Use of Neutrosophic Fuzzy Numbers to Model Inventory Problems

Inventory control is a very useful topic of operations research and a significant component of supply chain optimisation. Classical inventory models, such as the Economic Order Quantity (EOQ) and Economic Production Quantity (EPQ), traditionally assume crisp, well-defined parameters like constant demand rates, fixed holding and ordering costs, and deterministic lead times. However, in real-world scenarios, these parameters are often subject to various forms of uncertainty, vagueness, and incomplete information. Fuzzy logic and probabilistic approaches have been applied to mitigate these issues, but they still struggle with adequately representing the indeterminacy and contradictory nature of real data. To overcome these challenges, this study presents a comprehensive inventory model grounded in neutrosophic number theory, an extension of fuzzy numbers and interval numbers. The neutrosophic numbers are of the form a+bI, where a represents the certain part of the number and bI represents the indeterminacy part of the same number; a and b are either real numbers, complex numbers, or any other information. By incorporating these into the inventory model, the decision-makers can better represent ambiguous, imprecise, inconsistent, and incomplete data. In this model, key inventory parameters such as demand rate, unit cost, holding cost, shortage cost, and lead time are modelled as neutrosophic numbers. Two fundamental models of inventory control are developed using the neutrosophic numbers.