evaluating the energy supply chain in the petrochemical industry with the cost malmquist productivity index approach and fuzzy vikor con-sidering the importance coefficient of input variables

This study was conducted to evaluate the energy supply chain in the petrochemical industry with the approach of malmquist cost efficiency index and fuzzy vikor, taking into account the importance coefficient of input variables. after reviewing the literature, the inputs and outputs of the energy supply chain were first identified. then, the influential variables in the petrochemical industry in the energy supply chain were identified and prioritized with the fuzzy vikor approach. next, the weight of the input variables was calculated using the geometric mean, and the input variables were entered into the mathematical model based on their weight. based on the input type, a mathematical model was developed to estimate input costs to ensure output and supply chain efficiency in two consecutive years. then, the malmquist cost index was estimated based on the model outputs. the petrochemical company with the highest malmquist total cost index and the lowest output cost was selected as the optimal solution of the model. the value of the objective function indicates the input costs. our inputs include two variables: the number of employees and the value of materials used in fuel reproduction. petrochemicals 9, 7, 12, 10, 6, 5, 3, 4, 13, 11, 2, 8, 1, and 14 respectively have the lowest input costs, which is necessarily due to the efficiency of the petrochemicals; the efficiency of the petrochemicals is checked. the cost return is calculated from the relevant formula in the years 2021 and 2022. as seen, the yield in 2021 in petrochemicals 1, 11, 7, 13, and 14 is 1. the ratio of the outputs to the inputs is higher, so they are efficient. in petrochemicals 1, 7, 14, and 11, it is greater than 1 in 2022. therefore, the output to input ratio is more efficient. overall efficiency change (oec) examines the changes in cost efficiency over the period in question and reflects the displacement value and the efficiency frontier. evaluating the energy supply chain model in the petrochemical industry using the malmquist productivity index can help reduce production costs, better evaluate the industry, and formulate future policies for companies active in this field.