An Inventory Model for Weibull Deteriorating Items under Price-Stock Dependent Demand, Partial Backlogging, Inflation, and Time Discounting in Fuzzy Environment

Abstract

This paper presents an inventory model for Weibull deteriorating items where the demand is price-dependent and stock-dependent. It incorporates partial backlogging of shortages under inflation and time discounting in a fuzzy and intuitionistic fuzzy environment over a finite planning horizon. The demand rate is defined as when  ,  when , where is the basic market demand,  is the price sensitivity parameter,  is the selling price (assumed constant for simplicity),  is the stock attraction parameter, and  is the inventory level. Deterioration follows a two-parameter Weibull distribution , where  (scale parameter, ) and  (shape parameter). Shortages are permitted with partial backlogging, where the backlogging rate ,  is the waiting time,  is the backlogging parameter, and  represents the fraction of lost sales. The model minimizes the present value of the total cost, which includes ordering, holding, deterioration, shortage, and lost sales costs, adjusted for inflation. First, the crisp model is developed, then it is extended to fuzzy and intuitionistic fuzzy environments by considering the parameters , λ, and δ as triangular fuzzy or intuitionistic fuzzy numbers. The expected value method is used for defuzzification to obtain the optimal replenishment policy. Numerical examples illustrate the solutions in crisp, fuzzy, and intuitionistic fuzzy cases, along with sensitivity analysis on the key parameters. The results show that intuitionistic fuzzy models provide greater robustness under high uncertainty, which is useful for products like fashion goods or electronics.