Two-level Trade Credit Policy Research Articles

Sustainable inventory models with controllable deterioration under two-level trade credit policy and various carbon emissions regulations

Sustainable inventory models with controllable deterioration under two-level trade credit policy and various carbon emissions regulations

The Effect of Preservation Technology Investment on Inventory Model with Quadratic Demand Rate and Time dependent Holding Cost Under Two-Level Trade-Credit Policy

The Effect of Preservation Technology Investment on Inventory Model with Quadratic Demand Rate and Time dependent Holding Cost Under Two-Level Trade-Credit Policy

Optimal replenishment, pricing and preservation technology investment policies for non-instantaneous deteriorating items under two-level trade credit policy

<p style='text-indent:20px;'>In the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. In this paper, we consider an inventory model for non-instantaneous deteriorating items with price sensitive demand, time varying deterioration rate under two-level trade credit policy. Besides, to reduce deterioration rate, retailers invest some cost to prevent product degradation/decay, known as preservation technology, is also inserted. Consumption of such items within shelf life prevents to deterioration, which can be achieved by bulk sale. In order to stimulate the selling, trade-credit policy is also considered here. In the sequel, not only the supplier would offer fixed credit period to the retailer, but retailer also adopt the trade credit policy to the customers in order to promote the market competition. The retailer can accumulate revenue and interest after the customer pays for the amount of purchasing cost to the retailer until the end of the trade credit period offered by the supplier. The main objective is to determine the optimal replenishment, pricing and preservation technology investment strategies including whether or not invest in preservation technology and how much to invest in order to maximize the average profit of the system. It is proved that the optimal replenishment policy not only exists but is unique for any given selling price and preservation technology cost. An algorithm is presented to derive the optimal solutions of the model. Numerous theorems and lemmas have been inserted to obtain the optimal solution. Finally, numerical examples and managerial implications are incorporated to validate the proposed model.</p>

Two Level Trade Credit Policy Approach in Inventory Model with Expiration Rate and Stock Dependent Demand under Nonzero Inventory and Partial Backlogged Shortages

In present real life situations, the stock and expiration date directly impact on the demand of an item. In this context, this research work develops an inventory model for stock and expiration rate-dependent demand under a two-level trade credit policy. Specifically, the following three situations are studied: (i) trade credit policy without zero ending inventory; (ii) trade credit policy with zero ending inventory; (iii) trade credit policy with partial backlogged shortages. The proposed inventory model is formulated as a non-linear constrained optimization problem. Some theoretical results are derived, and an algorithm is stated in order to solve the proposed inventory model. The main objective of the inventory model is to determine the optimal cycle length, the optimal ending inventory level, and the optimal number of units displayed which maximize the total profit. Some numerical examples are solved. Finally, a sensitivity analysis is done with the aim to see the impacts of a variation of the input parameters on the decision variables and the total profit.

Impact of Energy and Carbon Emission of a Supply Chain Management with Two-Level Trade-Credit Policy

Supply chain management aims to integrate environmental thinking with efficient energy consumption into supply chain management. It includes a flexible manufacturing process, more product delivery to customers, optimum energy consumption, and reduced waste. The manufacturing process can be made more flexible through volume agility. In this scenario, production cannot be constant, and with the concept of volume agility, production is taken as a decision variable under the effect of optimum energy consumption. Considering a two-echelon supply chain, we consider a producer and supplier with two-level-trade-credit policies (TLTCP) with the optimum consumption. To reduce the integrated total inventory cost, we believe that demand is a function of the credit period and selling price. The cost function is analyzed, either with the credit period dependent demand rate or with the selling price dependent demand rate through the numerical examples under energy costs. Energy and carbon emission costs are introduced in setup/ordering cost, holding cost, and item cost for producer and supplier. The effect of inflation on the total cost cannot be ignored; this model is being developed for deteriorating items with the simultaneous impact of volume agility, energy, carbon emission cost, and two-level-trade-credit policies with inflation. This supply chain model was solved analytically and obtained the optimum decision variables in a quasi-closed form solution. An illustrative theorem is being utilized to analyze the optimum result for all the decision parameters. The convexity of the objective function is being obtained analytically as well as graphically. Finally, numerical examples and sensitivity analysis are employed to illustrate the present study and with managerial insights.

