An improved inventory model with partial backlogging, time varying deterioration and stock-dependent demand

a r t i c l e i n f o This paper expands an inventory model for deteriorating items with stock-dependent demand. This model provides time varying backlogging rate as well as time varying deterioration rate. The aim of this model is to determine the optimal cycle length of each product such that the expected total cost (holding, shortage, ordering, deterioration and opportunity cost) is minimized. Further, the necessary and sufficient conditions are provided to show the existence and uniqueness of the optimal solution. Lastly, some numerical examples, sensitivity analysis along with graphical representations are shown to illustrate the practical application of the proposed model. In recent years, many researchers/scientists have discussed on inventory models for deteriorating items. In daily life, the deterioration of items becomes a common factor. Generally, deterioration indicates the damages of the products. To highlight such type of phenomenon, Ghare and Schrader (1963) first developed a deteriorating inventory model with constant rate of decay. That model was again extended by Covert and Philip (1973) with two-parameter Weibull distribution. Dave and Patel (1981) derived an EOQ (economic order quantity) model for deteriorating items with time-proportional demand and without shortage. Sachan (1984) extended the model of Dave and Patel (1981) by allowing shortages. Later, several related articles were addressed EOQ models for deteriorating items with different increasing demands. Sarkar et al. (2013) presented an EOQ model for deteriorating items with finite production rate and time dependent increasing demand. In most of the above referred paper, the authors considered constant deterioration rate. But, in real life situation, items may deteriorate due to expiration of their maximum life time i.e., deterioration rate is proportional with time and the maximum life time can be controlled by the production system, i.e., the manufacturer can fix the maximum life time of the product. An inventory model with time dependent deterioration rate, shortage and ramp-type demand rate was discussed by Giri et al. (2003). Manna and Chaudhuri (2006) presented an EOQ model for deteriorating items for both time-dependent demand and deterioration. Loa et al. (2007) represented an integrated production-inventory model for imperfect production with Weibull distribution deterioration under inflation. An inventory model with general ramp type demand rate, Weibull deterioration rate and partial backlogging of unsatisfied demand was considered by Skouri et al. (2009). Sana (2010b) discussed an EOQ model with time varying deterioration and partial backlogging rate. In this model, the deterioration …