In this paper, we have described an inventory model for deteriorating item with preservation technology in time dependent demand with trade credit facility and partial backlogging. We have introduced an interesting factor preservation technology to reduce the deterioration rate. Shortages are allowed with a constant backlogging rate. Also, in this paper we have introduced trade credit policy in the perspective of retailers. Our main objective is to find the cycle length, preservation technology strategies and total profit. We have solved two numerical examples to validate our proposed inventory model and presented concavity graphically by using Matlab software for each example. Finally, we have presented a sensitivity analysis by changing one parameter at a time and keep rest of the parameters are same.

Here we developed an EOQ inventory model using price dependent demand taking deterioration as a factor. Also we use preservation technology cost to control deterioration and apply trade credit policy to attraact customers to buy more products.In this work shortages are allowed and fullly backlogged during the specific time period.Our main objective in this paper is to find optimal cycle length and preservation technology strategies while maximized the total profit. We have presented a numerical example to validate the work and analysed the sensitivity of different parameters used in this work using LINGO software and also shown graphically the profit function is concave using MATLAB software.

In this paper, the two warehouse inventory problem for deteriorating items with exponentially increasing time demand rate and shortages is considered. Here existing storage is known as own warehouse OW and the other is hired on rental basis known as rented warehouse RW. The model allows different levels of item deteriorat ion in both warehouses. Here replen ishment rate is fin ite. The stock is transferred fro m RW to OW in continuous release pattern and the associated transportation cost is taken into account. Shortage in OW is allowed and excess demand is backlogged. An attempt is made to incorporate the different preservation facilities in own and rented warehouses for deteriorating items with exponentially time dependent demand. It is also assume that the preservation facility in RW is better than OW. For the general model, we give the equations for the optimal policy and cost function and we discuss some special case. A numerical examp le is given to illustrate the solution procedure of the model.