In this paper, an inventory model is studied with ramp type demand rate where holding cost is expressed as linearly increasing function of time. The study includes some features that are likely to be associated with certain types of inventory, like inventory of seasonal fruits and vegetables, newly launched fashion items, etc. When stock on hand is zero, the inventory manager offers a price discount to customers who are willing to backorder their demand. The optimum ordering policy and the optimum discount offered for each backorder are determined by minimizing the total cost in a replenishment interval.

This paper considers the economic order quantity (EOQ) model over a finite horizon, in which demand rate follows a two-parameter Weibull time-dependent, shortages are allowed and completely backlogged. Mathematical formulations are derived under two different circumstances i.e. case I: The permissible delay is less than or equal time to finish positive inventory for settling the account, and case II: The permissible delay period is greater than time to finish positive inventory for settling the account. Based on the optimal solutions some important results are derived and numerical examples are provided to validate the proposed model. Finally, sensitivity analysis is provided to analyze the effect of changes with the variation in one parameter at a time on the optimal solution.

This paper derives a deterministic inventory model for deteriorating items with inventory dependent demand rate. This study develops an order level inventory model with single warehouse where shortages are allowed and it is completely backlogged. The planning horizon is finite. This paper shows that there exists a unique optimal cycle time to minimize the total inventory cost per cycle. Truncated Taylor’s series expansion is used for finding closed form optimal cycle time, optimal time to finish positive inventory and optimal total inventory cost per cycle. The numerical example is given to validate the proposed model. The sensitivity analysis of the solution with the changes of the values of parameters associated with the model has also been discussed.

This paper presents an order level inventory system with time
dependent Weibull deterioration and ramp type demand rate where
production and demand are time dependent. The proposed model of this
paper considers economic order quantity under two different cases. The
implementation of the proposed model is illustrated using some
numerical examples. Sensitivity analysis is performed to show the
effect of changes in the parameters on the optimum solution.