Conditions Of Permissible Delay Research Articles

The Replenishment Decision for EOQ Inventory Model under Permissible Delay in Payments

This paper discusses the economic order quantity (EOQ) under conditions of permissible delay in payments. In 1985, Goyal assumed that: (1) The unit selling price and the unit purchasing price are equal. (2) At the end of the credit period, the account is settled. The retailer starts paying for higher interest charges on the items in stock and returns money of the remaining balance immediately when the items are sold. The main purpose of this paper is to modify Goyal’s model to presume that the unit selling price and the unit purchasing price are not necessarily equal to reflect the real-life situations. Furthermore, this paper will propose that at the end of the credit period, the retailer will borrow 100% purchasing cost from the bank to pay off the account. Comparing with Goyal’s model, it is also shown that the optimal cycle times in this paper are not longer than those of Goyal’s model. Three theorems are developed to determine the optimal cycle time and the optimal order quantity. Numerical examples are given to illustrate these theorems.

A Deteriorating Inventory Model with Stock-Dependent Demand and Partial Backlogging under Conditions of Permissible Delay in Payments

In this paper, a deterministic inventory model is developed for deteriorating items with stock-dependent demand and shortages. The conditions of permissible delay in payments are also taken into consideration. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be inversely proportional to the waiting time for the next replenishment. Numerical examples are presented to illustrate the model.

On the economic order quantity under conditions of permissible delay in payments

In this note, I amend Goyal's model by considering the difference between unit price and unit cost. I then establish an easy analytical closed-form solution to the problem. The theoretical results obtained here reveal the following two managerial phenomena. (1) In certain cases, the economic replenishment interval and order quantity decreases under the permissible delay in payments, which contradicts to Goyal's conclusion. It makes economic sense for some customers to order less quantity (or shorten the replenishment time interval) and to take the benefits of the permissible delay more frequently. (2) If a supplier wants to reduce his/her large level of inventory, then he/she should charge an excessive interest rate on his/her customer's outstanding amount after the credit term expires. Consequently, his/her customers will order to buy more quantity than the classical economic order quantity. As a matter of fact, these two managerial phenomena have been demonstrated in the decision making of using credit cards. For example, most credit card companies provide card holders 25 days of grace period, and charge 18–20% interest on the amount past due (ie, the second phenomenon). However, for a well-established credit card holder, he/she will take the benefit of 25 days of grace period constantly, but will not spend over his/her limit and face an excessive finance charge (ie, the first phenomenon).

A finite time horizon inventory model with deterioration and time-value of money under the conditions of permissible delay in payments

A varying deterioration rate, time-value of money and the condition of permissible delay in payments used in conjunction with the EOQ model are the focus of discussion. The replenishment number and fraction of each cycle in which there is no shortage are both determined to minimize the present value of inventory cost over a finite planning horizon. Two special cases and numerical examples are presented to illustrate the model.

An inventory model for deteriorating items under the condition of permissible delay in payments

In economic order quantity (EOQ) models, it is often assumed that the payment of an order is made on the receipt of items by the inventory system. However, such an assumption is not quite practical in the real world. Under most market behaviors, it can be easily found that a vendor provides a credit period for buyers to stimulate demand. In this paper, a varying rate of determination and the condition of permissible delay in payments used in conjunction with the economic order quantity model are the focus of discussion. Numerical examples are presented to illustrate the proposed models.

An inventory model for deteriorating items with linear trend demand under the condition of permissible delay in payments

In this article, we consider the inventory replenishment problem with varying rate of deterioration and condition of permissible delay in payments, in which the restrictive assumption of constant demand rate is relaxed, and take a linear trend in demand into consideration. An algorithm is developed to determine the optimal replenishment cycle. We also provide a special case to illustrate the proposed model. Finally, a numerical example is presented to illustrate the optimization procedure. Sensitivity analysis of the parameter value is also carried out.

An inventory model for deteriorating items with partial backlogging and permissible delay in payments

The paper deals with an inventory model with a varying rate of deterioration and partial backlogging rate under the condition of permissible delay in payments. The existing literature on the subject generally deal with situations where the payment of an order is made on the receipt of items by the inventory system and shortages are either completely backlogged or fully lost. In this paper, a varying deterioration rate of time and the condition of permissible delay in payments used in conjunction with the economic order quantity model are the focus of discussion. In addition, the shortages are neither completely backlogged nor completely lost assuming the backlogging rate to be inversely proportional to the waiting time for the next replenishment. Numerical examples are presented to illustrate the model.

