Two-level Trade Credit Financing Research Articles

Inventory model for sustainable operations of fixed-life products: Role of trapezoidal demand and two-level trade credit financing

Trade credit financing has emerged as an efficient tool for retailers due to its ability to attract more customers and increase demand for fixed-life products like fruit jam, sauce, air-cooler etc. This work proposes an inventory model to minimize retailers' total cost for fixed-life products following a time-dependent trapezoidal demand and two-level trade credit financing. Four cases are discussed based on different trade credit periods, and optimal solutions are analytically characterized through sustainable order quantity with complete backlogging of shortages. A numerical example is presented followed by a sensitivity analysis of the sustainability parameters to validate the impact of trade credit interactions on the retailer's overall cost. The model shows that a higher trade credit period to the retailer and a lower trade credit period from the retailer to the customer effectively reduces the retailer's total cost under certain specific cases. It generates evidence that the higher the trade credit period, the lesser the total cost under the optimal order quantity, and the higher the sustainability of the inventory system. This work has implications for retailers dealing with fixed-life products from various industries like dairy, grocery, processed fruits and vegetables to adopt sustainable inventory replenishment policies for their businesses.

Optimal ordering policy for a retailer with consideration of customer credit under two-level trade credit financing

In practice, to promote sales and alleviate the default risk of customers, the retailer frequently offers its good credit customers full trade credit while offers bad credit customers partial trade credit. In other words, both types of customers receive a credit period simultaneously, but the bad credit customers must pay a fraction of the purchase cost at the time of buying productions as a collateral deposit. By contrast, for the sake of self-interest, the supplier chooses to provide the partial trade credit for its retailer on account of reducing the credit risk. Numerous researchers assume that the retailer has the powerful decision-making right and he/she can obtain the full trade credit, however, very few academicians have studied that the supplier offers the retailer partial trade credit, which is more realistic and significant. In this paper, we establish an economic order quantity model for a retailer who receives a partial trade credit by its supplier, and offers a full or partial trade credit to its good or bad credit customers respectively based on the cost minimization of the retailer. Then, the optimal ordering strategy of the retailer under different conditions is given. Finally, through numerical examples and sensitivity analysis, we derive the influence of related parameters on retailer’s order decision and managerial insights.

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 replenishment and credit policy in an inventory model for deteriorating items under two-levels of trade credit policy when demand depends on both time and credit period involving default risk

In this paper, we examine an optimal dynamic decision-making problem for a retailer’s inventory system of deteriorating items under two-level trade credit financing where the supplier, as well as the retailer, offers trade credit to the subsequent downstream member, the demand rate of which varies simultaneously with time and the length of credit period that is offered to the customers. The deterioration rate is non-decreasing over time. In addition, the risk of default increases with the credit period length. A generalized model is presented to determine the optimal trade credit and replenishment strategies that maximize the retailer’s annual total profit. We then demonstrate that the retailer’s optimal credit period and replenishment cycle time not only exist but also are unique. Thus, the search of the global optimal solution reduces to finding a local solution. Finally, we run several numerical examples to illustrate the problem and gain managerial insights.

Three-layered integrated inventory model for deteriorating items with quadratic demand and two-level trade credit financing

ABSTRACTIn this study, the three-layered integrated production – inventory model – is formulated in which a distributor and a retailer observe quadratic demand and a manufacturer runs the production proportional to the quadratic demand. The inventory of every player is subject to deterioration at a constant rate. The model considers two-level trade credit financing. The total cost of the integrated inventory system is minimised with respect to a number of shipments from the manufacturer to the distributor and the distributor to the retailer and each player's replenishment times. A solution procedure is worked out to obtain the best possible decision for the players of the supply chain. The results are validated with numerical examples for different scenarios. Managerial decisions are suggested.

