The stochastic process and the squeezed state representation of photons was applied to study the propagation of the entangled photons produced in a nonlinear micro PANDA ring resonator. The four-wave mixing process for generating entangled photon is also analyzed to get the stochastic equation of motion of the entangled photon states. The external spectrum correlation for entangled photon generation is also achieved in analytic form. The results are appropriate to be a quantum processing device to use in quantum computer.

The objective of this research is to use a stochastic process for building a model using Bayesian parameter estimation. The model is applied to the of crash prices and future prices of rice in Thailand for 120 moths including monthly closing average price of white rice 5% non-glutinous paddy 15% and Hom Mali non-glutinous paddy 105. The data are time series data containing autocorrelation trend seasonality and outliers. The algorithms are turned into codes in OpenBugs and the performance of the model is evaluated using simulation in R. The model with a Weibull cumulative distribution function trend the model with an exponential cumulative distribution function trend and the exponential smoothing model are compared. The root mean squared error (RMSE) mean absolute percentage error (MAPE) and mean absolute error (MAE) are used as the criteria. The results show that the model with the model with an exponential cumulative distribution function trend gives smallest RMSE MAPE and MAE for the crash prices of non-glutinous paddy 15% and Hom Mali non-glutinous paddy 105 for both model fitting part and model validation part. The model with a Weibull cumulative distribution function trend gives the smallest RMSE MAPE and MAE for the closing average price of white rice 5% for both model fitting part and model validation part.

The objectives of this research were to select the most appropriate forecasting model for uncertain demand of hot-rolled steel and to find the purchase amount and the reorder point of some raw materials in order to minimize the total cost of production in an iron and steel production planning. The three forecasting models which were exponential model ARIMS model and the proposed Bayesian model were studied. An iron and steel factory in Samutprakarn province was a prototype for this study. Because of their uncertain high demand the Steel H-Beam Steel plate steel round bar and black steel round bar with various sizes were selected and their parameters including demand rate inventory cost back order cost and setup cost were collected. The study found that the proposed Bayesian forecasting model is the most appropriate. The predicted demand and all parameter values were used to find the purchase amounts and the reorder points of the raw materials under the (rQ) policy of the stochastic inventory model.

The objectives of this research were to find the distribution of food demand for laying hens and to find the optimum amount of that food production which had minimum cost. The data consisted of customer purchase orders for the food of laying hens price of food for laying hens cost per unit for the food inventory cost related to food of laying hens in which the food was out of stock such as fine overtime urgent purchase for material. They were collected in 2008-2009 form a factory in Nakhonratchasima province. The collected data were analized in order to explore the distribution of the monthly food demand for the laying hens and to see the rate of inventory per unit. The results were used in the stochastic linear programming model for aggregate planning in which the optimum production minimum cost could be obtained. Programming algorithm in MATLAB and tools in Linprog software were used to get the solution. The distribution of the food demand for laying hens and the random numbers were used in the model. The study found that the distribution of food demand for laying hens every month has normal distribution (January to December). The monthly average amount of production from January to December were 10936.94 12913.74 11898.12 13096 15443.26 14916.33 10322.64 10818.21 11393.11 11700.72 9706.05 and 11702.05 respectively. The minimum total cost average for 12months was Baht 62422386.98.