An EOQ inventory model for deteriorating items with time-dependent deterioration rate, ramp-type demand rate and shortages

This paper presents an economic order quantity (EOQ) model for deteriorating items having time proportional deterioration rate, time dependent ramp-type demand rate and shortages. Shortages are allowed to occur in the inventory system and completely backlogged. The ramp-type demand rate is deterministic and varies with time up to a certain point and then becomes constant. The three-parameter Weibull distribution rate indicates the change in deterioration rate with respect to time and takes into account of the items which are already deteriorated while receiving into an inventory system as well as items those might start deteriorating in future. To start with, the model is developed for shortages, but is also valid for the seasonal items and newly launched high tech products like computers, laptops, mobile phones and automobiles, etc. The purpose of this study is to develop an optimal policy, so that the average total cost is minimised by optimising the procurement time point. Furthermore, the solution procedure and the numerical example are provided to illustrate the proposed model. Finally, sensitivity analysis of the various parameters on optimal solution is carried out.