An International Journal of Optimization and Control: Theories & Applications (IJOCTA)

On analyzing two dimensional fractional order brain tumor model based on orthonormal Bernoulli polynomials and Newton's method

2023-08-11T09:48:55+03:00

Recently, modeling problems in various field of sciences and engineering with the help of fractional calculus has been welcomed by researchers. One of these interesting models is a brain tumor model. In this framework, a two dimensional expansion of the diffusion equation and glioma growth is considered. The analytical solution of this model is not an easy task, so in this study, a numerical approach based on the operational matrix of conventional orthonormal Bernoulli polynomials (OBPs) has been used to estimate the solution of this model. As an important advantage of the proposed method is to obtain the fractional derivative in matrix form, which makes calculations easier. Also, by using this technique, the problem under the study is converted into a system of nonlinear algebraic equations. This system is solved via Newton's method and the error analysis is presented. At the end to show the accuracy of the work, we have examined two examples and compared the numerical results with other works.

Scheduling of distributed additive manufacturing machines considering carbon emissions

2023-11-04T12:59:59+03:00

Additive manufacturing is a rapidly growing technology shaping the future of manufacturing. In an increasingly competitive economy, additive manufacturing can help businesses to remain agile, innovative, and sustainable. This paper introduces the multi-site additive manufacturing (AM) machine scheduling problem considering carbon emissions caused by production and transportation. A mixed-integer linear programming model is developed aiming to optimise two separate objectives addressing economic and environmental sustainability in a multiple unrelated AM machine environment. The former is the total cost caused by production, transportation, set-up and tardiness penalty and the latter is the total amount of carbon emissions caused by production and transportation. The model is coded in Python and solved by Gurobi Optimizer. A numerical example is provided to represent the basic characteristics of the problem and show the necessity of the proposed framework. A comprehensive computational study is conducted under 600s and 1800s time limits for two main scenarios and the results have been elaborated. This article introduces the concept of considering both economic and environmental sustainability caused by production and transportation, proposing the first mathematical model and measuring its performance through a comprehensive experimental study.

Bin packing problem with restricted item fragmentation: Assignment of jobs in multi-product assembly environment with overtime

2023-11-04T13:00:14+03:00

This paper studies the assignment problem of multi product assembly jobs to days. The problem aims to minimize the amount of overtime while avoiding assembly delays for jobs that can be fragmented into smaller sub-tasks. When sequence-dependent setup times are negligible, the problem considered transforms into the bin packing problem with restricted item fragmentation where jobs represent items and days stand for bins. We present a mixed integer programming model of the problem by extending earlier formulations in the literature. Computational experiments show that the mathematical model obtained optimal solutions for majority of instances tested within reasonable computation times.