Optimization of flexo process parameters to reduce the overall manufacturing cost

The flexo process parameters play an important role in ink transfer and will lead to wastage of inks, substrate, solvents and printed stocks if not monitored and controlled. The work focuses on optimizing the flexo process parameters for 40 microns 3-layer polyethylene (PE) film with Blue Nitrocellulose (NC) ink to reduce overall manufacturing cost while maintaining the print quality for diaper application. An experimental design was conducted for the response Ink GSM (grams per square meter), ?E and Print Mottle with factors such as ink viscosity, anilox volume, plate dot shape and substrate opacity. The data was analyzed through Main Effect, Interaction Plot and Analysis of Variance (ANOVA). The regression models were developed for the response to validate the predictive ability of model. The process optimization resulted in reduction of Ink GSM, ?E and Print Mottle by 18%, 52% and 1% respectively. The ink consumption reduced by 18.26% with minimized print defects, thereby reducing the overall manufacturing cost.

An EOQ model for deteriorating items analyzing retailer’s optimal strategy under trade credit and return policy with nonlinear demand and resalable returns

This paper presents an EOQ model where demand is dependent upon time and selling price. In the proposed model of inventory, the retailer allows its unsatisfied customers to return their product whereas the manufacturer offers a full trade credit policy to the retailer. To make our model realistic, we have assumed that the product returned can be resold with the same selling price. Number of returns is a function of demand. In this proposed inventory model considering deterioration, the retailer does not fully reimburse its customers for the returned product. The primary purpose of this inventory model is to determine the optimal selling price, optimal order quantity, and optimal replenishment cycle length in order to maximize the retailer’s total profit earned per unit time. A numerical example is also presented and a sensitivity analysis is carried to highlight the findings of the suggested inventory model.

Multi-objective regression modeling for natural gas prediction with ridge regression and CMARS

Residential customers are the main users generally need a great quantity of natural gas in distribution systems, especially, in the wintry weather season since it is particularly consumed for cooking and space heating. Hence, it ought to be non-interruptible. Since distribution systems have a restricted ability for supply, reasonable planning and prediction through the whole year, especially in winter seasons, have emerged as vital. The Ridge Regression (RR) is formulated mainly to decrease collinearity results through shrinking the regression coefficients and reducing the impact in the model of variables. Conic multivariate adaptive regression splines ((C)MARS) model is constructed as an effective choice for MARS by using inverse problems, statistical learning, and multi-objective optimization theories. In this approach, the model complexity is penalized in the structure of RR and it is constructed a relaxation by utilizing continuous optimization, called Conic Quadratic Programming (CQP). In this study, CMARS and RR are applied to obtain forecasts of residential natural gas demand for local distribution companies (LDCs) that require short-term forecasts, and the model performances are compared by using some criteria. Here, our analysis shows that CMARS models outperform RR models. For one-day-ahead forecasts, CMARS yields a MAPE of about 4.8%, while the same value under RR reaches 8.5%. As the forecast horizon increases, it can be seen that the performance of the methods becomes worse, and for a forecast one week ahead, the MAPE values for CMARS and RR are 9.9% and 18.3%, respectively.

A fractional model in exploring the role of fear in mass mortality of pelicans in the Salton Sea

The fear response is an important anti-predator adaptation that can significantly reduce prey's reproduction by inducing many physiological and psychological changes in the prey. Recent studies in behavioral sciences reveal this fact. Other than terrestrial vertebrates, aquatic vertebrates also exhibit fear responses. Many mathematical studies have been done on the mass mortality of pelican birds in the Salton Sea in Southern California and New Mexico in recent years. Still, no one has investigated the scenario incorporating the fear effect. This work investigates how the mass mortality of pelican birds (predator) gets influenced by the fear response in tilapia fish (prey). For novelty, we investigate a modified fractional-order eco-epidemiological model by incorporating fear response in the prey population in the Caputo-fractional derivative sense. The fundamental mathematical requisites like existence, uniqueness, non-negativity and boundedness of the system's solutions are analyzed. Local and global asymptotic stability of the system at all the possible steady states are investigated. Routh-Hurwitz criterion is used to analyze the local stability of the endemic equilibrium. Fractional Lyapunov functions are constructed to determine the global asymptotic stability of the disease-free and endemic equilibrium. Finally, numerical simulations are conducted with the help of some biologically plausible parameter values to compare the theoretical findings. The order $\alpha$ of the fractional derivative is determined using Matignon's theorem, above which the system loses its stability via a Hopf bifurcation. It is observed that an increase in the fear coefficient above a threshold value destabilizes the system. The mortality rate of the infected prey population has a stabilization effect on the system dynamics that helps in the coexistence of all the populations. Moreover, it can be concluded that the fractional-order may help to control the coexistence of all the populations.

