A deterministic inventory model with two levels of storage (own warehouse and rented warehouse) with non-instantaneous deteriorating items is studied. The supplier offers the retailer a trade credit period to settle the amount. Different scenarios based on the deterioration and the trade credit period have been considered. In this article, we have framed two models considering single warehouse (Model-I) and two warehouses (Model-II) for non-instantaneous deteriorating items. The objective of this work is to minimize the total inventory cost and to find the optimal length of replenishment and the optimal order quantity. Mathematical theorems have been developed to determine the existence and the uniqueness of the optimal solution. Computational algorithms for the two different models are designed to find the optimal order quantity and the optimal cycle time. Comparison between the optimal solutions for the two models is also given. Numerical illustrations and managerial insights obtained demonstrate the application and the performance of the proposed theory.

This article discusses an economic order quantity model for non-instantaneous deteriorating items in which the demand is assumed to be a linear function of time over an infinite planning horizon. In addition, the salvage value associated with the deteriorated units is also considered. The shortages are allowed and partially backlogged. A mathematical model is framed to obtain the replenishment policy which aids the retailer to minimize the total inventory cost. The objective of this work is to minimize the total inventory cost and to find the optimal length of replenishment and the optimal order quantity. The theory developed in this article is illustrated using numerical examples. A computational algorithm is designed to find the optimal solution. Sensitivity analysis is carried out to study the changes in the effect on the optimal solutions and some managerial insights are obtained.

This article discusses a vendor-buyer inventory model with permissible delay in payments and controllable lead time in which the order quantity, lead time and the number of shipments delivered from vendor to the buyer in a production cycle are decision variables. Here the production process is imperfect. The lead time is crashed and the crashing cost is an exponential function of lead time. Based on the lead time demand, two models are developed, that is, lead time demand follows a normal distribution in the first model and then distribution free approach is considered in the second model to minimize the joint total expected cost per unit time. Efficient computational algorithm is designed to find the optimal solution. Numerical examples are provided to illustrate the results obtained. Sensitivity analysis is carried out to study the changes in the effect on optimal solution and some managerial phenomena are obtained through sensitivity analysis.