Down-stream Trade Credit Research Articles

Optimal inventory policies for time varying deteriorating items with dynamic demand under upstream and downstream trade credit by discounted cash-flow analysis

Optimal inventory policies for time varying deteriorating items with dynamic demand under upstream and downstream trade credit by discounted cash-flow analysis

Dual channel supply chain inventory policies for controllable deteriorating items having dynamic demand under trade credit policy with default risk

Presently in the commercial environment, because of the high level of market globalization and rapid increase in industrialization, supply chain synchronization is playing an increasingly significant role in the proper management of the whole system including several factors at the same time. In real business world, both manufacturer and retailer accept credit to make their business position strong, as credit not only strengthens their business relationships but also increases the scale of their profits. The long period of credit may increase the demand ratebut simultaneously it can also increase the credit risk. We investigate a two-layer supply chain model under dynamic demand with a manufacturer and a retailer maintaining decaying items with controllable deterioration rates under two levels of trade credit policies. For the time of trade credit granted to the retailer, the manufacturer bears opportunity costs. To promote sales and optimize sales volume, both supply chain participants give trade credit periods to downstream members and due to the credit period, both of them are facing default risk. Both members work together to invest in preservation technologies to abate the rate of degradation. The proposed models are developed for both the centralized and the decentralized scenarios. A closed form model having profit maximization problem is developed for both the centralized and the decentralized scenarios. The focus of this study is to obtain the optimal selling price, replenishment cycle time, preservation technology cost, upstream and downstream trade credit period to optimize supply chain profit. The paper’s novelty lies in introducing two level trade credit with default risk considering decaying items with controllable deterioration and price and credit sensitive customer’s demand in a dual channel supply chain inventory policy. It is found that joint supply chain model can be able to enhance the total profit of the whole supply chain. Lastly, sensitivity analysis highlights the influence of major model parameters using numerical examples.

Decaying items inventory models with partial linked-to-order upstream trade credit and downstream full trade credit

In practice, any member of supply chain may offer full or partial trade credit contract to his downstream level. Full trade credit is the case that the latter is allowed to defer whole payment to the end of credit period. In partial trade credit, however, the downstream supply chain member must pay for a proportion of the purchased goods at first, and can delay paying for the rest until the end of credit period. This paper considers a two-level trade credit, where the supplier offers order-quantity-dependent partial trade credit to a retailer, who suggests full trade credit to his customers. An economic order quantity (EOQ) inventory model of a deteriorating item with expiration dates is formulated here. Theoretical results are developed to obtain the optimal solutions to the problem. Numerical examples and sensitivity analysis are performed to justify the proposed models and theoretical results and managerial insights are provided.

Controllable carbon emissions in an inventory model for perishable items under trade credit policy for credit-risk customers

The incorporation of credit risk and environmental regulations has been attended to considerably in the literature of inventory models; however, papers rarely developed a model considering both of these issues concurrently. Thus, jointly incorporate these two challenges makes sense to address the mentioned gap in the literature and outline insights for future works in practice. This study develops an inventory model for deteriorating items which (a) items deteriorate continuously and have their specific expiration dates; (b) carbon is emitted due to ordering and warehousing operations when a cap-and-tax policy is regulated and emissions can be controlled by investing in green technology; (c) two levels of trade credit is offered when the customer must pay a prepayment. The purpose of this study is to compare the retailer's total profit for different values of upstream and downstream trade credit periods to achieve efficient pricing and replenishment decisions. An algorithm is developed to find the optimal value for the investment in green technology. Numerical experiments and sensitivity analysis are elaborated to validate the mathematical formulation. Finally, findings are summarized and managerial implications are addressed.

Optimal credit period and ordering policy with credit-dependent demand under two-level trade credit

This paper investigates the retailer's trade credit strategy and ordering policy in a two-echelon supply chain consisting of one supplier and one retailer. The retailer accepts upstream trade credit from the supplier while offers downstream trade credit to consumers, and the relationship between the upstream and downstream credit period is uncertain. The market demand depends on both the downstream trade credit and the random initial demand rate, and granting downstream trade credit increases not only sales but also default risk. This paper tries to find the retailer's optimal decisions on credit period, replenishment cycle, and order quantity so as to maximize the retailer's profit. It is shown that there exists a unique decision for the retailer. Some numerical examples are given to verify our results and provide more managerial insights. It is found that the retailer is more willing to provide trade credit under higher marginal profit, and that providing downstream trade credit is beneficial to both the retailer and supplier.

