The optimal ordering policy of the EOQ model under trade credit depending on the ordering quantity from the DCF approach

This paper discusses the optimum order quantity of the EOQ model that is not only dependent on the inventory policy but also on firm’ credit policy. Here, the conditions of using a discounted cash-flows (DCF) approach and trade credit depending on the quantity ordered are discussed. We consider that if the order quantity is less than at which the delay in payments is permitted, the payment for the item must be made immediately. Otherwise, the fixed trade credit period is permitted.     

Retailer’s optimal replenishment and payment policies in the EPQ model under cash discount and two-level trade credit policy

The main purpose of this paper is to investigate the retailer’s optimal cycle time and optimal payment time under the supplier’s cash discount and trade credit policy within the economic production quantity (EPQ) framework. In this paper, we assume that the retailer will provide a full trade credit to his/her good credit customers and request his/her bad credit customers pay for the items as soon as receiving them. Under this assumption, we model the retailer’s inventory system as a cost minimization problem to determine the retailer’s optimal inventory cycle time and optimal payment time under the replenishment rate is finite. Then, an algorithm is established to obtain the optimal strategy. Finally, numerical examples are given to illustrate the theoretical results and obtain some managerial phenomena.     

A Production Lot-Size Model for Perishable Items Under Two Level Trade Credit Policy for a Retailer with a Powerful Position in a Supply Chain System

This paper investigates a production lot-size inventory model for perishable items under two levels of trade credit for a retailer to reflect the supply chain management situation. We assume that the retailer maintains a powerful position and can obtain full trade credit offered by supplier yet retailer just offers the partial trade credit to customers. Under these conditions, retailer can obtain the most benefits. Then, we investigate the retailer’s inventory policy as a cost minimization problem to determine the retailer’s inventory policy. A rigorous mathematical analysis is used to prove that the annual total variable cost for the retailer is convex, that is, unique and global-optimal solution exists. Mathematical theorems are developed to efficiently determine the optimal ordering policies for the retailer. The results in this paper generalize some already published results. Finally, numerical examples are given to illustrate the theorems and obtain a lot of managerial phenomena.     

The simplified solution procedure for deteriorating items under stock-dependent demand and two-level trade credit in the supply chain management

Min et al. [1] (J. Min, Y.W. Zhou, J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Appl. Math. Model. 34 (2010) 3273–3285.) develop an inventory model for deteriorating items under stock-dependent demand and two-level trade credit. They provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could maximize the retailer’s average profit per unit time. Basically, their paper is correct and interesting. Recently, several researchers have been showing a huge interest in developing simple and easy to implement solution procedures in management science. Therefore this paper indicates that Min et al.’s solution procedure can be further improved and simplified. So, the main purpose of this paper is to present simple and easy to understand solution procedures to locate the optimal solutions of an inventory model that considers deteriorating items under stock-dependent demand and two-level trade credit.     

信用期下时滞变质品供应链库存和定价的Stackelberg均衡策略

在允许缺货和考虑资金机会成本情况下,根据时滞变质品的基本库存模型,分别构建了信用期下供应商为领导者(SL)和零售商为领导者(RL)的Stackelberg博弈模型。通过分析SL和RL下的Stackelberg博弈模型唯一均衡解,得到两个模型中均衡解的解析表达式。最后,根据数值算例分析得出:(1)在SL供应链中信用期并不总使整个供应链协调,然而在RL供应链中信用期的协调效果较好;(2)延长信用期或增加零售价格均能刺激零售商多订货;(3)在两个模型中,零售价格均随变质时刻递增,且整条供应链达到Pareto改进;(4)SL中供应商变动信用期与RL中零售商变动价格相比,SL供应链收益更高;而当信用期和价格固定,其他参数变动时,RL供应链收益更大。     

基于二层信用支付的变质物品库存模型

基于时变需求的库存问题一直是库存管理者关注的重点之一,大多数基于二层信用支付的库存模型都是假设需求率为常数.假设需求率是时间的指数函数,建立了二层信用支付条件下的变质物品库存模型,并证明了最优解是存在且唯一的,给出了确定最优补货策略的算法步骤,最后通过数值例子对主要参数进行了灵敏度分析.     

Analysis of a fuzzy economic order quantity model for deteriorating items under retailer partial trade credit financing in a supply chain

This paper investigates the economic order quantity (EOQ) — based inventory model for a retailer under two levels of trade credit to reflect the supply chain management situation in the fuzzy sense. It is assumed that the retailer maintains a powerful position and can obtain the full trade credit offered by the supplier yet the retailer just offers a partial trade credit to customers. The demand rate, holding cost, ordering cost, purchasing cost and selling price are taken as fuzzy numbers. Under these conditions, the retailer can obtain the most benefits. Study also investigates the retailer’s inventory policy for deteriorating items in a supply chain management situation as a cost minimization problem in the fuzzy sense. The annual total variable cost for the retailer in fuzzy sense is defuzzified using Graded Mean Integration Representation method. Then the present study shows that the defuzzified annual total variable cost for the retailer is convex, that is, a unique solution exists. Mathematical theorems and algorithms are developed to efficiently determine the optimal inventory policy for the retailer. Numerical examples are given to illustrate the theorems and the algorithms. Finally, the results in this paper generalize some already published results in the crisp sense.     

