In this paper, a deterministic inventory model with depletion rate dependent holding cost is developed. The demand rate is a power function of the on-hand inventory behind to a certain stock level, at which the demand rate becomes a constant. Shortages are allowed and partially backlogged with the function of waiting time of next replenishment. It is also proved in this model that the optimal replenishment policy not only exists but also is unique. Furthermore, it is provided a simple solution procedure for finding the maximum total profit per unit time. Numerical examples have also been given to illustrate the model and real managerial fact in inventory holding for stock dependent demand.

This study investigates optimal pricing and inventory policies for non-instantaneous deteriorating items with permissible delay in payment. The demand rate is as known, continuous and differentiable function of price while holding cost rate, interest paid rate and interest earned rate are characterized as independent fuzzy variables rather than fuzzy numbers as in previous studies. Under these general assumptions, we first formulated a fuzzy expected value model (EVM) and then some useful theoretical results have been derived to characterize the optimal solutions. An efficient algorithm is designed to determine the optimal pricing and inventory policy for the proposed model. The algorithmic procedure is demonstrated by means of numerical examples.

Determining the optimal inventory control and selling price for deteriorating items is of great significance. In this paper, a joint pricing and inventory control model for deteriorating items with price- and time-dependent demand rate and time-dependent deteriorating rate with partial backlogging is considered. The objective is to determine the optimal price, the replenishment time, and economic order quantity such that the total profit per unit time is maximized. After modeling the problem, an algorithm is proposed to solve the resulted problem. We also prove that the problem statement is concave function and the optimal solution is indeed global.

In this paper, a new multi-item inventory system is considered with random demand and random lead time including working capital and space constraints with three decision variables: order quantity, safety factor and backorder rate. The demand rate during lead time is stochastic with unknown distribution function and known mean and variance. Random constraints are transformed to crisp constraints with using the chance-constrained method. The Minimax distribution free procedure has been used to lead proposed model to the optimal solution. The shortage is allowed and the backlogging rate is dependent on the expected shortage quantity at the end of cycle. Two numerical examples are presented to illustrate the proposed solution method.

In this paper, we presents an inventory problem where initially, a retailer purchases Q(=P+R) units and after fulfilling the backlogged quantities, there is a P unit of the on-hand inventory. It continuously declines to meet the customer’s demand, which depends on the on-hand inventory level up to the time t = t1. After that the inventory level declines by constant demand up to t = t2. Thereafter, shortage occurs and it accumulates at the rate ?(T-t) till t = T when the next batch arrives. This whole cycle repeats itself after the cycle length T. The proposed model of this paper is investigated under various conditions and the implementation of the proposed model is presented through some numerical examples.

For today’s high competitive market, when immensity purchasing of inventory becomes convenient or obligatory, to discover an alternative market in order to maximize the revenue earned is a tradition. In this paper, we considered an inventory model for seasonal products with Weibull rate of deterioration having two potential markets, say, primary and alternate. To handle the inventory up to the next season will result an increase in total cost. So it is a favorable task to transfer the remaining stock to the alternate market even at a slightly differ in selling price. Solution procedure, numerical examples and sensitivity analysis for different variables are presented to illustrate the model.

This paper presents production-inventory models for deteriorating items with increasing-steady-decreasing demand pattern under the effect of inflation and time value of money. This type of demand behavior can be observed in some fashion products or seasonal products in general. Shortages are allowed with partial backlogging of demand and a two-parameter Weibull-distribution function is used for the deterioration of items in order to make the models more generalized and realistic. The models generate optimal values of initial production run time, onset of shortages, production recommencement time, and total production quantity that minimizes the total relevant costs of production and inventory for any given set of system parameters. Various possible production strategies available for items with variable demand pattern are examined to determine the optimal production strategy. The discounted cash flow approach and trust region optimization methods are used to obtain the optimal results. The Numerical examples and sensitivity analysis show that the optimal production strategy may vary with changes in system parameters.