An Inventory Model for Perishable Goods with Demand that Varies Probabilistically with Selling Price Using a Pentagonal Fuzzy Framework

Managing inventory for perishable goods in industries such as food processing and pharmaceuticals poses significant challenges due to the uncertain nature of demand, which is often influenced by factors such as price, timing, and product shelf life. Pentagonal Fuzzy Numbers (PFNs) provide a more realistic representation of expert judgment by considering five distinct evaluation points, thereby enhancing the accuracy and flexibility of uncertainty modeling in production inventory systems. To address these complexities, this study proposes an analytical inventory model formulated within a pentagonal fuzzy framework in place of triangular or trapezoidal fuzzy numbers. The model effectively handles deteriorating items considering a probabilistic demand rate function and applying two defuzzification techniques: Graded Mean Integration Representation (GMIR) and Signed Distance (SD). The primary objective of the model is to maximize total average profit function by simultaneously optimizing the cycle length and selling price. Analytical optimization is carried out using MATLAB software (version R2021b), supported by detailed numerical examples for all three cases and a sensitivity analysis conducted under both crisp and fuzzy environments. This analysis highlights the influence of key system parameters on model performance. Additionally, the graphical results are presented in a simplified and focused format to effectively illustrate the optimal outcomes derived from the model.