THE OPTIMAL CYCLE TIME FOR EXPONENTIALLY DETERIORATING PRODUCTS UNDER TRADE CREDIT FINANCING

ABSTRACT This paper considers the problem of determining the optimal cycle time for exponentially deteriorating products under the condition of permissible delay in payments. Theorem 1 demonstrates that the annual net profit function is concave. With the concavity, Theorem 2 shows a specific number that can be used to decide the optimal cycle time of the annual net profit function. Theorem 3 reveals the relationship between the optimal cycle time and the annual net profit function. Finally, the algorithm to find the optimal cycle time is derived out. Numerical examples are provided to illustrate the algorithm.

The convexities of the present value functions of all future cash outflows in inventory and credit

In this paper, an inventory model under the conditions of permissible delay in payments and time value of money will be considered. The main purpose is to characterize and decide the behaviour and optimal inventory cycle time of the present value function of all future cash outflows. We explore the properties of the present value functions of all future cash outflows and show that they are convex. Bounds for the optimal inventory cycle time are provided. The bounds will be useful in search procedures for determining the optimal inventory cycle time.

An inventory model with stock-dependent demand under conditions of permissible delay in payments

In the economic order quantity models, it is often assumed that the payment of an order is made on the receipt of items by the inventory system. Such assumption is usually not fulfilled in practice. The phenomenon that a supplier may offer a credit period to the retailers in order to stimulate demand is very common in the market. In this paper, the stock-dependent demand rate and conditions of permissible delay in payments used in conjunction with the economic order quantity model are the focus of discussion. We shall be concern with finding the optimal replenishment cycle under conditions of permissible delay in payments. Numerical examples are presented to illustrate the proposed models.

Economic order quantity model when delay in payments is permissible

In 1985, Goyal derived the mathematical model to get the economic order quantity under conditions of permissible delay in payments. The inventory model developed in this paper analyses the same problem under different assumptions from that of Goyal, obtaining different results.

A discrete-in-time probabilistic inventory model for deteriorating items under conditions of permissible delay in payments

An inventory model is developed for items that deteriorate continuously in time when demand is a random variable. It is assumed that the supplier allows delayed payment for settling the replenishment account. The model is continuous in units but discrete in time. A numerical example is given to illustrate the derived results

A theorem on the determination of economic order quantity under conditions of permissible delay in payments

This article discusses the economic quantity under conditions of permissible delay in payments. First, this article shows that the total annual variable cost function is convex. Second, with convexity, a theorem is developed to determine the economic order quantity. The theorem also reveals that the economic order quantity under conditions of permissible delay in payments is generally higher than the economic order quantity given by the classical economic order quantity model. Numerical examples are given to illustrate the thorem.

A theorem on the determination of economic order quantity under conditions of permissible delay in payments

This article discusses the economic quantity under conditions of permissible delay in payments. First, this article shows that the total annual variable cost function is convex. Second, with convexity, a theorem is developed to determine the economic order quantity. The theorem also reveals that the economic order quantity under conditions of permissible delay in payments is generally higher than the economic order quantity given by the classical economic order quantity model. Numerical examples are given to illustrate the thorem.

Determining optimal retail price and lot size under day-terms supplier credit

This paper deals with the problem of determining the retailer's optimal price and lot size simultaneously under the condition of permissible delay in payments. It is assumed that the customer's demand rate is represented by a constant price elasticity function which is a decreasing function of retail price. Investigation of the properties of an optimal solution allows us to develop an algorithm whose validity is illustrated using an example problem. Also, the effect of credit period on the retailer's pricing and lot sizing policy is examined through sensitivity analysis.

Retailer's pricing and lot sizing policy for exponentially deteriorating products under the condition of permissible delay in payments

This article deals with the problem of determining the retailer's optimal price and lot size simultaneously when the supplier permits delay in payments for an order of a product whose demand rate is represented by a constant price elasticity function. It is assumed that inventory is depleted not only by customer's demand but also by deterioration. Investigation of the properties of an optimal solution allows us to develop an algorithm whose validity is illustrated using an example problem.

Joint price and lot size determination under conditions of permissible delay in payments and quantity discounts for freight cost

This paper deals with the problem of determining the retailer's optimal price and lot size simultaneously under conditions of permissible delay in payments. It is assumed that the ordering cost consists of a fixed set-up cost and a freight cost, where the freight cost has a quantity discount offered due to the economies of scale. The constant price elasticity demand function is adopted, which is a decreasing function of retail price. Investigation of the properties of an optimal solution allows us to develop an algorithm whose validity is illustrated through an example problem.

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