Showing papers in "International Journal of Optimization and Control : Theories & Applications in 2022"

Uncertainty-based Gompertz growth model for tumor population and its numerical analysis

Abstract: For treating cancer, tumor growth models have shown to be a valuable resource, whether they are used to develop therapeutic methods paired with process control or to simulate and evaluate treatment processes. In addition, a fuzzy mathematical model is a tool for monitoring the influences of various elements and creating behavioral assessments. It has been designed to decrease the ambiguity of model parameters to obtain a reliable mathematical tumor development model by employing fuzzy logic.The tumor Gompertz equation is shown in an imprecise environment in this study. It considers the whole cancer cell population to be vague at any given time, with the possibility distribution function determined by the initial tumor cell population, tumor net population rate, and carrying capacity of the tumor. Moreover, this work provides information on the expected tumor cell population in the maximum period. This study examines fuzzy tumor growth modeling insights based on fuzziness to reduce tumor uncertainty and achieve a degree of realism. Finally, numerical simulations are utilized to show the significant conclusions of the proposed study.

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

Abstract: 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.

Genocchi polynomials as a tool for solving a class of fractional optimal control problems

Abstract: In this research, we use operational matrix based on Genocchi polynomials to obtain approximate solutions for a class of fractional optimal control problems. The approximate solution takes the form of a product consisting of unknown coefficients and the Genocchi polynomials. Our main task is to compute the numerical values of the unknown coefficients. To achieve this goal, we apply the initial condition of the problem, the Tau and Lagrange multiplier methods. We do error analysis as a means to study the behaviour of the approximate solutions.

Optimization of flexo process parameters to reduce the overall manufacturing cost

Abstract: 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.

A belief-degree based multi-objective transportation problem with multi-choice demand and supply

Abstract: This paper focusses on the development of a Multi-choice Multi-objective Transportation Problem (MCMOTP) in the uncertain environment. The parameters associated with the objective functions in MCMOTP are regarded as uncertain variables and the other parameters associated with supply capacity and demand requirements are considered under the multi-choice environment. In this paper, two ranking criteria have been utilized to convert the uncertain objectives into their crisp form. Using these two ranking criteria for the uncertain MCMOTP model, two deterministic models have been developed namely, Expected Value Model (EV Model) and Optimistic Value Model (OV Model). The multi-choice parameters in the constraints are converted to a single choice parameters with the help of binary variable approach. The EV and OV models are solved directly in the LINGO 18.0 software using minimizing distance method and fuzzy programming technique. At last, a numerical illustration is provided to demonstrate the application and algorithm of the models. The sensitivity of the objective functions in OV Model is also examined with respect to the confidence levels to investigate variation in the objective functions.

Optimal matchday schedule for Turkish professional soccer league using nonlinear binary integer programming

Abstract: Sports scheduling problems are interesting optimization problems that require the decision of who play with whom, where and when to play. In this work, we study the sports scheduling problem faced by the Turkish Football Federation. Given the schedule of games for each round of the season, the problem is to determine the match days with the goal of having a fair schedule for each team. The criteria we employ to establish this fairness are achieving an equal distribution of match days between the teams throughout the season and the ideal assignment of games to different days in each round of the tournament. The problem is formulated as a nonlinear binary integer program and is solved optimally for each week. Our results indicate that significant improvements over the existing schedule can be achieved if the optimal solution is implemented.

A numerical scheme for the one-dimensional neural field model

Abstract: Neural field models, typically cast as continuum integro-differential equations, are widely studied to describe the coarse-grained dynamics of real cortical tissue in mathematical neuroscience. Studying these models with a sigmoidal firing rate function allows a better insight into the stability of localised solutions through the construction of specific integrals over various synaptic connectivities. Because of the convolution structure of these integrals, it is possible to evaluate neural field model using a pseudo-spectral method, where Fourier Transform (FT) followed by an inverse Fourier Transform (IFT) is performed, leading to a new identical partial differential equation. In this paper, we revisit a neural field model with a nonlinear sigmoidal firing rate and provide an efficient numerical algorithm to analyse the model regarding finite volume scheme. On the other hand, numerical results are obtained by the algorithm.

Optimizing seasonal grain intakes with non-linear programming: An application in the feed industry

Abstract: In the feed sector, 95% of the input costs arise from the supply of raw materials used in feed production. The selling price is determined by competition in free market conditions. Due to the use of similar technologies and the very small share of production costs in total costs, it is unlikely that a competitive advantage will be gained through innovations in production. Between 30% and 50% of grain products are used in feed ration analysis. Cereals can only be harvested at a certain time of the year. Due to this limited time frame, feed production enterprises have to balance their financial burdens with their operational needs while making their annual stocks. The study was carried out to cover all the relevant businesses of the company, which has feed factories in four regions of Turkey. Based on the season data of the year 2020-2021, the grain purchase planning for the year 2021-2022 was tried to be optimized with non-linear programming. While creating the mathematical model, grain prices, interest rates, production needs according to production planning, sales according to sales forecasts, factory stocking capacities, licensed warehouse rental, transportation, handling and transshipment costs were taken into account. With this unique paper, in the cattle feed production sector, storage, transportation and handling costs will be minimized. Cost advantage will be provided with optimum purchase planning in the season. According to the grain pricing forecast and market data for the 2021-2022 season, model can provide a cost advantage of 0.7%. Model will also provide insight to the managers for additional storage space investments.

A new generalization of Rhoades' condition

Abstract: In this paper, our aim is to obtain a new generalization of the well-known Rhoades' contractive condition. To do this, we introduce the notion of an S-normed space. We extend the Rhoades' contractive condition to S-normed spaces and define a new type of contractive conditions. We support our theoretical results with necessary illustrative examples.

Financial efficiency of companies operating in the Kosovo food sector: DEA and DEAHP

Abstract: Data Envelopment Analysis (DEA) evaluates a large number of input and output variables using mathematical programming techniques and analyzes the effectiveness of similar decision making units (DMU). Unlike traditional methods, the most important advantage of DEA is that the weights of input and output variables can be defined by the analyzer. In this study, the limitations of the DEA weights were determined using the AHP, which considers expert opinion. In addition, an alternative judgment scale was used for the Saaty judgment scale, which is used as a standard in the AHP method, and thus a more sensitive analysis was performed. There have been studies dealing with the comparison of judgment scales, but few studies on consistency sensitivity are needed. This point has also been addressed in this study. Subsequently, the financial efficiency of 27 companies operating in the food sector in Kosovo was evaluated with the weight-restricted DEA model, first created using the unweighted DEA model and then the AHP model, and the two models were compared. This paper is the first one of its kind since there are no previous studies regarding the examination of the financial efficiency of companies operating in the Kosovo food sector based on the DEAHP method.