Recently much work has reported regarding EOQ models for deteriorating items with delay in payments. Most of these papers considered that there is no change of money value over time. But money value changes due to inflation. Hence, in this paper we develop and analyze an EOQ model for deteriorating items with the assumption that delay in payments is allowed under inflation. It is assumed that the life time of the commodity is random and follows a Weibull distribution. It is further assumed that the demand rate is time dependent and follows power pattern, with different values of indexing parameter the demand rate may increase or decrease or remains constant. Using the differential equations the instantaneous state of inventory at a given time is obtained explicitly. With plausible cost considerations under inflation the total cost function over the horizon is derived. The net profit rate function is also obtained. By maximizing the net profit rate function the optimal ordering and price policies are obtained. It is observed through sensitivity analysis that the deterioration distribution parameters, demand rate parameters and inflation rate have significant influence on the optimal operating policies of the model. The permissible delay in payments affects the ordering quantity and cycle time. This model also includes some of the earlier models as particular cases for specific values of the parameters.

Economic production quantity models usually assume that the production is fixed and finite. However, due to various random factors effecting the production, the production process becomes random. This paper deals with the development and analysis of economic production quantity model in which the production is random and follows a generalized Pareto distribution. The generalized Pareto distribution is capable of including different types of production rates. Here it is further assumed that the lifetime of the commodity is random and follows a two parameter Weibull distribution. The Weibull decay includes constant, increasing and decreasing rates of deterioration. It is also assumed that the demand is dependent on selling price. Assuming that shortages are allowed and fully backlogged the instantaneous state of on hand inventory is derived. With suitable cost considerations the total cost function and profit rate function are obtained and minimized with respect to the production uptime and downtime. The optimal production uptime, downtime, production quantity and selling price are derived. A numerical illustration demonstrating the solution procedure of the model is presented. The sensitivity analysis of the model revealed that the production and deteriorating distributions parameters have significant influence on the optimal production schedule and production quantity. This model is extended to the case of without shortages. This model also includes some of the earlier models as particular cases for specific or limiting values of the parameters.

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--------------------------------------------------------ABSTRACT-----------------------------------------------------------In this paper we focus on mixed model analysis for regression model to take account of over dispersion in random effects. Moreover, we present the Data Exploration, Box plot, QQ plot, Analysis of variance, linear models, linear mixed -effects model for testing the over dispersion parameter in the mixed model. A mixed model is similar in many ways to a linear model. It estimates the effects of one or more explanatory variables on a response variable. In this article, the mixed model analysis was analyzed with the R-Language. The output of a mixed model will give you a list of explanatory values, estimates and confidence intervals of their effect sizes, P-values for each effect, and at least one measure of how well the model fits. The application of the model was tested using open-source dataset such as using numerical illustration and real datasets.

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