An application of parametric approach for interval differential equation in inventory model for deteriorating items with selling-price-dependent demand

Abstract

Due to the uncertainty of market economy as well as fluctuation of customer’s demand, appropriate modelling of an inventory problem is a challenging task to the researchers/OR practitioners. In order to overcome this type of challenging situation, in this article, using the parametric approach of interval a non-deterministic inventory model for deteriorating items with partially backlogged shortages and interval-valued deterioration rate has been developed. Here, the demand rate is considered to be interval-valued and dependent upon the selling price which is also interval-valued. Also, all the parameters (like ordering cost, holding cost, etc.) except the backlogging parameter have been considered as interval-valued. The corresponding problem has been formulated as a maximization problem with an interval-valued objective. Then, to solve the said problem, we have used different variants of the QPSO algorithm with interval fitness using interval ranking. Then, the computational results have been illustrated with the help of three numerical examples. Finally, the sensitivity of the solution has been analysed with the changes in the values of different parameters associated with the model and a fruitful conclusion has been drawn.