Fuzzy Inventory Model for Instantaneous Deterioration with Split Demand and Complete Backlogging
DOI:
https://doi.org/10.66972/iscis21202611Keywords:
Inventory management, Inventory control model, Deteriorating product, Trapezoidal fuzzy number, Signed distance methodAbstract
This study develops an inventory control model for deteriorating items with a demand rate divided into two components: stock-dependent demand before inventory depletion and constant demand thereafter. The deterioration rate is assumed to be constant, and shortages are fully backlogged. To handle parameter uncertainty, all key parameters are modeled as trapezoidal fuzzy numbers and defuzzified using the signed distance method. The model determines the optimal replenishment policy by identifying the order quantity, the inventory depletion time, and the corresponding minimum total cost. Numerical examples illustrate the model in both fuzzy and crisp environments. The convexity of the total cost function is confirmed through graphical analysis, while sensitivity analysis evaluates the impact of changes and uncertainty in the fuzzy parameters on decision-making for inventory. The results demonstrate that the fuzzy model offers a robust and flexible tool for decision-making, particularly in settings where cost components and deterioration behavior are uncertain.
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