二层信用策略下部分延期付款的库存模型

当前二层信用期相关文献考虑的都是零售商提供给其顾客相同的信用期,但现实中零售商往往会根据物品的种类不同提供给顾客不同的信用期.为研究此问题,建立了优化供货周期使零售商平均相关成本最小的库存模型,证明了最优供货周期的存在性,并给出实例加以说明.     

The simplified solution algorithm for an integrated supplier-buyer inventory model with two-part trade credit in a supply chain system

Ho et al. [Ho, C.H., Ouyang, L.Y., Su, C.H., 2008. Optimal pricing, shipment and payment policy for an integrated supplier-buyer inventory model with two-part trade credit, European Journal of Operational Research 187, 496-510] discussed the integrated inventory model with two-part trade credit and presented an algorithm to solve it. Basically, Ho et al.’s inventory model is correct and interesting. However, this paper indicates that the solution algorithm described in Ho et al. (2008) can be simplified further. So, this paper can not only derive the optimally closed-form formulations for the optimal numbers of shipments but also develop different algorithms to improve those in Ho et al. (2008). Numerical examples illustrate that the algorithm to locate the optimal solution is rather accurate and rapid.     

基于信用支付和现金折扣的变质物品库存模型

本文在供应商提供给零售商定期信用支付和现金折扣情况下,研究了零售商的变质物品最优库存问题。基于信用支付和现金折扣的两种支付条件下,分四种情况建立库存模型,并给出了寻求变质物品最优订购周期和最优付款时间的有效算法。最后,给出算例以及最优解,以说明本模型及求解过程。     

Two-phase pricing and inventory management for deteriorating and fashion goods under trade credit

This study models a finite horizon inventory problem for deteriorating and fashion goods under trade credit and partial backlogging conditions. Demand may vary with price or time. The supplier can extend credit to the retailer. As a result, the retailer does not have to pay for goods immediately upon acquiring them, and can instead earn interest on the retail price of the goods between the time they are sold and the end of the credit period. The proposed model considers two-phase pricing and inventory decisions. In other words, it determines both the optimal prices and the lengths of the in-stock and stock-out period. This paper is the first to consider different price decisions for in-stock and stock-out periods under trade credit. We develop an algorithm to determine the optimal pricing and replenishment strategy while still maximizing the total profit. Further, this study shows that the proposed two-phase pricing strategy is superior to a one-phase pricing strategy in terms of profit maximization. Computational analysis illustrates the solution procedures and the impacts of the related parameters on decisions and profits. The results of this study can serve as references for business managers or administrators.     

Optimal retailer's ordering policies in the EOQ model under trade credit financing

The main purpose of this note is to modify the assumption of the trade credit policy in previously published results to reflect the real-life situations. All previously published models implicitly assumed that the supplier would offer the retailer a delay period, but the retailer would not offer the trade credit period to his/her customer. In most business transactions, this assumption is debatable. In this note, we assume that the retailer also adopts the trade credit policy to stimulate his/her customer demand to develop the retailer's replenishment model. Furthermore, we assume that the retailer's trade credit period offered by supplier M is not shorter than the customer's trade credit period offered by retailer N(M?N). Under these conditions, we model the retailer's inventory system as a cost minimization problem to determine the retailer's optimal ordering policies. Then a theorem is developed to determine efficiently the optimal ordering policies for the retailer. We deduce some previously published results of other researchers as special cases. Finally, numerical examples are given to illustrate the theorem obtained in this note.     

Integrated inventory problem under trade credit in fuzzy random environment

This paper is concerned with an integrated inventory problem under trade credit where both the demand rate and deteriorating rate are assumed to be uncertain and characterized as fuzzy random variables with known distributions. The objective of this paper is to determine the optimal inventory policy by optimizing simultaneously the replenishment cycle length and trade credit period. At first, three decision criteria are given: (1) expected value criterion, (2) chance-constrained criterion and (3) chance maximization criterion. Then, after building the fuzzy random models based on the above decision criterion, a hybrid intelligent algorithm by integrating fuzzy random simulation and genetic algorithm is employed to deal with these models. At the end, three numerical examples are given to illustrate the benefits of the models and show the effectiveness of the algorithms.     

