Retail management policy through firefly algorithm under uncertainty using Dempster-Shafer theory for production firm

With the emergence of challenges in production and inventory fields, there is a need for innovative management concepts. Due to the sensitivity and popularity of smart electronic gadgets, inventory management is highly likely to be damaged in production and holding processes. This study presents a model in uncertain conditions to investigate real-life situations and apply the results. In this model, due to the product's vulnerability, the damage rate is considered one of the most important parameters. In this research, Dempster-Shafer's theory is applied to deal with the uncertainty condition of a stochastic damaging rate. As traditional methods cannot search for parametric continuous space, genetic algorithms, and firefly algorithms are used to solve them. Finally, by performing sensitivity analysis and evaluation of algorithms, it is shown that the genetic algorithm uses less amount of time than the firefly algorithm. On the other hand, the total cost of a system with a genetic algorithm is greater than the firefly algorithm. Although the answers obtained from the two algorithms used are almost equal, the firefly algorithm provides a better answer for the optimal objective function. In the genetic algorithm, the optimal values are found to be $0.68756 for the damaging rate and $1896.22 for the total cost. Conversely, the firefly algorithm yields optimal values of $0.68395 for the damaging rate and $1895.1576 for the total cost. These results highlight the efficacy of both algorithms in optimizing the specified parameters, providing valuable insights for inventory management systems.