This paper deals with the development of an inventory model for time varying demand and constant demand; and time dependent holding cost and constant holding cost for case 1 and case 2 respectively. Previous models incorporating that the holding cost is constant for the entire inventory cycle. Mathematical model has been developed for determining the optimal order quantity, the optimal cycle time and optimal total inventory cost for both cases. Differential calculus is used for finding optimal solution. Numerical examples are given for both cases to validate the proposed model. Sensitivity analysis is carried out to analyze the effect of changes in the optimal solution with respect to change in various parameters.

Deterioration, a continuous process of all items, may be low or high for different items. This paper develops an inventory model for stock-dependent demand and time varying holding cost under different trade credits, considering four different situations. The second order approximations are used for exponential terms. Optimal solutions are obtained using Mathematica 9.0 software. Numerical examples and sensitivity analysis are provided to illustrate the proposed model.

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This study presents an inventory model to determine an optimal ordering policy for non-deteriorating items and timedependent demand rate with delay in payments permitted by the supplier under inflation and time discounting. Mathematical models have been derived under two different situations, i.e. Case I: The permissible delay period is less than or equal to replenishment cycle period for settling the account and Case II: The permissible delay period is greater than replenishment cycle period for settling the account. This study determines the optimal cycle period and optimal payment period for item so that the annual total relevant cost is minimized. An algorithm is given to obtain optimal solution. The main purpose of this paper is to investigate the optimal (minimum) total present value of the costs over the time horizon H for both cases (i.e. case I and II). An algorithm is used to obtain the minimum total present value of the costs over the time horizon H. Finally, a numerical example and sensitivity analysis demonstrate the applicability of the proposed model and managerial insights.