Artificial bee colony optimization-inspired synergetic study of fractional-order economic production quantity model
- PDF / 1,659,663 Bytes
- 19 Pages / 595.276 x 790.866 pts Page_size
- 50 Downloads / 217 Views
METHODOLOGIES AND APPLICATION
Artificial bee colony optimization-inspired synergetic study of fractional-order economic production quantity model Mostafijur Rahaman1 · Sankar Prasad Mondal2 · Ali Akbar Shaikh3 Manas Kumar Maiti6 · Rituparna Mondal7 · Debashis De5
· Prasenjit Pramanik4 · Samarjit Roy5 ·
© Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Inventory control is one of the most widely recognized issues in the reality. This investigation manages the utilization of fractional derivatives and integration on an inventory control problem. The memory of a dynamical model is a highly concerned issue which is commonly neglected by the models described in terms of integer-order differential equation. The memory capturing the power of fractional derivative (in Caputo’s sense) is utilized here to describe an economic production quantity model with deterioration when the demand depends on price and stock and production is stock dependent. Also, this study covers the integer-order model with the same assumptions as a memoryless model and a particular case of the fractional model. Due to the complex nature of the model, numerical optimization with the help of a modified artificial bee colony algorithm is done instead of the analytical approach of optimization. Finally, we have performed a sensitivity analysis in order to make a fruitful conclusion. Keywords Fractional-order differential equation · EPQ model · Laplace transformation · ABC algorithm
1 Introduction
Communicated by V. Loia. & Sankar Prasad Mondal [email protected] 1
Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah 711103, India
2
Department of Applied Science, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, Nadia, West Bengal 741249, India
3
Department of Mathematics, University of Burdwan, Golapbag, Burdwan, West Bengal, India
4
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, Paschim Medinipur, West Bengal, India
5
Department of Computer Science and Engineering, Maulana Abul Kalam Azad University of Technology, West Bengal, Haringhata, Nadia, West Bengal 741249, India
6
Department of Mathematics, Mahishadal Raj College, Mahishadal, Purba-Medinipur, West Bengal 721628, India
7
Applied Mathematics and Humanities Department, Sardar Vallabhbhai National Institute of Technology, Surat, Gujrat, India
Fractional calculus (FC) is a branch of mathematics which old enough as the traditional integer-order calculus. In the late seventeenth century, the foundation stone for the establishment of FC was laid by the conversation between two famous mathematicians L’Hospital and Liebnitz. Liebnitz’s response to the question of L’Hospital on the existence of derivative of 12 the order was “an apparent paradox from which 1-day useful consequences will be drawn”. Surprisingly, the application of FC in the practical field of science and technology is neglected for decades and centuries looking at
Data Loading...
