Fundamentals of Inventory Control in Crisp, Probability and Fuzzy Environments

This chapter presents a foundational overview of inventory control strategies across crisp, probabilistic, and fuzzy environments. Aimed at beginners in inventory theory, it introduces key terminologies, classifications of inventory, cost components, and the purpose of effective inventory management. It begins with the classical Economic Order Quantity (EOQ) models under deterministic assumptions, elaborating various extensions including production models and scenarios allowing shortages. Each model is mathematically formulated with clear notations and corollaries. Incorporating uncertainty, the study progresses to probabilistic inventory models, addressing scenarios where demand follows a known probability distribution. These models aim to minimize the total expected cost by deriving optimal order quantities under both discrete and continuous demand conditions. This chapter’s most novel contribution lies in exploring fuzzy inventory models, designed for situations where cost and demand information is vague or imprecise rather than random. Utilising triangular and trapezoidal fuzzy numbers, the study addresses fuzzification of the EOQ formula and proposes methods for defuzzification. Through a comprehensive blend of theoretical development and applied techniques, the chapter bridges classical inventory theory with modern fuzzy set applications, offering practical insights for researchers and practitioners in operations research and supply chain management.