Manufacturing Inventory Model for Deteriorating Items with Maximum Lifetime under Two-Level Trade Credit Financing

In the present study, an inventory model is developed especially for a manufacturer where manufactured product not only deteriorates continuous but also has a maximum lifetime. It is assumed that supplier offers full trade credit period of M to the manufacturer while due to the strong position in the market, manufacturer provides partial trade credit period of N to his/her wholesaler. The objective of the problem is to minimize the total inventory cost. By applying convex fractional programming results, necessary and sufficient conditions are obtained to obtain an optimal solution. Few theorems have been developed to determine manufacturer’s optimal policies. Teng (1985), Teng (2002), Huang (2003), Teng and Goyal (2007), Chen and Teng (2014), and Wu and Chan (2014) are special case of our proposed model. Theorems are illustrated with the help of numerical examples. In addition, some managerial insights on the basis the numerical examples are also concluded.

Production inventory model for two-level trade credit financing under the effect of preservation technology and learning in supply chain

AbstractThe present study investigated the inventory model for a retailer under two levels of trade credit to reflect the supply chain management. Supplier offers trade credit period of M to the retailer while in turn retailer provides a trade credit period of N to his/her customers. The supplier is willing to provide the retailer a full trade credit period for payments and the retailer offers the partial trade credit period to his/her customers. Here, selling items are considered as perishable items such as fruits, fresh fishes, gasoline, photographic films, etc. so that its potential worth decreases. It is assumed that decay in potential worth of items can be increased by using preservation technology. The demand is considered as the function of selling price and trade credit. Ordering cost can be reducing due to learning by doing phenomenon. By applying convex fractional programming results, we obtain necessary and sufficient conditions of an optimal solution. Some theorems are developed to determine r...

Retailer’s inventory system in a two-level trade credit financing with selling price discount and partial order cancelations

Retailer’s inventory system in a two-level trade credit financing with selling price discount and partial order cancelations

Manufacturer-retailer inventory model for deteriorating items with price-sensitive credit-linked demand under two-level trade credit financing and profit sharing contract

AbstractA supply chain of single manufacturer and single retailer is analyzed when units in warehouse are subject to deterioration at a constant rate. The demand is a decreasing function of selling price and increasing function of credit period offered by the retailer to the customers. Manufacturer follows a lot-for-lot production strategy. The manufacturer ensures delay payment to the retailer with agreement that the retailer will share a fraction of the profit realized during the credit period. The total joint profit of the supply chain is maximized with respect to replenishment time, selling price, and credit period. An algorithm is described to find the best strategy. Numerical examples are given to validate the proposed problem. Sensitivity analysis is carried out to examine important model parameters.

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.

Retailer's inventory system in a two-level trade credit financing with selling price discount and partial order cancellations

In today's fast marketing over the Internet or online, many retailers want to trade at the same time and change their marketing strategy to attract more customers. Some of the customers may decide to cancel their orders partially with a retailer due to various reasons such as increase in customer's waiting time, loss of customer's goodwill on retailer's business, and attractive promotional schemes offered by other retailers. Even though there is a lag in trading and order cancellation, this paper attempts to develop the retailer's inventory model with the effect of order cancellations during advance sales period. The retailer announces a price discount program during advance sales period to promote his sales and also offers trade credit financing during the sales periods. The retailer availing trade credit period from his supplier offers a permissible delay period to his customers. The customer who gets an item is allowed to pay on or before the permissible delay period which is accounted from the buying time rather than from the start period of inventory sales. This accounts for significant changes in the calculations of interest payable and interest earned by the retailer. The retailer's total cost is minimized so as to find out the optimal replenishment cycle time and price discount policies through a solution procedure. The results derived in mathematical theorems are implemented in numerical examples, and sensitivity analyses on several inventory parameters are obtained.

Supply chain management for two-level trade credit financing with selling price dependent demand under the effect of preservation technology

The present paper investigated the economic order quantity inventory model for a retailer under two-levels of trade credit to reflect the supply chain management (SCM). Here, it is assumed that the selling items are perishable such as fruits, fresh fishes, gasoline, photographic films, etc. It is assumed that potential worth of items can be increased by using preservation technology and the retailer’s trade credit period (M) offered by the supplier is longer than the customer’s trade credit period (N) offered by the retailer. It also assumed that the demand of the customer depends on the selling price of items. Theorems are developed to determine retailer’s optimal ordering policies and numerical examples are given to illustrate these theorems. It also observed that Goyal (1985), Shah (1993), Chung (1998) and Huang (2003) are the particular case of our proposed model. In addition, some managerial insights from the numerical examples are also concluded.

