Quality control is considered a critical aspect of plastic materials in the injection molding process. Two types of deformations occur during the injection molding process, namely, volumetric shrinkage and warpage. This study aims to optimize the warpage of the polyethylene terephthalate preform (PET) used for the packing of carbonated drinks. PET warpage results in an uneven distribution of material over the wall surface of the preform and causes variation in wall thickness. During the filling operation of carbonated drinks, the preforms are subjected to high pressure at the points where the wall thickness is at a minimum, which induces a high-stress concentration. Under high pressure, the preforms are ruptured at the points where the warpage is at a maximum (stress concentration area), causing wastage of the beverage as well as the preform. In this study, the Taguchi method and analysis of variance (ANOVA) are used to determine the most significant parameters to induce warpage during the molding process. Then, we optimize the process parameters in order to reduce warpage through a numerical approach using SolidWorks Plastics. The result shows that the ambient temperature and melting temperature are the most critical parameters that contribute to the warpage, yielding 42.115% and 41.278%, respectively. Among the 6 parameters considered for this study, the pressure holding time contributes a minimum of 0.5961% to the yielding of the warpage. Overall, by optimizing the process parameters, warpage of the PET preform is minimized by 7.7202%, which helps to reduce wastage of the carbonated drink as well as the rejection rate of the preform during the filling operation. In a nutshell, the quality of the preform is improved.

In this paper, a mathematical model is developed for the modified settings of an automatic filling machine to minimize the filling time of orders for different volumes of dairy product and flavors. The linear programming model is solved using the Simplex method to find an optimal solution to the optimization problem. The results of the model are used for sequencing the processing of orders using one-dimensional rules with the aim of obtaining an optimal sequence for the most valued performance measure. The comparative analysis of the one-dimensional rules showed that Shortest Processing Time (SPT) is better than the other rules for minimization of the average time past due. Additionally, the results of the model for the new machine settings, when compared with previous similar studies, yielded encouraging results.

This paper is related to the fractional view analysis of coupled Burgers equations, using innovative analytical techniques. The fractional analysis of the proposed problems has been done in terms of the Caputo-operator sense. In the current methodologies, first, we applied the Elzaki transform to the targeted problem. The Adomian decomposition method and homotopy perturbation method are then implemented to obtain the series form solution. After applying the inverse transform, the desire analytical solution is achieved. The suggested procedures are verified through specific examples of the fractional Burgers couple systems. The current methods are found to be effective methods having a close resemblance with the actual solutions. The proposed techniques have less computational cost and a higher rate of convergence. The proposed techniques are, therefore, beneficial to solve other systems of fractional-order problems.