Imperfect Reworking Process Consideration in Integrated Inventory Model under Permissible Delay in Payments

The inventory models under conditional trade credit in a supply chain system

Most researchers established their inventory lot-size models under trade credit financing by assuming that the supplier offers the retailer fully permissible delay in payments and the products received are all non-defective. However, in the real business environment, it often can be observed that the supplier offers the retailer a fully permissible delay in payments only when the order quantity is greater than or equal to the predetermined quantity Q d . In addition, an arriving order lot usually contains some defective items due to imperfect production processes or other factors. To capture this reality, the paper extends Huang (2007) economic order quantity (EOQ) model with partially permissible delay in payments to consider defective items. We formulate the proposed problem as a profit maximization EOQ model in which the replenishment cycle time is the decision variable. Then we use the arithmetic-geometric mean inequality approach to determine the optimal solution under various situations. An algorithm to obtain the optimal solution is also provided. Finally, the numerical examples and sensitivity analysis are given to illustrate the results.

The purpose of this inventory model is to investigate the retailer’s optimal replenishment policy under permissible delay in payments. In this paper, we assume that the supplier would offer the retailer partially permissible delay in payments when the order quantity is smaller than a predetermined quantity (W). The most inventory systems are usually formed without considering the effect of deterioration of items which deteriorate continuously like fresh fruits, vegetables etc. Here we consider the loss due to deterioration. In real world situation, the demand of some items varies with change of seasons and occasions. So it is more significant if the loss of deterioration is time dependent. Considering all these facts, this inventory model has been developed to make more realistic and flexible marketing policy to the retailer, also establish the result by ANOVA analysis by treating different model parameters as factors.

In this paper, an inventory policy for the production units is presented with stochastic inflation, variable demand rate, deteriorating and ameliorating items in warehouse and permissible delay in payment. Shortages, backlogging and lost sale, are allowable. Also, inflation is constantly changing due to economic, political, social and cultural issues in the real world and we assume it uniform distribution. The demand rate is depended on selling price and permissible delay in payment and increases as delay in payment increases, however, decreases as selling price increases. The objective function considers optimal pricing policy, the number of production cycles and time fraction without shortage. So, the purpose is to derive the optimal replenishment policy that minimises the net present value of total cost per unit time. The study shows that the optimal solution not only exists but also is unique. Finally, some numerical examples and sensitivity analysis on parameters are made to validate the results of the proposed inventory system.

In today’s competitive business environment, it is very common that suppliers are always willing to provide the purchaser with certain incentives. As a result, suppliers frequently offer two distinct alternatives to increase possible volume of procurement. One is that if the order quantity is greater than or equal to a predetermined quantity, the purchaser obtains a longer permissible delay in payments. The other is that if the order quantity is greater than or equal to a predetermined quantity, the purchaser gets a cash discount with a shorter permissible delay in payments. Viewed from above perspective, this study develops an inventory model with order-size dependent trade credit, in which the supplier provides not only a permissible delay but also a cash discount to the customers. Moreover, an efficient algorithm is provided to obtain the optimal solution, and then an empirical case is investigated to illustrate the theoretical results from both thesupplier and customer viewpoints. Key words: Inventory, deteriorating items, delay in payments, trade credit, cash discount.

A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments

Multivariate demand is a practical approach in today's business scenario. The entropy of a system is a measurement of the amount of disorder. Inflation is one of the major factors in inventory modeling. It makes the inventory model to realistic. Permissible delay in payment also plays an important role in a highly competitive market. It is a promotional tool to push the product, which indirectly reduces the selling price of the product. This paper developed an Entropic inventory model of imperfect product quality with multivariate demand and permissible delay in payment under the inflationary environment. The finding of this paper is that cost of entropy behaves the same as the selling price and EOQ. The numerical example is carried out using the software MATHEMATICA12.0. Sensitivity Analysis is carried out to see the behavior of different parameters.

This article wants to investigate the retailer’s optimal cycle time and optimal payment time under supplier credits including conditionally permissible delay in payments and cash discount depending on retailer payment time. That is, the retailer can obtain fully permissible delay in payments and cash discount if the payment is paid before the period of full delay payments permitted by the supplier. Otherwise, the retailer will just obtain partially permissible delay in payments within the period of partial delay payments permitted by the supplier. The supplier uses this policy to attract retailer to pay the payment as soon as possible to shorten its collection period. Mathematical models have been derived for obtaining the optimal cycle time and optimal payment time for item so that the annual total relevant cost is minimized. One theorem is developed to efficiently determine the optimal replenishment and payment policy for the retailer.

Optimal pricing and ordering policy under permissible delay in payments

In this work, we propose a stochastic inventory model under the situations that delay in imbursement is acceptable. Most of the inventory model on this topic supposed that the supplier would offer the retailer a fixed delay period and the retailer could sell the goods and accumulate revenue and earn interest with in the credit period. They also assumed that the trade credit period is independent of the order quantity. Limited investigators developed EOQ model under permissible delay in payments, where trade credit is connected with the order quantity. When the order quantity is a lesser amount of the quantity at which the delay in payment is not permitted, the payments for the items must be made immediately. Otherwise, the fixed credit period is permitted. However, all these models were completely deterministic in nature. In reality, this trade credit period cannot be fixed. If it is fixed, then retailer will not be interested to buy higher quantity than the fixed quantity at which delay in payment is permitted. To reflect this situation, we assumed that trade credit period is not static but fluctuates with the ordering quantity. The demand throughout any arrangement period follows a probability distribution. We have calculated the total variable cost for every unit of time. The optimum ordering policy of the scheme can be found with the aid of three theorems (proofs are provided). An algorithm to determine the best ordering rule with the assistance of the propositions is established and numerical instances are provided for clarification. Sensitivity investigation of all the parameters of the model is presented and deliberated. Some previously published results are special cases of the consequences gotten in this paper.

ABSTRACTFor a supply chain coordination to be effective and profitable, it requires a working mechanism among the members of a supply chain to financially entice some players to cooperate. Permissible delay in payments is one of the most commonly practised incentives by businesses to achieve this cooperation. This paper investigates a two-level (manufacturer–retailer) supply chain, with a permissible delay in payments as a decision variable. First, the paper modifies three known models of different production and shipping policies to account for delays in payments; it then compares them and highlights the production policy that performed the best with total system cost as a performance measure. A sensitivity analysis is also utilised to test and identify the limitations of the three models.

Using the convexities of total annual relevant costs to determine the optimal cycle times of inventory models for deteriorating items with permissible delay in payments

A two warehouse inventory model for deteriorating items is considered with exponential demand rate and permissible delay in payment. Shortage is not allowed and deterioration rate is constant. In the model, one warehouse is rented and the other is owned. The rented warehouse is provided with better facility for the stock than the owned warehouse, but is charged more. The objective of this model is to find the best replenishment policies for minimizing the total appropriate inventory cost. A numerical illustration and sensitivity analysis is provided.

The main purpose of this paper wants to investigate the effect of trade credit policy with limited storage capacity within the economic order quantity (EOQ) framework. Goyal is frequently cited when the inventory systems under conditions of permissible delay in payments are discussed. But Goyal assumed that the retailer’s storage capacity is unlimited. This assumption is debatable. So, we want to extend Goyal’s model to the case that the retailer’s storage capacity is limited. Then, two theorems present solution procedures to locate the optimal cycle times of the annual total relevant cost function. In essence, the inventory model discussed in this paper generalizes that of Goyal. Finally, numerical examples are given to illustrate all theorems obtained in this paper.

An integrated inventory model under conditions of order processing cost reduction and permissible delay in payments