Retailer’s optimal ordering and payment strategy under two-level and flexible two-part trade credit policy

Trade credit has been widely used as a marketing strategy to boost sales and a tool for short-term financing. The existing literature usually study flexible two-part trade credit contract and two-level trade credit policy separately. In this paper, an inventory model is formulated for a supply chain simultaneously adopting flexible trade credit contract and two-level trade credit policy. In particular, the supplier offers the retailer with a flexible two-part trade credit contract, which allows the retailer to pay any fraction of the purchasing cost within a short credit period at a discounted price and the rest at full price within the maturity of the contract. Meanwhile, the retailer allows his/her customer to defer payment for a fixed period of time. The inventory model aims at determining the retailer’s optimal ordering and payment strategy. A solution procedure is proposed and closed-form solutions are derived. Numerical results indicate that offering flexible trade credit can reduce the retailer’s total cost while offering two-level trade credit contract will increase the retailer’s total cost and reduce the retailer’s early payment fraction.

Optimal credit periods under two-level trade credit

In a two-echelon single-supplier and single-retailer supply chain with permissible delay in payment, we investigate the two-level trade credit policy in which the supplier offers the retailer with limited capital a credit period and in turn the retailer also provides a credit period to customers. The demand rate is sensitive to both retail price and the customerso credit period. By using the backward induction method, we analytically derive the unique equilibrium of both credit periods in the Stackelberg game to determine the retaileros pricing strategy. We find that the optimal retail price is not always decreasing in the credit period offered by the supplier to the retailer. In addition, we characterize the conditions under which the retailer is willing to voluntarily provide customers a credit period. Numerical examples and sensitivity analysis of key parameters are presented to illustrate the theoretical results and managerial insights.

An inventory model with variable demand incorporating unfaithfulness of customers under two level trade credit

In this research work, an inventory model has been developed under two-level trade credit policy with unfaithful customers. A percentage of the total customers are treated as unfaithful customers. Demand is influenced by customers' credit period, credit amount and selling price. Due to the vagueness of some parameters, the proposed model is formulated in both the crisp and fuzzy environments. The main purpose of this research work is to determine the optimal replenishment policy so that the total profit of the retailer is maximised. The existence of a solution to the problem is discussed theoretically and then some numerical experiments are undertaken. To find the marketing decision of a generalised model (when the number of variables increases) and for the fuzzy objectives, a soft computing technique is used. Some sensitivity analyses are performed to provide some managerial insights. Finally a conclusion is drawn and some future research directions are proposed. [Received: 14 November 2017; Accepted: 2 January 2019]

Two-level trade credit with default risk in the supply chain under stochastic demand

In the business world, both the supplier and the retailer accept the credit to make their business position strong, because the credit not only strengthens their business relationships but also increases the scale of their profits. The long period of credit may increase the demand rate but simultaneously it can also increase the credit risk. This paper investigates the two-echelon supply chain model consisting of a supplier supplying a product to a single retailer, which sells this product to the end customers, under the two-level trade credit policy. The supplier offers the retailer a credit time, and the retailer also provides credit time to the end customers for settling the account. The credit time offered by the retailer is lesser than the credit time offered by the supplier, but they both are facing the default risk. Supplier decides to charge compound interest on the principal amount of the retailer if s/he fails to pay within credit time. Whereas, the retailer faces the uncertain demand from customers that may increase the chance of facing stock-out by the customers, taken as partially backlogged. The demand rate of the supplier is dependent on the two decision variables: a) the quantity of the retailer’s order; and b) the credit period offered by the supplier. The main objective of this paper is to determine the distribution-free optimal order quantity of the retailer with an optimal credit period of the supplier, which maximize the profitability of the total supply chain. To find the optimal solution mathematical formulation for the supplier and the retailer has been developed in the solution procedure. Adequate numerical example with uniform distribution has been given to justify the solution procedure. Ultimately, sensitivity analysis of the major parameters, managerial implication, with concluding remarks and future research are discussed.

An inventory model of deteriorating items with a credit period-based new demand function in a finite time horizon

In today's competitive market, the trade credit plays an important role to increase demands of customers/buyers. Here, we consider a two-level trade credit policy in which a delay in payment is offered by supplier to retailer and also an another delay in payment is offered by retailer to his/her all customers. In this model, it is proposed that the demand function is dependent on the length of the customer's credit period and also the duration of offering the credit period. The purpose of this model is to establish a deterministic EOQ model of deteriorating items for the retailer to maximise the total profit and the number of replenishment cycle in finite time horizon. We develop an algorithm to find out the optimal solutions. Also, the model is explained with the help of numerical examples and sensitivity analysis is given to illustrate the features of the proposed model with respect to some parameters.

