Fuzzy optimization model of two parameter Weibull deteriorating rate with quadratic demand and variable holding cost under allowable shortages

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.