Levels Of Trade Credit Policy Research Articles

An EOQ model for deteriorating item with promotional effort and credit linked demand

In the traditional supply chain models, it is observed that usually suppliers offer to the retailers a credit period and also the retailer to the customers to stimulate sales and reduce inventory. This practice of retailers increases the default risk of the percentage of customers not willing to pay back. In this paper, an inventory model has been developed under two levels of trade credit policy with customers' default risk consideration for a deteriorating item having a maximum lifetime. The supplier offers a partially permissible delay in payment per order and the retailer, in turn, provides a part of it to customers. Here, both demand and default risk are functions of the customer's trade credit period, whereas demand is also promotional effort sensitive. To mimic the changing market, the inventory costs are assumed to be imprecise. The models are illustrated numerically and some sensitivity analyses are presented. [Received: 13 January 2017; Revised: 14 September 2017; Revised: 10 June 2018; Accepted: 10 December 2018]

A two-warehouse probabilistic model with price discount on backorders under two levels of trade-credit policy

It is impossible in this competitive era to assess the demand for items in advance. So, it is essential to refer to a stochastic demand function. In this paper, a probabilistic inventory model for deteriorating items is unfolded. Here, the supplier as well as the retailer adopt the trade-credit policy for their customers with the aim of promoting the market competition. Shortages are included into the model, and when stock on hand is zero, the retailer offers a price discount to those customers who are willing to back-order their demands. We consider two different warehouses in which the first one is an Own Warehouse (OW) where the deterioration is constant over time and the other is a Rented Warehouse (RW), and where the deterioration rate follows a Weibull distribution. An algorithm is provided for finding the solutions of the formulated model.Global convexity of the cost function is established which shows that our proposed model is very helpful for any supplier or retailer to finalize the optimal ordering policy. Beside of this, we target to increase the total profit for retailer by reducing the corresponding total inventory cost. The theoretical concept is justified with the help of some numerical examples. A sensitivity analysis of the optimal solution with respect to the major parameters is also provided in order to stabilize our model. We finalize the paper through a conclusion and a preview onto possible future studies.

An integrated inventory model with variable holding cost under two levels of trade-credit policy

This paper presents an integrated vendor-buyer model for deteriorating items. We assume that the deterioration follows a constant rate with respect to time. The vendor allows a certain credit period to buyer in order to promote the market competition. Keeping in mind the competition of modern age, the stock-dependent demand rate is included in the formulated model which is a new policy to attract more customers. Shortages are allowed for the model to give the model more realistic sense. Partial backordering is offered for the interested customers, and there is a lost-sale cost during the shortage interval. The traditional parameter of holding cost is considered here as time-dependent. Henceforth, an easy solution procedure to find the optimal order quantity is presented so that the total relevant cost per unit time will be minimized. The mathematical formation is explored by numerical examples to validate the proposed model. A sensitivity analysis of the optimal solution for important parameters is also carried out to modify the result of the model.

Optimal replenishment and credit policy in supply chain inventory model under two levels of trade credit with time- and credit-sensitive demand involving default risk

Traditional supply chain inventory modes with trade credit usually only assumed that the up-stream suppliers offered the down-stream retailers a fixed credit period. However, in practice the retailers will also provide a credit period to customers to promote the market competition. In this paper, we formulate an optimal supply chain inventory model under two levels of trade credit policy with default risk consideration. Here, the demand is assumed to be credit-sensitive and increasing function of time. The major objective is to determine the retailer’s optimal credit period and cycle time such that the total profit per unit time is maximized. The existence and uniqueness of the optimal solution to the presented model are examined, and an easy method is also shown to find the optimal inventory policies of the considered problem. Finally, numerical examples and sensitive analysis are presented to illustrate the developed model and to provide some managerial insights.

Optimal ordering policy under two stage trade credits financing for deteriorating items using discounted cash flow approach

This paper develops an inventory model under two levels of trade credit policy by assuming the demand is a function of credit period offered by the retailer to the customers for deteriorating items using discounted cash flow (DCF) approach. Mathematical model is then developed to determine the optimal replenishment policy for the retailer. Next, we show that the total annual cost per unit time is a convex function of cycle time. We then provide an algorithm to find the optimal solution. We use numerical example to illustrate the algorithm. Finally, sensitivity analysis of the optimal solution with respect to the parameters of the system and some managerial implications are provided.

An EOQ inventory system of ameliorating items for price dependent demand rate under retailer partial trade credit policy

This paper studies the optimal ordering decision in the economic ordering quantity framework under two levels of trade credit policy where demand rate is a selling price dependent with ameliorating items whose value or utility or quantity increase over the time. In this paper, it is assumed that the retailer maintains a powerful decision-making right and can obtain the full trade credit offered by the supplier yet retailer just offers the partial trade credit to his/her customers. Furthermore, we consider that the items which were already sold but not yet paid for by customers would also incur interest charges or capital cost, which is not considered in the existing studies concerning retailer partial trade credit. For the objective function sufficient conditions for the existence and uniqueness of the optimal solution are provided. An efficient algorithm is designed to determine the optimal pricing and inventory policies for the retailer. Finally we obtain a lot of managerial insights from numerical examples. The results would provide valuable references for retailer in controlling the inventory of ameliorating items. The results also show that it is very necessary and realistic to consider the capital cost incurred by the items which were already sold but not yet paid for by customers under retailer partial trade credit policy.

