An Inventory Management Framework Designed for Deteriorating Items with Time Sensitive Demand and Shortages under All Unit Price Discount Policy Incorporating a Fuzzy Approach

Authors : Md. Rukonuzzaman; Aminur Rahman Khan

Volume/Issue : Volume 9 - 2024, Issue 2 - February

Google Scholar : http://tinyurl.com/md3vrzdm

Scribd : http://tinyurl.com/hn9deabd

Abstract : The conventional inventory model, known as the crisp inventory model, assumes that parameters have precise and certain values. However, in real-world scenarios, it is observed that uncertainties or imprecisions in the environment prevent the exact definition of all parameters. To address this uncertainty, fuzzy set theory may be applied, providing decision- makers with mathematical tools to formulate inventory models that reflect real-world conditions. This study explores two inventory models: a traditional crisp model and its corresponding fuzzy counterpart. The focus is on a non-instantaneous deteriorating item with time- sensitive demand under a unit price discount policy, considering fully backlogged shortages and incorporating salvage value for deteriorated units. In the fuzzy environment, parameters such as demand, deterioration rate, salvage, and cost components like ordering cost, holding cost, and shortages cost are represented as triangular fuzzy numbers. The Signed distance method is utilized for defuzzification of fuzzy outputs. Numerical examples are offered to justify and compare the anticipated crisp and fuzzy models. Additionally, a sensitivity analysis for the fuzzy model is conducted to provide managerial implications.

Keywords : Crisp inventory model,Fuzzy inventory model, Non-instantaneous,Time-sensitive demand, Price discount policy, Fully backlogged shortages, Salvage value, Triangular fuzzy number,Defuzzification, Signed distance method.

The conventional inventory model, known as the crisp inventory model, assumes that parameters have precise and certain values. However, in real-world scenarios, it is observed that uncertainties or imprecisions in the environment prevent the exact definition of all parameters. To address this uncertainty, fuzzy set theory may be applied, providing decision- makers with mathematical tools to formulate inventory models that reflect real-world conditions. This study explores two inventory models: a traditional crisp model and its corresponding fuzzy counterpart. The focus is on a non-instantaneous deteriorating item with time- sensitive demand under a unit price discount policy, considering fully backlogged shortages and incorporating salvage value for deteriorated units. In the fuzzy environment, parameters such as demand, deterioration rate, salvage, and cost components like ordering cost, holding cost, and shortages cost are represented as triangular fuzzy numbers. The Signed distance method is utilized for defuzzification of fuzzy outputs. Numerical examples are offered to justify and compare the anticipated crisp and fuzzy models. Additionally, a sensitivity analysis for the fuzzy model is conducted to provide managerial implications.

Keywords : Crisp inventory model,Fuzzy inventory model, Non-instantaneous,Time-sensitive demand, Price discount policy, Fully backlogged shortages, Salvage value, Triangular fuzzy number,Defuzzification, Signed distance method.