Retailer’s ordering policy for demand depending on the expiration date with limited storage capacity under supplier credits linked to order quantity and discounted cash flow

ABSTRACT Many products deteriorate with time and have a maximum lifetime. An expiration date will be marked. And then the product will no longer be sold after the expiration date. Thereafter, the demand rate for the deteriorated item will near zero as its expiration date is due. Thus, to consider the demand rate incorporates with the expiration date is practical. Furthermore, as the storage capacity is limited, the retailer needs to rent a warehouse to store the excess quantities than can be stored. Consequently, to consider a two-warehouse inventory model is necessary. Nowadays, the supplier often provides a cash discount or permissible delay in payments to its retailers, if the order quantity attains a certain amount. Likewise, the retailer also provides a downstream trade credit period to his customers. In addition, the cost is usually affected by the present value of time. For these reasons considered, a supplier-retailer-customer chain model here is established. The main task of this research is to find the optimal replenishment cycle and order quantity to keep the present value of the total relevant cost per unit time as minimum as possible. Numerical examples are performed for illustration and sensitivity analysis on the expiration date is conducted.

An Inventory Model for Ramp-Type Demand with Two-Level Trade Credit Financing Linked to Order Quantity

In the traditional economic order quantity (EOQ) model, it is assumed that the demand rate is constant. Thereafter, many researchers developed inventory model with time-varying demand to reflect sales in different phases of product life cycle in the market. However, in practice, especially for fashionable and high-tech product, the demand rate during the growth stages of its life cycle increases significantly with linear or exponential in the growth stage and then gradually stabilizes, and remains near constant in the maturity stage. It can be taken a ramp-type demand rate into account. Furthermore, in today’s supply chain, a supplier usually offers a permissible delay in payment to retailers to encourage them to buy more products, and a retailer in turn provides a downstream trade-credit period to its customers. Therefore, this paper focus on 1) ramp-type demand rate and 2) the upstream and downstream trade credit financing linked to order quantity for retailer is considered. The objective is to find the optimal replenishment cycle and order quantity to keep the total relevant cost per unit time as minimum as possible. The study shows that in each case discussed, the optimal solution not only exists but also is unique. Numerical examples are provided to illustrate the proposed model. Finally, some relevant managerial insights based on the results are characterized.

Optimal Ordering Policy for Deteriorating Items with Limited Storage Capacity under Two-Level Trade Credit Linked to Order Quantity by a Discounted Cash-Flow Analysis

Nowadays, the supplier often provides cash discount or permissible delay in payments to its retailers, if the order quantity attains a certain amount. Likewise, the retailer also provides a downstream trade credit period to his customers. In practice, as the supplier provides price discounts for bulk purchases, the retailer may purchase more goods than can be stored in its owned warehouse and store the excess quantities in a rented warehouse. Thus, a two-warehouse inventory model is needed to be considered. Further, the cost is usually affected by the present value of time and products deteriorate as time increases. Therefore, this paper develops a supplier-retailer-customer chain inventory model in which 1) two-level trade credit linked to order quantity is considered; 2) storage capacity is limited; 3) the effect of inflation and time value of money by a discounted cash-flow analysis is taken into account. The demand rate is linearly increasing with time and the deterioration rate is constant. Based on the viewpoint of cost minimization, the objective is to find the optimal replenishment cycle and order quantity to keep the present value of the total relevant cost per unit time as minimum as possible. The research shows that in each case discussed, the optimal solution for each case exists uniquely. Finally, numerical examples are provided for illustration and some managerial insights based on the numerical results are also presented.

Joint pricing and production decisions for new products with learning curve effects under upstream and downstream trade credits

Today's leading companies generate a substantial portion of their sales from new products. For example, Apple Inc. generates almost 60% of its sales revenue from products launched in the past four years. Hence, the importance of new products cannot be overestimated. Pricing strategy is particularly important during the introductory stage of a new product, when the learning curve effect is most pronounced. Although the learning curve effect reduces production cost significantly during the introduction period of a new product, most researchers have assumed that the production cost remains constant throughout a product's lifecycle. In our opinion, failing to consider this learning curve phenomenon may lead to biased solutions. Furthermore, suppliers often offer manufacturers a short-term interest-free loan (i.e., trade credit) to stimulate sales, while manufacturers adjust price to influence consumer purchasing decisions. However, most researchers have not considered the combined effects of pricing strategy on demand, learning curve effect on production cost, and trade credit influence on lot size. Therefore, we propose an inventory model to determine optimal lot-sizing and pricing strategies with both upstream and downstream trade credit, manufacturer's production cost which follows a learning curve effect, and production quantity influenced by both selling price and trade credit. Then we derive the conditions of the optimal solution. Numerical examples and sensitivity analysis are performed to examine results and provide managerial insights. These results show that the learning curve effect significantly lowers selling price, while tremendously increasing both profit and demand.