An inventory model of deteriorating items with a credit period-based new demand function in a finite time horizon

In today's competitive market, the trade credit plays an important role to increase demands of customers/buyers. Here, we consider a two-level trade credit policy in which a delay in payment is offered by supplier to retailer and also an another delay in payment is offered by retailer to his/her all customers. In this model, it is proposed that the demand function is dependent on the length of the customer's credit period and also the duration of offering the credit period. The purpose of this model is to establish a deterministic EOQ model of deteriorating items for the retailer to maximise the total profit and the number of replenishment cycle in finite time horizon. We develop an algorithm to find out the optimal solutions. Also, the model is explained with the help of numerical examples and sensitivity analysis is given to illustrate the features of the proposed model with respect to some parameters.

Optimising an integrated production–inventory system under cash discount and retailer partial trade credit policy

ABSTRACTIn this article, we develop a single-manufacturer, single-retailer production–inventory model considering price-sensitive demand and a two-level trade credit policy. The manufacturer adopts a ‘two-part strategy’, viz. cash discount and delayed payment while offering trade credit to the retailer. The retailer, on the other hand, offers a partial trade credit to his/her customers. We model the integrated production–inventory system as a profit maximisation problem and design iterative algorithms to determine the optimal decisions. A numerical example is taken to illustrate the developed model. Sensitivity analysis is carried out to study the influence of key model parameters on the optimal solution. Finally, the performance of the integrated model is also compared with the non-integrated model.

An integrated inventory model for deteriorating items with price-dependent demand under two-level trade credit policy

ABSTRACTThis article analyses an inventory system with two models for deteriorating items under two-level trade credit policy. In model I, the demand rate is influenced by both displayed stock and selling price. In model II, the demand rate depends on the selling price. In this work, a retailer who purchases the items enjoys a fixed credit period offered by his/her supplier and, in turn, also offers a credit period to his/her customers in order to promote the competition. We provide the necessary and sufficient conditions of the existence and uniqueness of the optimal solutions that could maximise the retailer's average profit per unit time. A numerical example is provided to illustrate and support the developed models.

Analysis of credit linked demand in an inventory model with varying ordering cost.

In this paper, we have considered an economic order quantity model for deteriorating items with two-level trade credit policy in which a delay in payment is offered by a supplier to a retailer and also an another delay in payment is offered by the retailer to his/her all customers. Here, it is proposed that the demand function is dependent on the length of the customer’s credit period and also the duration of offering the credit period. In this article, it is considered that the retailer’s ordering cost per order depends on the number of replenishment cycles. The objective of this model is to establish a deterministic EOQ model of deteriorating items for the retailer to decide the position of customers credit period and the number of replenishment cycles in finite time horizon such that the retailer gets the maximum profit. Also, the model is explained with the help of some numerical examples.

The retailer’s optimal decision on order quantity and credit periods under two-level trade credit policy

In this paper, we propose an inventory model under two-level trade credit policy, where the supplier offers quantity discounts and allows the retailer to choose the period of delay in payments that determines the unit purchasing cost, and so retailer's unit purchasing cost is a function of both ordering quantity and his/her allowed credit period. Furthermore, the demand function is relevant to the credit period offered by the retailer to his/her customers. Our objective here is to maximize the retailer's total profit per unit time by solving the optimal decision on ordering quantity and two credit periods. An effective algorithm is developed to determine the optimal solution to the problem. Numerical examples are provided to illustrate the impact of the model parameters on the optimal solutions.

The EPQ model with deteriorating items under two levels of trade credit in a supply chain system

There are two kinds of two levels of trade credit policies addressed by Huang [15] and Teng [29], respectively. Liao [24] presents the EPQ model with deteriorating items under two-level trade credit policy from the viewpoint of Huang [15], while Chang, Teng and Chern [2] discuss the model from the viewpoint of Teng [29]. However, errors are found in the process of the modeling in Chang et al. [2]. The main purpose of this study is to improve the model of Chang et al. [2] and develop a more general EPQ inventory model. A theorem is also provided for practitioners to make right decisions.

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 fuzzy framework for coordinating pricing and inventory policies for deteriorating items under retailer partial trade credit financing

In this paper, we proposed a generalized economic order quantity (EOQ) – based inventory model using a trade credit policy in a fuzzy sense. 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, partially provides customers a permissible delay period N. This study considers fuzzy EOQ model to allow for: (1) selling price dependent demand rate which is imprecise in nature, (2) a profit maximization objective and (3) an imprecise holding cost, ordering cost, purchasing cost, interest earned and interest charged rate. Besides, the cases N⩽M and N⩾M are explored thoroughly. The objective function for the retailer in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method. For the defuzzified 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, numerical examples are presented to illustrate the proposed model and the effect of key parameters on optimal solution is examined.

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.

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.