Some qualitative properties of nonlinear fractional integro-differential equations of variable order

The existence-uniqueness criteria of nonlinear fractional integro-differential equations of variable order with multiterm boundary value conditions are considered in this work. By utilizing the concepts of generalized intervals combined with the piecewise constant functions, we transform our problem into usual Caputo’s fractional differential equations of constant order. We develop the necessary criteria for assuring the solution's existence and uniqueness by applying Schauder and Banach fixed point theorem. We also examine the stability of the derived solution in the Ulam-Hyers-Rassias (UHR) sense and provide an example to demonstrate the credibility of the results.

A computational approach for shallow water forced Korteweg–De Vries equation on critical flow over a hole with three fractional operators

The Korteweg–De Vries (KdV) equation has always provided a venue to study and generalizes diverse physical phenomena. The pivotal aim of the study is to analyze the behaviors of forced KdV equation describing the free surface critical flow over a hole by finding the solution with the help of q-homotopy analysis transform technique (q-HATT). he projected method is elegant amalgamations of q-homotopy analysis scheme and Laplace transform. Three fractional operators are hired in the present study to show their essence in generalizing the models associated with power-law distribution, kernel singular, non-local and non-singular. The fixed-point theorem employed to present the existence and uniqueness for the hired arbitrary-order model and convergence for the solution is derived with Banach space. The projected scheme springs the series solution rapidly towards convergence and it can guarantee the convergence associated with the homotopy parameter. Moreover, for diverse fractional order the physical nature have been captured in plots. The achieved consequences illuminates, the hired solution procedure is reliable and highly methodical in investigating the behaviours of the nonlinear models of both integer and fractional order.

On self-similar solutions of time and space fractional sub-diffusion equations

In this paper, we have considered two different sub-diffusion equations involving Hilfer, hyper-Bessel and Erdelyi-Kober fractional derivatives. Using a special transformation, we equivalently reduce the considered boundary value problems for fractional partial differential equation to the corresponding problem for ordinary differential equation. An essential role is played by certain properties of Erd\'elyi-Kober integral and differential operators. We have applied also successive iteration method to obtain self-similar solutions in an explicit form. The obtained self-similar solutions are represented by generalized Wright type function. We have to note that the usage of imposed conditions is important to present self-similar solutions via given data.

Theory and applications of new fractional-order chaotic system under Caputo operator

This paper introduces the properties of a fractional-order chaotic system described by the Caputo derivative. The impact of the fractional-order derivative has been focused on. The phase portraits in different orders are obtained with the aids of the proposed numerical discretization, including the discretization of the Riemann-Liouville fractional integral. The stability analysis has been used to help us to delimit the chaotic region. In other words, the region where the order of the Caputo derivative involves and where the presented system in this paper is chaotic. The nature of the chaos has been established using the Lyapunov exponents in the fractional context. The schematic circuit of the proposed fractional-order chaotic system has been presented and simulated in via Mutltisim. The results obtained via Multisim simulation of the chaotic circuit are in good agreement with the results with Matlab simulations. That provided the fractional operators can be applied in real- worlds applications as modeling electrical circuits. The presence of coexisting attractors for particular values of the parameters of the presented fractional-order chaotic model has been studied.

Comparative assessment of smooth and non-smooth optimization solvers in HANSO software

The aim of this study is to compare the performance of smooth and nonsmooth optimization solvers from HANSO (Hybrid Algorithm for Nonsmooth Optimization) software. The smooth optimization solver is the implementation of the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method and the nonsmooth optimization solver is the Hybrid Algorithm for Nonsmooth Optimization. More precisely, the nonsmooth optimization algorithm is the combination of the BFGS and the Gradient Sampling Algorithm (GSA). We use well-known collection of academic test problems for nonsmooth optimization containing both convex and nonconvex problems. The motivation for this research is the importance of the comparative assessment of smooth optimization methods for solving nonsmooth optimization problems. This assessment will demonstrate how successful is the BFGS method for solving nonsmooth optimization problems in comparison with the nonsmooth optimization solver from HANSO. Performance profiles using the number iterations, the number of function evaluations and the number of subgradient evaluations are used to compare solvers.

Analysis of make-to-stock queues with general processing times and start-up and lost sales costs

We consider a make-to-stock environment with a single production unit that corresponds to a single machine or a line. Production and hence inventory are controlled by the two-critical-number policy. Production times are independent and identically distributed general random variables and demands are generated according to a stationary Poisson process. We model this production-inventory system as an M/G/1 make-to-stock queue. The main contribution of the study is to extend the control of make-to-stock literature by considering general production times, lost sales and fixed production costs at the same time. We characterize the long-run behaviour of the system and also propose a simple but very effective approximation to calculate the control parameters of the two-critical-number policy. An extensive numerical study exhibits the effects of the production time distribution and the system parameters on the policy control levels and average system cost.