In this article, a probabilistic inventory model is developed for items that deteriorate at a constant rate and the demand is a random variable. It is also assumed that the supplier will offer a delay period to the retailer for payment and the retailer also extends the trade credit policy to his\her customer. Under these assumptions, we have constructed two separate models: one for discrete cycle time and another for continuous cycle time. To determine the global optimal ordering policies for both the models, we have developed and proved three separate theorems. Some already published results (for probabilistic inventory models) are special cases of our article. Finally, numerical examples are presented to demonstrate the developed models and the solution procedure.

In this work, we propose a stochastic inventory model under the situations that delay in imbursement is acceptable. Most of the inventory model on this topic supposed that the supplier would offer the retailer a fixed delay period and the retailer could sell the goods and accumulate revenue and earn interest with in the credit period. They also assumed that the trade credit period is independent of the order quantity. Limited investigators developed EOQ model under permissible delay in payments, where trade credit is connected with the order quantity. When the order quantity is a lesser amount of the quantity at which the delay in payment is not permitted, the payments for the items must be made immediately. Otherwise, the fixed credit period is permitted. However, all these models were completely deterministic in nature. In reality, this trade credit period cannot be fixed. If it is fixed, then retailer will not be interested to buy higher quantity than the fixed quantity at which delay in payment is permitted. To reflect this situation, we assumed that trade credit period is not static but fluctuates with the ordering quantity. The demand throughout any arrangement period follows a probability distribution. We have calculated the total variable cost for every unit of time. The optimum ordering policy of the scheme can be found with the aid of three theorems (proofs are provided). An algorithm to determine the best ordering rule with the assistance of the propositions is established and numerical instances are provided for clarification. Sensitivity investigation of all the parameters of the model is presented and deliberated. Some previously published results are special cases of the consequences gotten in this paper.

This paper develops an economic order quantity model for deteriorating products that assumes price and stock depending demand. Shortages are permitted with partial backlogging. The proposed model focused on two things. The first one is the consideration of the fact that the deterioration rate can be reduced by the use of preservation technology investment and the second one is using the assumption that the unit purchase cost has a hostile bond with the order size to maximize the total profit. The idea of salvage/recover cost is considered and merged in this model. The solution technique of proposed optimization model is exemplified by a couple of numerical illustrations. Concavity of the average profit function is shown by plotting graphs. Sensitivity investigation is done to study the effect of changing the value of all parameters in the projected maximization model.