This paper deals with developing an inventory model for two warehouses. In today’s business era, there are various types of conditions such as discounts, bulk storage and seasonal products forcing the buyer to purchase the order more than owned warehouse capacity. To store the excess unit of purchase order, buyer arrange additional storage space called as rented warehouse. It is known that the demand of the seasonal products (as woolen garments) increases at the beginning of the season up to a certain time and then stabilizes to a constant rate for the remaining time of the season. The ramp type demand rate forces the buyer to store a higher quantity of the product at the beginning of the season. Most of the physical goods undergo decay or deterioration over time so we study deteriorating seasonal products in this paper. This two warehouse inventory model is developed with inflation and shortages. The model starts with rent warehouse, in first rent warehouse’s inventory level is depleted due to demand and deterioration. At this time own warehouse is depleted due to deterioration only. But after that the inventory level of owned warehouse is depleted due to both demand and deterioration. The shortages are considered in owned warehouse, which is partially backlogged. Numerical solution of the model is obtained to verify the optimal solution. Comprehensive sensitivity analysis has been carried out for showing the effect of variations in the parameters. The model is solved analytically by minimizing the total cost.

This study deals with an economic order quantity model to find out the optimal selling price and optimal ordering quantity for the products which deteriorates over time. The demand for the products depends on available stock level and selling price of the products. The shortages are allowed, and it is assumed that the occurring shortages are partially backlogged. Depending on the rate of backlogging two models are presented in this study. The first model assumes a constant rate of backlogging, while in second model the backlogging rate is assumed to be dependent on waiting time. Numerical example and sensitivity analysis are presented to illustrate the results of the proposed model.

This paper deals with the co-ordination of a single producer, multi distributors and multi retailers for a supply chain management to get the maximum profit at minimum investment when shortages is permitted at the retailer‘s end and they are the partially backlogged. Most previous studies on supply chain have dealt with a moderately simpler chain with a single producer and a single buyer. The requirement of the producer is directly proportional to demand of the distributor, while the demand of the distributor is dependent on retailers’ requirement. This passes on rationally to the whole supply chain. The proposed model of this paper considers deteriorating items where the deterioration rate is considered as constant.