Optimal Ordering Policy with Stock-Dependent Demand Rate Under Retailer’s Two Stages Trade Credit Financing Using Discounted Cash Flow (DCF) Approach

Many researchers have assumed one stage trade credit financing. In this study, we considered two levels of trade credit policy using Discounted Cash Flow (DCF) approach. Demand rate is considered to be stock-dependent for the first level (credit demand) and constant for second level (cash demand). Mathematical models are derived under two different circumstances i.e., case I: The permissible delay period is less than or equal to the cycle time and case II: The permissible delay period is greater than or equal to the cycle time for settling the account. An algorithm is provided to determine the optimal order quantity and annual profit. In addition, numerical examples are presented to demonstrate the solution process. Finally, sensitivity analysis of the optimal solution is discussed with respect to different parameters.

An economic lot sizing production model for deteriorating items under two level trade credit

This paper develops an economic lot-sizing production model for deteriorating items with time dependent quadratic demand and delay in payments under two levels of trade credit policy. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer in turn provides customers a permissible delay period N. Cases where M < N and are investigated. In addition, the demand rate is assumed to be time and deterioration rate dependent quadratic demand. This paper deals with the problem of determining the optimal replenishment cycle length, optimal total cost and economic order quantity for an integrated inventory system under both two-level trade credit and time dependent quadratic demand rate. Numerical examples are presented to illustrate the developed model.

A comprehensive extension of the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity

Recently, Kreng and Tan [Expert Systems with Applications 37 (2010) 5514–5522] developed an economic order quantity (EOQ) model under two levels of trade credit policy in which the supplier offers to the wholesaler a permissible delay period M, and the wholesaler also provides its retailers a permissible delay period N (with M>N). In this paper, we point out some inappropriate mathematical expressions in both interest charged and interest earned in Kreng and Tan. For generality, we then extend their model to allow the following facts: (1) the interest rate Ic charged by the supplier is not necessarily higher than the interest rate Ie earned by the wholesaler, and (2) the permissible delay period M offered by the supplier is independent of the permissible delay period N offered by the wholesaler. Furthermore, we study the necessary and sufficient conditions for finding the optimal solution, and thus establish several theoretical results to characterize the solution that provides the minimum annual total relevant cost. Finally, numerical examples are given to illustrate the theoretical results and obtain some managerial insights.

An Inventory Model with Imperfect Item under Two Levels of Trade Credit Policy

An Inventory Model with Imperfect Item under Two Levels of Trade Credit Policy

Three stage trade credit policy in a three-layer supply chain–a production-inventory model

The main purpose of this paper is to investigate the optimal replenishment lot size of supplier and optimal production rate of manufacturer under three levels of trade credit policy for supplier–manufacturer–retailer supply chain. The supplier provides a fixed credit period to settle the accounts to the manufacturer, while the manufacturer gives a fixed credit period to settle the account to the retailer and the retailer, in turn, also offers a credit period to each of its customers to settle the accounts. We assume that the supplier supplies the raw material to the manufacturer and sends back the defective raw materials to the outside supplier after completion of inspection at one lot with a sales price. The system always produces good items in the model. Also, we consider the idle times of supplier and manufacturer. Finally, numerical examples are provided to illustrate the behaviour and application of the model with graphical simulation.

Two Level of Trade Credit

Abstract In this paper, an attempt is made to characterize the preservation technology for deteriorating items to reduce the deterioration rate. This model formulates an inventory model for deteriorating items, where demand depends on selling price and credit period offered by the retailer to the customers. Here, supplier allows a fixed credit period to the retailer to settle the account and retailer offers some trade credit to his customers. The concept of credit-linked demand develops a new inventory model under two levels of trade credit policy. A solution procedure is presented to determine an optimal replenishment cycle and total cost per unit time. Results have been validated with relevant example. In a way, the proposed model provides a unique theory to reduce the deterioration rate under two levels of trade credit policy. With the help of sensitivity analysis, impact of various parameters on the cycle length and total cost has been discussed.

Replenishment decisions under two-level credit policy for flexible credit linked demand

Trade credit affects the conduct of business significantly for many reasons. For the supplier who offers trade credit, it is an effective means of price discrimination as well as efficient method to stimulate the demand of his products. Trade credit in the form of permissible delay in payments has direct influence on inventory as well as on the demand of an item. Unfortunately, the influence of credit period on demand has received very little attention in the literature, whereas in reality, length of the offered credit period has positive influence on the demand rate which may be instant or delayed. Hence, to consider the flexible influence of trade credit on the demand of an item, a discrete logistic credit linked demand function has been developed which takes care of both the instant as well as delayed impact of the credit period on the demand rate. Based on the EOQ model, this paper analyses the problem of the retailer who has to decide his trade credit period and cycle length simultaneously under the two levels of trade credit policy. An example is given to illustrate the theoretical results. Computational results provide some interesting policy implications.

