An inventory system for varying deteriorating pharmaceutical items with price-sensitive demand and variable holding cost under partial backlogging in healthcare industries

This paper presents an inventory system for deteriorating pharmaceutical items with price-sensitive demand. Mostly existing studies of pharmaceutical inventory models consider the rate of deterioration as constant, which is not logical in the context of healthcare industries because pharmaceutical products (medicine or drugs) deteriorate significantly. Hence, the rate of deterioration is considered as time-dependent and follows a three-parameter Weibull distribution. In most of the developed models it is believed that the different costs related with inventory remain the same all the time whereas in realistic situations, manufacturing cost of medicine, the cost of maintaining the pharmaceutical products in the cold store or even the cost of keeping the patient's record increases with time. Thus, the cost of the holding of items is taken as time-dependent. Shortages are allowed in this study and are partially backlogged. The main objective of this study is to optimize the total average cost of the system by computing the optimal ordering quantity and the optimal time interval. Finally, a numerical illustration with sensitivity analysis is given to exemplify the proposed study.