An Extensive Study On Inventory Management Systems A Fuzzy Approach

Abstract

Managing inventory effectively is crucial for businesses to succeed in a competitive market. Proper inventory management helps streamline operations, reduce expenses, improve customer satisfaction, and boost profits by maintaining optimal stock levels that meet demand without overstocking or wasting resources. Consequently, effective inventory management is a necessity for every business. Inventory constraints often fluc- tuate over time, necessitating close monitoring of stock levels and timely adjustments to ensure sustainable growth and profitability. This challenge has driven researchers, since the early 20th century, to develop optimal policies for various inventory problems using mathematical models. However, contemporary inventory problems often involve inher- ent uncertainty or imprecision in parameters due to factors such as alternative products, digital advertising, e-commerce platforms, and various socio-economic influences. This thesis presents a systematic approach to developing optimal strategies for in- ventory problems characterized by imprecision, utilizing fuzzy set theory and its ap- plications. The study aims to demonstrate how imprecision affects optimal policies by developing both a crisp model and a fuzzy model for each inventory problem. In the crisp model, inventory constraints are deterministic, whereas in the fuzzy model, certain constraints incorporate imprecision or uncertainty. The research is structured into seven chapters. The first chapter provides an intro- duction, a literature survey, and the foundational preliminaries of the research topic. Chapter 2 focuses on developing a profit maximization policy for retailers managing inventory with non-instantaneous deteriorating items and imprecise costs. In Chapter 3, an optimal strategy is derived for a retailer s inventory facing imprecise demand, dete- rioration, and backlog rates. Chapter 4 formulates an effective replenishment policy for a retailer s inventory dealing with Weibull deteriorating products, which have a linearly incr