A sustainable economic order quantity model with fuzzy inflation rate, fuzzy promotional effort and fuzzy deterioration rate

This study represent the exploration of an economic order quantity (EOQ) model where it is perceived that inventory cost at starting time and estimated inventory cost are not necessarily the same. The reason is assumed as delay in time interval between cost estimation and actual starting time of the inventory. Inflation of money, promotional strategies and debilitation rate of decaying items are included in the model. Instability in political ground or uncertain situation of a country as well as the whole world create more instability in the economic system. Thus, inflation of money is considered. The model includes deterioration rate in fuzzy sense, fuzzy inflation and fuzzy promotional index. Therefore, the model is solved by method of signed distance, triangular fuzzy and trapezoidal fuzzy for maximization of profit. Carbon emissions due to transportation is calculated for adding sustainability concept to the model. Optimal order quantity, optimal shortage quantity, optimal selling period and optimal shortage period are found to make the model distinctive. The formulated model is thoroughly explained for both crisp, triangular fuzzy and trapezoidal fuzzy environment and it is concluded that trapezoidal fuzzy number is better in its applicability for decision maker. Because, under the trapezoidal fuzzy environment, the profit value is increased by 10.51% as compared to crisp environment and 3.89% with respect to triangular fuzzy environment. One more finding is that, trapezoidal fuzzy number is better with its simple arithmetic operation as well as easy 1 2 and intuitive interpretation approach. The finding is supported in respect to profitability from the proposed model. A practical example from a fertilizer company is considered in the model to add a real touch. Sensitivity analysis is performed supported by graphical representation. Comparative analysis is derived to show the uniqueness of the model. The model ends with conclusion and direction to possible future study.