A fuzzy inventory model with time dependent Weibull deterioration, quadratic demand and partial backlogging

Abstract

In this paper, we developed a fuzzy inventory model for time dependent Weibull deterioration and quadratic demand rate. Shortages are allowed and are partially backlogged. In the present situation, two different cases for the fuzzy inventory model are considered. Case 1: the coefficients present in the demand are the initial rate of demand (crisp) which is considered to be a constant and the rate with which the demand rate increases and also the increase in rate of change in the demand rate itself are taken to be the fuzzy numbers. Case 2: all the coefficients of the quadratic demand are considered as fuzzy numbers. The fuzziness is also introduced for the partial backlogging in both cases. In the fuzzy EOQ model, all the fuzzy related parameters are expressed in triangular fuzzy numbers. The main objective of the paper is to minimise the total cost both in crisp and fuzzy environments. To defuzzify the total cost we used the signed distance method. A numerical example is given to show the applicability of the different models. Sensitivity analysis is carried out to reflect the effect of changes in the parameters on the optimum solution.