A finite horizon deteriorating inventory model with two-phase pricing and time-varying demand and cost under trade credit financing using particle swarm optimization

In this paper, we consider a deterministic economic order quantity model with generalized type demand, deterioration and unit purchase cost functions under two levels of trade credit policy. Our objective is to find the optimal values of selling prices, replenishment number and replenishment scheme which maximize the total profit over the finite planning horizon. We establish the inventory system and provide structural properties of the optimal solution that facilitate computation. A particle swarm optimization with constriction factor is coded and used to solve the mixed-integer nonlinear programming problem by employing the properties derived from this paper. At the end, some numerical examples are used to illustrate the features of the proposed model.

Optimal Policy for EOQ Model with Two Level of Trade Credits in One Replenishment Cycle

In general, a supplier/retailer frequently offer trade credit to stimulate their respective sales. The main purpose of this paper is to investigate the optimal supplier/retailer’s replenishment decisions under two levels of trade credit policy within the economic order quantity (EOQ) framework. This paper deals with the supplier/retailer’s inventory replenishment problem under two levels of trade credit in one replenishment cycle. A different approach of two levels of trade credit is used, which give more freedom to the supplier/retailer in business. In addition, the easy-to-use procedure is developed to efficiently find the optimal cycle time for the retailer under minimizing annual total relevant cost. Finally, a numerical example is given to illustrate these results.

An EPQ-based inventory model for exponentially deteriorating items under retailer partial trade credit policy in supply chain

The main purpose of this paper is to investigate the optimal retailer’s replenishment decisions for deteriorating items under two levels of trade credit policy to reflect supply chain management situation within the economic production quantity (EPQ) framework. In this paper, it is assumed that the retailer maintains a powerful decision-making right and can obtain the full trade credit offered by the supplier yet retailer just offers the partial trade credit to his/her customers. Under these conditions, the retailer can obtain the most benefits. Then, we model the retailer’s inventory system as a cost minimization problem to determine the retailer’s optimal replenishment decisions under the supply chain management. Some easy-to-use theorems are developed to efficiently determine the optimal replenishment decisions for the retailer. We deduce some previously published results of other researchers as special cases. Finally, numerical examples are given to illustrate the theorems obtained in this paper. Then, as well as, we obtain a lot of managerial phenomena from numerical examples.

A note on the optimal manufacturer's policies in the EPQ model under two levels of trade credit policy

Teng and Chang [European Journal of Operational Research 195 (2009) 358–363] consider optimal manufacturer's policies in the EPQ model under two levels of trade credit policy. The main purposes of this note are twofold: (1) This note explains why equation (17) in Teng and Chang (2009) is not true in general. So, the validity of the proof of Theorems 1 and 2 in Teng and Chang (2009) is doubtful. (2) The inventory models in Teng and Chang (2009) are correct and interesting. However, processes of proofs and arguments of Theorems 1 and 2 in Teng and Chang (2009) fill shortcomings. From the viewpoint of logic, their proofs are not complete. So, the main purpose of this paper is to overcome those shortcomings and present complete proofs for Teng and Chang (2009).

The simplified solution procedures for the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity in a supply chain system

Kreng and Tan [Kreng, V. B. & Tan, S. J. (2010). The optimal replenishment decisions under two levels of trade credit policy depending on the order quantity. Expert Systems with Applications 37, 5514–5522] explore the optimal replenishment decisions under two levels of trade credit policy depending on the order quantity. Their inventory model is new and interesting. However, this paper indicates that their solution procedures can be improved further. So, the main purpose of this paper is to incorporate and simplify them for Kreng and Tan (2010).

A particle swarm optimization for solving joint pricing and lot-sizing problem with fluctuating demand and trade credit financing

Pricing is a major strategy for a retailer to obtain its maximum profit. Furthermore, under most market behaviors, one can easily find that a vendor provides a credit period (for example 30 days) for buyers to stimulate the demand, boost market share or decrease inventories of certain items. Therefore, in this paper, we establish a deterministic economic order quantity model for a retailer to determine its optimal selling price, replenishment number and replenishment schedule with fluctuating demand under two levels of trade credit policy. A particle swarm optimization is coded and used to solve the mixed-integer nonlinear programming problem by employing the properties derived in this paper. Some numerical examples are used to illustrate the features of the proposed model.

Optimal retailer replenishment decisions in the EPQ model for deteriorating items with two level of trade credit financing

This paper deals with the problem of determining the optimal retailer's replenishment decisions for deteriorating items under two levels of trade credit policy within the economic production quantity framework. We assume that the supplier would offer the retailer a delay period and the retailer also adopts the trade credit policy to stimulate his/her customer demand to develop the retailer's replenishment model. Then, we investigate the retailer's inventory system for deteriorating items as a cost minimisation problem to determine the retailer's optimal inventory policy and it has been proved that there exists a unique optimal cycle time to minimise the annual total variable cost for the retailer. In addition, two theorems are developed to efficiently determine the optimal ordering policies for the retailer. Some previously published results of other authors will be special cases of this paper. Finally, numerical examples are used to illustrate all results obtained in this paper.