Artificial bee colony optimization-inspired synergetic study of fractional-order economic production quantity model

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.