Inventory policy for an item with inflation induced purchasing price, selling price and demand with immediate part payment

In this paper, an inventory policy for an item is presented with inflation and selling price dependent demand under deterministic and random planning horizons allowing and not allowing shortages. In addition, there is a provision for (i) an immediate part payment (variable) to the wholesaler, (ii) borrowing some money from money lending source for the immediate part payment, (iii) earning a discount on purchasing price and relaxation on credit period from the wholesaler against the advance payment and (iv) delay in payment for the rest allowed by wholesaler. The payment to the source is made at the end of the business period with some interest charged. Against the above conjectures, inventory models under the finite (crisp) and random planning horizons have been formulated with respect to the retailer's point of view for maximum profit. The nonlinear optimization method - Generalized Reduced Gradient (GRG) method is used to find the optimal solutions and the corresponding maximum profits for the different sets of given numerical data. Some sensitivity analyses are made and presented graphically. As particular cases, the results of the crisp models and the case without shortages are obtained from those of the stochastic model and the case with shortages respectively.