Trade credit competition between two retailers in a supply chain under credit-linked retail price and market demand

The paper considers a supply chain system in which the sole manufacturer supplies the same product to two retailers who compete in offering trade credit period to customers. Both the market demand and retail prices vary with the trade credit periods offered by the retailers. The manufacturer also provides a trade credit period to both the retailers to settle down their accounts. The net profit function of the supply chain is derived considering possible relationships among the trade credit periods offered by the manufacturer and the retailers and the time when each retailer receives the last payment from his customer. An algorithm is developed to find the optimal solution of the proposed model. From the numerical study, it is observed that a two-level trade credit financing can increase profits not only for the manufacturer and the retailers but also for the whole supply chain.

A Global Optimizing Policy for Decaying Items with Ramp-Type Demand Rate under Two-Level Trade Credit Financing Taking Account of Preservation Technology

An inventory system for deteriorating items, with ramp-type demand rate, under two-level trade credit policy taking account of preservation technology is considered. The objective of this study is to develop a deteriorating inventory policy when the supplier provides to the retailer a permissible delay in payments, and during this credit period, the retailer accumulates the revenue and earns interest on that revenue; also the retailer invests on the preservation technology to reduce the rate of product deterioration. Shortages are allowed and partially backlogged. Sufficient conditions of the existence and uniqueness of the optimal replenishment policy are provided, and an algorithm, for its determination, is proposed. Numerical examples draw attention to the obtained results, and the sensitivity analysis of the optimal solution with respect to leading parameters of the system is carried out.

Two-echelon inventory model for deteriorating items with credit period dependent demand including shortages under trade credit

In real life situation, it is observed that demand of an item depends on the length of the credit period offered by the retailer to his customers which has a positive impact on demand of an item. But the impact of credit period on demand has received a very little attention by researchers. Furthermore, by allowing shortages as backlogging, the impact on the cost from the decay of the products can be balanced out. A profitable decision policy between a supplier and the retailers can be characterized by an agreement on the permissible delay in payments. Recently, Jaggi et al. (Eur J Oper Res 190:130–135, 2008) have investigated the impact of credit linked demand on the retailer’s optimal replenishment policy. The objective of this study is to extend Jaggi et al. (Eur J Oper Res 190:130–135, 2008) model by incorporating deterioration and backlogging. That is, we formulate a two-echelon inventory model for deteriorating items with credit period dependent demand including shortages under two-level trade credit financing and determine the retailer’s optimal replenishment policy when both the supplier as well as the retailer offers the credit period to stimulate customer demand. Furthermore, we establish some useful theorems to characterize the optimal solution and provide an easy and useful computational algorithm with the help of computer code using the software Matlab 7.0 to determine the optimal shortage point, cycle length, ordering quantity and credit period. A numerical example is included to illustrate the solution procedure for the mathematical model developed. Finally, we implement sensitivity analysis of the optimal solution with respect to the major parameters of the system and obtain some important managerial insights.

Ordering policies for deteriorating inventory with storage constraint under two-level trade credit financing for stock-dependent demand

Most of the previously published models 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. Based on this argument a two-warehouse inventory model for deteriorating items under two-level trade credit financing is derived with stock-dependent demand. Sensitivity analysis of the optimal solution with respect to the parameters of system is carried out with the help of a numerical example.

An Inventory System for Deteriorating Products with Ramp-Type Demand Rate under Two-Level Trade Credit Financing

An inventory system for deteriorating products, with ramp-type demand rate, under two-level trade credit policy is considered. Shortages are allowed and partially backlogged. Sufficient conditions of the existence and uniqueness of the optimal replenishment policy are provided, and an algorithm, for its determination, is proposed. Numerical examples highlight the obtained results, and sensitivity analysis of the optimal solution with respect to major parameters of the system is carried out.

An Inventory Model for Deteriorating Items with Credit Period Dependent Demand under Two-Level Trade Credit Financing

An Inventory Model for Deteriorating Items with Credit Period Dependent Demand under Two-Level Trade Credit Financing