Optimal ordering policy for deteriorating items under down-stream trade credit dependent quadratic demand with full up-stream trade credit and partial down-stream trade credit

Nowadays, the use of the offer of delay payment is a very impressive tool to boost the market demand by attracting more customers. In this paper, we propose an inventory model, in which a retailer receives a permissible delay on the entire purchase expanse from the manufacturer (i.e., an up-stream full trade credit). In comparison, the retailer asks customers to pay some percent of purchasing cost at the time of receiving the product to reduce default risk (i.e., a down-stream partial trade credit). We consider the product with maximum fixed-life time deterioration and to reduce deterioration of the product, seller spends capital on preservation technology to preserve the item. Here, down-stream trade credit dependent quadratic demand is debated which is suitable for the products whose demand increases initially and afterward it starts to decrease. Industries like fashion and electronics most probably deals with this type of demand. The objective is to minimise the total relevant cost of retailer with respect to cycle time, down-stream trade credit and investment for preservation technology. The model is supported with numerical examples. Sensitivity analysis is done to derive insights for decision-maker. Graphical results, in three dimensions, are exhibited with supervisory decisions.

Optimal ordering policy for deteriorating items under down-stream trade credit dependent quadratic demand with full up-stream trade credit and partial down-stream trade credit

Optimal ordering policy for deteriorating items under down-stream trade credit dependent quadratic demand with full up-stream trade credit and partial down-stream trade credit

Economic order quantity models with upstream partial trade credit and downstream full trade credit

Traditional EOQ models are assumed that it is upstream full trade credit and down steam partial trade credit. In most business transactions, this assumption is debatable. In this note, this paper establishes a new EOQ model under two levels of trade credit, in which the supplier offers to the retailer a partial trade credit period for payments even if the order quantity is less than W, and simultaneously the retailer in turn provides a full trade credit period to its customers. Furthermore, we assume that the trade credit period (N) offered by the retailer to the customers is less than or equal to the trade credit period (M) offered by the supplier. And the retailer starts earning revenue from time N to time (T + N), not from time 0 to time T. Six theorems are developed to determine retailer’s optimal ordering policies and numerical examples are given to illustrate these theorems.

Optimal inventory policies for deteriorating items with trapezoidal-type demand patterns and maximum lifetimes under upstream and downstream trade credits

In general, the demand rate moving through a product life cycle can be reasonably depicted by a trapezoidal-type pattern: it initially increases during the introduction and growth phases, then remains reasonably constant in the maturity phase, and finally decreases in the decline phase. It is evident that perishable products deteriorate continuously over time and can not be sold after its maximum lifetime. Thus, the deterioration rate of a product is increasing with time and closely related to its maximum lifetime. Furthermore, it has been hard to obtain loans from banks since the global financial meltdown in 2008. Hence, over 80% of firms in the United Kingdom and the United States sell their products on various short-term, interest-free loans (i.e., trade credit) to customers. To incorporate those important facts, we develop an inventory model by (1) assuming the demand pattern is trapezoidal, (2) extending the deterioration rate to 100% as its maximum lifetime is approaching, (3) using discounted cash-flow analysis to calculate all relevant costs considering the effects of upstream and downstream trade credits, and (4) including the costly purchase cost into the total cost, which is omitted in previous studies. Then, the order quantity that maximizes the present value of the profit is uniquely determined. Finally, through numerical examples, managerial insights are provided.

Two layers green supply chain imperfect production inventory model under bi-level credit period

This article focuses on an integrated production inventory model with rework of the imperfect units and stock dependent demands of the customer from several retailers. There is an opportunity to build a model to measure the amount of carbon emissions during the time of production and the corresponding rate of carbon emission parameters are random which follows Beta distribution. Here, the rate of imperfectness is assumed to be a function of time and production rate. In this paper, a manufacturer–retailer–customer chain system is developed in which the retailer gets an upstream trade credit period from the manufacturer and retailers offer a downstream trade credit period to customers to stimulate demand as well as sales and reduce inventory. The model has been developed as a profit maximization problem with respect to the manufacturer and retailers. Finally, several numerical examples and sensitivity analysis are provided to illustrate the model.

Imperfect economic production quantity model with upstream trade credit periods linked to raw material order quantity and downstream trade credit periods

In this study, we propose an imperfect economic production quantity model with both upstream and downstream trade credits. Trade credit is offered to the manufacturer by the supplier if the order quantity of raw material exceeds a predetermined value. Moreover, customers are permitted to pay the purchasing cost to the manufacturer after receiving the products. However, defective items are sometimes produced during the production process. Therefore, another assumption is made that defective items are produced during the production period and they all become perfect after a reworking process. In order to solve the model in several different cases, we show that all of the proposed costs functions are convex and optimal solutions are obtained mathematically for the production lot size and backlogged shortage. Furthermore, to discover the effects of a two-level trade credit period and the reworking of defective items, illustrative examples are provided as well as a sensitivity analysis to demonstrate the results of the model.

