In this paper, a fuzzy inventory model with a Weibull deterioration rate, a
quadratic demand rate, and a variable holding cost under permissible
shortages has been developed. The deterioration rate is expressed by a
two-parameter Weibull distribution. During a shortage, some buyers wait for
the actual product, while others do not. This shortfall is considered
partially backlogged in this model. Some buyers wait for the actual product
during such shortages, but many do not. Therefore, partially backlogged
shortages are taken into account in this approach. In a traditional
inventory model, all parameters such as purchasing cost, shortage cost,
holding cost, etc. are predetermined. However, there will be some
variations. As a result, fuzzy factors are more accurate to deal with the
real world?s problems. This research attempts to cut down the cost in a
fuzzy environment by using quadratic demand, shortage, Weibull deterioration
rate, and variable holding cost. Costs such as ordering, shortage, and
deterioration are addressed as pentagonal fuzzy numbers that are defuzzified
using a graded mean representation approach. Finally, sensitivity analysis
was carried out to investigate the influence of cost parameters on total
inventory cost. A numerical example is used to validate the proposed model
in a real-world system.