随机需求下供应链商业信用契约协调

研究一个供应商和一个零售商构成的两级供应链面对随机需求时的商业信用契约协调问题。通过分析商业信用对供应商与零售商各自目标利润及供应链的总利润的影响,建立了商业信用契约协调模型,推导了最优信用期和最优订货量,指出通过信用策略可以使双方实现对利润的合理分配与协调。最后通过数值算例说明了所得结论。     

供应链金融创新中下侧风险规避银行的贷款额度分析

针对供应链金融创新中季节性存货质押融资业务的重要风险控制指标--贷款额度展开研究,首先借鉴贸易融资中`` 主体＋债项"的风险评估思路,考虑委托监管模式的物流特征及成本收益结构,分析了借款企业的现金流状况及其性质;进而,将已有相关研究关于银行风险中性的假设拓展到银行下侧风险规避,分析了季节性存货质押融资中符合银行风险容忍水平的最高贷款额度.研究表明：下侧风险限制能够有效控制季节性存货质押融资业务的风险,使贷款符合银行设置的风险容忍水平.     

Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing

In a supplier-retailer-buyer supply chain, the supplier frequently offers the retailer a trade credit of S periods, and the retailer in turn provides a trade credit of R periods to her/his buyer to stimulate sales and reduce inventory. From the seller’s perspective, granting trade credit increases sales and revenue but also increases opportunity cost (i.e., the capital opportunity loss during credit period) and default risk (i.e., the percentage that the buyer will not be able to pay off her/his debt obligations). Hence, how to determine credit period is increasingly recognized as an important strategy to increase seller’s profitability. Also, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. However, only a few researchers take the expiration date of a deteriorating item into consideration. This paper proposes an economic order quantity model for the retailer where: (a) the supplier provides an up-stream trade credit and the retailer also offers a down-stream trade credit, (b) the retailer’s down-stream trade credit to the buyer not only increases sales and revenue but also opportunity cost and default risk, and (c) deteriorating items not only deteriorate continuously but also have their expiration dates. We then show that the retailer’s optimal credit period and cycle time not only exist but also are unique. Furthermore, we discuss several special cases including for non-deteriorating items. Finally, we run some numerical examples to illustrate the problem and provide managerial insights.     

The optimal pricing and ordering policy for an integrated inventory model when trade credit linked to order quantity

In traditional inventory models, it is implicitly assumed that the buyer must pay for the purchased items as soon as they have been received. However, in many practical situations, the vendor is willing to provide the buyer with a permissible delay period when the buyer’s order quantity exceeds a given threshold. Therefore, to incorporate the concept of vendor–buyer integration and order-size-dependent trade credit, we present a stylized model to determine the optimal strategy for an integrated vendor–buyer inventory system under the condition of trade credit linked to the order quantity, where the demand rate is considered to be a decreasing function of the retail price. By analyzing the total channel profit function, we developed some useful results to characterize the optimal solution and provide an iterative algorithm to find the retail price, buyer’s order quantity, and the numbers of shipment per production run from the vendor to the buyer. Numerical examples and sensitivity analysis are given to illustrate the theoretical results, and some managerial insights are also obtained.     

关于信用期内含缺陷产品EOQ模型

考虑到在实际中供应链上游供应商提供给下游零售商的信用支付期通常为一个订货周期,建立了缺陷率服从一定分布的缺陷产品在信用支付策略下的最优订货批量模型.模型中允许缺货发生并且以最大期望利润为目标函数,通过分析得到模型最优解.最后给出仿真实验,并且分析了模型参数变化对最优解的影响.     

An extension of inventory models incorporating financing agreements with both suppliers and customers

In a recent article, Min et al. [J. Min, Y.W. Zhou, J. Zhao, An inventory model for deteriorating items under stock-dependent demand and two-level trade credit, Appl. Math. Model. 34 (2010) 3273–3285] presented an inventory model for a retailer with inventory-level-dependent demand as well as upstream and downstream financing agreements. The purpose of this note is twofold: (1) to relax the boundary condition imposed in their model that ensures the entire stock is depleted at the end of each order cycle and (2) to resolve the potential unbounded solution resulting from a linear demand function by constraining the maximum inventory level. The effects of these changes on the retailer’s profitability are examined and some practical generalizations of the model are presented.     

An uncooperative order model for items with trade credit,inventory-dependent demand and limited displayed-shelf space

This paper considers a two-echelon supply chain where a supplier sells a single product through a retailer, who faces an inventory-dependent demand. The supplier hopes to incentive the retailer to order more items by offering trade credit. The retailer places the ordered items on the display shelf (DS) with limited space and stocks the remaining items (if any) that exceed the shelf capacity in his/her backroom/warehouse (BW). From the supplier’s perspective, we focus mainly on under which conditions the supplier should offer trade credit and how he/she should design such trade credit policy and corresponding ordering policy to obtain much more benefits. From the retailer’s perspective, we discuss whether the retailer needs BW and exactly how many items need to be stocked in BW when the supplier offers trade credit. We formulate a “supplier-Stackelberg” game model, from which we obtain the conditions under which the presented simple trade credit policy not only increases the overall chain profit but also each member’s profit. We also show that the trade credit policy is always more beneficial to the retailer than to the supplier if it is offered.