Optimal strategy for a manufacturer-retailer inventory system with defective items under retailer partial trade credit policy

In order to reduce default-risk, a retailer in practice frequently requests its credit risk customers to pay a part of the purchase amount as collateral deposit at the time of ordering, and then offers a trade credit for the outstanding balance (partial down-stream trade credit). In contrast, the retailer usually receives a full trade credit on the purchase amount from the manufacturer (up-stream full trade credit). The present study develops a single manufacturer single retailer integrated supply chain model under two-level trade credit in which the retailer receives a full trade credit from the manufacturer but offers a partial trade credit to its customers. The manufacturer delivers the retailer’s order quantity in a number of equal shipments. An arriving lot from the manufacturer contains a certain proportion of defective items. The market demand rate is sensitive to the length of the customer’s trade credit period which is offered by the retailer. The present study aims to determine the optimal replenishment cycle time, the order quantity and the number of lots from the manufacturer to the retailer such that the total profit of the integrated supply chain system is maximized. Solution algorithms are designed to find the optimal solution of the model. The theoretical results developed in the paper are illustrated through a numerical example. Sensitivity analysis of some important parameters is presented to study their influence on the optimal solution.

Optimal ordering policy with trade credit and variable deterioration for fixed lifetime products

In a supply chain, the supplier frequently offers the retailer a trade credit period, and the retailer in turn provides a trade credit period to her/his customer to stimulate sales and reduce stock inventory. 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) deteriorating items not only deteriorate continuously but also have their expiration dates. We then show that the retailer's optimal cycle time not only exists but also is 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.

Optimal ordering policy for an inventory system with linearly increasing demand and allowable shortages under two levels trade credit financing

To reduce default risk, a retailer may offer a partial down-stream trade credit to its credit-risk customers who should pay a portion of their purchasing costs at the time of receiving items as a collateral deposit, and then receive a permissible trade credit on the rest of the outstanding amount. To reflect this fact, we consider an inventory model with linear time dependent demand under two levels of trade credit and allowable shortages. Depending on the relationship between up-stream and down-stream trade credit periods, several cases are considered and the necessary and sufficient conditions are derived for finding the optimal solution. We also present a simple algorithm to determine the optimal solution. Numerical examples are provided to illustrate the solution procedure. Sensitivity analysis of important model-parameters is performed and some relevant managerial implications are discussed.

Retailer’s optimal credit period and cycle time in a supply chain for deteriorating items with up-stream and down-stream trade credits

In practice, the supplier often offers the retailers a trade credit period $$M$$ and the retailer in turn provides a trade credit period $$N$$ to her/his customer to stimulate sales and reduce inventory. From the retailer’s perspective, granting trade credit not only 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 customer will not be able to pay off his/her debt obligations). Hence, how to determine credit period is increasingly recognized as an important strategy to increase retailer’s profitability. Also, the selling items such as fruits, fresh fishes, gasoline, photographic films, pharmaceuticals and volatile liquids deteriorate continuously due to evaporation, obsolescence and spoilage. In this paper, we propose an economic order quantity model for the retailer where (1) the supplier provides an up-stream trade credit and the retailer also offers a down-stream trade credit, (2) the retailer’s down-stream trade credit to the buyer not only increases sales and revenue but also opportunity cost and default risk, and (3) the selling items are perishable. Under these conditions, we model the retailer’s inventory system as a profit maximization problem to determine the retailer’s optimal replenishment decisions under the supply chain management. We then show that the retailer’s optimal credit period and cycle time not only exist but also are unique. We deduce some previously published results of other researchers as special cases. Finally, we use some numerical examples to illustrate the theoretical results.

Inventory and credit decisions for time-varying deteriorating items with up-stream and down-stream trade credit financing by discounted cash flow analysis

Abstract In today's competitive markets, most firms in United Kingdom and United States offer their products on trade credit to stimulate sales and reduce inventory. Trade credit is calculated based on time value of money on the purchase cost (i.e., discounted cash flow analysis). Recently, many researchers use discounted cash flow analysis only on the purchase cost but not on the revenue (which is significantly larger than the purchase cost) and the other costs. For a sound and rigorous analysis, we should use discounted cash flow analysis on revenue and costs. In addition, expiration date for a deteriorating item (e.g., bread, milk, and meat) is an important factor in consumer's purchase decision. However, little attention has been paid to the effect of expiration date. Hence, in this paper, we establish a supplier–retailer–customer supply chain model in which: (a) the retailer receives an up-stream trade credit from the supplier while grants a down-stream trade credit to customers, (b) the deterioration rate is non-decreasing over time and near 100 percent particularly close to its expiration date, and (c) discounted cash flow analysis is adopted for calculating all relevant factors: revenue and costs. The proposed model is an extension of more than 20 previous papers. We then demonstrate that the retailer's optimal credit period and cycle time not only exist but also are unique. Thus, the search of the optimal solution reduces to a local one. Finally, we run several numerical examples to illustrate the problem and gain managerial insights.