The logistic equation can be fitted using different types of numerical methodology depending on the type of data being analyzed.
The logistic models assumes that the observed value of a variable is independent of all other previous observations. The logistic function maps the relationship between the value of a variable x and the mean of all other variables measured over the interval k from 0 to t. It is important to realize that the range of the probability density function does not necessarily coincide with the range of sample mean or standard deviation for the same variable. This is because the range of the distribution does not deviate too much from the mean average.
The chi-square or confidence interval is another statistical method often used in operations research. The chi-square gives rise to a point estimate of the value of the parameter estimate. These confidence intervals are widely used in the economic and business sciences. The confidence interval will depend on the data sampling and statistical analysis, so it must be considered carefully before drawing any conclusions about the data.
A logistic regression is another statistical method often used in operations research. It can be fitted by using the normal curve approach. The logistic regression uses the natural log of the output value as input into the model and estimates the probability of the original output value. This type of statistical method is based on the theory of logistic regression that says that the probability of the original value plotted against the corresponding value obtained through the model can be graphed as a function of time.
Another popular statistic is the chi-squared or kappa-squared statistic. This relies on the mathematical probability concept. The kappa-squared is different from the binomial and Student’s t-statistics in the sense that the parameters are chosen so that their mean and standard deviation are equal to 1. This is a more accurate way of measuring the deviation of the statistical estimate from the actual or expected values.
Other statistical methods in operations research include the binomial logistic, lattice-thority, and normal curve. Binomial logistic equation and lattice-thority probability are examples of lattice-thority probability. The binomial logistic equation is a mathematical model that helps to express the probability axiom directly in the analytical form. Operations research statistics in this field deal mostly with economic, accounting, and business mathematics.