production inventory model for deteriorating items with shortages and salvage value under reverse logistics

in this paper, a production inventory model is developed for the business enterprise which consists of three wings. the first wing is for manufacturing new items, the second wing is for collecting the returned items, while third wing is for remanufacturing the returned item. in this model we consider the fact that the storage item is deteriorated during storage periods and salvage value is incorporated to the deteriorated items. the demand, deterioration, production, remanufacturing and return rates are time dependent. the shortages are allowed and fully backlogged. the model is solved analytically by minimizing the total inventory cost. the model can be applied for optimizing the total inventory cost of deteriorating items inventory under reverse logistic for a business enterprise where demand and deterioration both is function of time.