Advance sustainable inventory management through advertisement and trade-credit policy

Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime

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.

In this paper, we formulate and solve an economic order quantity model with default risk. Our main purpose is to investigate retailer’s optimal replenishment time and credit period for deteriorating items under selling price-dependent demand while maximizing profit per unit time. Here, shortages are allowed and items are partially backlogged for interested customers. We show that optimal replenishment time and credit period not only exist but they are also unique. We solve the proposed problem analytically. An algorithm is presented to derive the optimal solution of the model. The mathematical model is evaluated by numerical examples. We use Mathematica to obtain a global maximum solution to the optimal cycle time and the optimal credit period for the proposed model. A sensitivity analysis with respect to major parameters is performed in order to examine the stability of our model. At the end of the paper, conclusions are drawn and an outlook of possible future directions is depicted.

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

To boost the sale is the prime objective for promoters. For this purpose, they generally allow credit period. In this article, we have considered an inventory model in which supplier gives credit period to retailer and to increase the sale, retailer passes it to end customers. This phenomenon is known as two level trade credits. By allowing credit period we may encounter with the issue of default risk which has been taken care of while calculating profit function for the system. Also, each and every inventory product gets deteriorated over the time as per its nature and such deteriorating products have its maximum life time as well. The present inventory model deals with such products. Quadratic demand is discussed here which is suitable for the products for which demand increases initially and after sometimes it shows decreasing pattern. Finally, retailer's total profit is maximized with respect to credit period and cycle time. Numerical examples are given to validate the model. Sensitivity analyses are done to filter significant inventory parameters.

A note on “Seller’s optimal credit period and cycle time in a supply chain for deteriorating items with maximum lifetime”

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

ABSTRACTThis study considers sustainability issues and default risks in the context of joint inventory control and trade credit financing for Non-Instantaneous Deteriorating Items (NIDIs) in a supplier-retailer-customer system, in which the supplier offers an upstream full trade credit to the retailer and the retailer, in turn, provides a downstream partial trade credit to her/his customers. Demand rate is sensitive to the amount of carbon emissions, the length of the credit period suggested by the retailer to its customers and selling price. The main objective of this study is to optimize credit period, order quantity, and replenishment cycle time in order to maximize retailer’s total profit and minimize carbon emissions at the same time. For solving the proposed problem, we apply an approximation method to simplify the profit function and transform the problem into a constrained Signomial Geometric Programming (SGP) problem, then a global optimization approach is used for solving the model.Finally, a numerical illustration and sensitivity analysis are performed to demonstrate the problem and the solution procedure. Some useful managerial insights are obtained from computational results. The results show that the retailer will increase its total profit by considering trade credit policy and non-instantaneous deteriorating phenomenon.

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.

The main purpose of this paper is to relax the Ouyang et al.’s model (2004) using the algebraic method to determine the optimal inventory replenishment policy for the retailer under finite replenishment rate and permissible delay in payments. Ouyang et al. (2004) assumed that the retailer would not consider paying payment until receiving all items. The purpose of this paper is to relax this assumption and establish the retailer’s inventory system as a cost minimization problem to determine the retailer’s optimal inventory cycle time. Then, an algebraic approach is provided and an easy-to-use theorem is derived to efficiently determine the optimal cycle time. Finally, numerical examples are given to illustrate the results and managerial insights are drawn.

In this study, the authors develop a supplier-retailer optimal integrated strategy where the retailer's demand is price sensitive and the supplier's supply is random. It is assumed that the supplier's supply follows a normal distribution and the supplier may offer credit period to the retailer. The expected profit is maximised with respect to the unit price charged and the credit period offered by the supplier. The computational steps are provided to obtain the supplier's and the retailer's decision variables under individual (non-cooperative) as well as joint (cooperative) strategies. The sensitivity analysis of the parameters is carried out using a numerical example. The authors observe that it is beneficial to consider negotiating the optimal pricing and trade credit policies.

This paper develops an economic ordering quantity (EOQ) model with stock dependent demand and imperfect items under the effect of inflation and time value of money. In this model, the lifetime of a defective item follows a Weibull distribution and the imperfect items are reworked at a cost to become the perfect one. In this article, the model is considered with finite replenishment rate under progressive payment scheme within the cycle time and the retailer is allowed a trade-credit offer by the supplier to buy more items. During the credit period, the retailer can earn more by selling their products. The interest on purchasing cost is charged for the delay of payment by the retailer. The objective of this model is to minimize the total inventory cost of the retailer by finding the optimal cycle length and the optimal order quantity. Numerical examples are given to demonstrate the results. Sensitivity analysis of the model with respect to several system parameters has been carried out and the implications are discussed in detail.

Study on operation strategy of a silica gel-water adsorption chiller in solar cooling application

In order to increase sales over and above cash sales, firms generally give trade credit to their customers. Trade credit policy through its influence on demand becomes a determinant of inventory policy which is intended to meet that demand. Therefore, inventory and trade credit policies are interrelated which should be determined simultaneously in a systems perspective. However, inventory policy is generally determined independent of the credit policy. This paper develops a mathematical model for simultaneously determining inventory and credit policies when demand rate consists of: 1 cash demand rate 2 credit demand rate depending upon date-terms credit period. Discounted cash flow approach has been used to establish the model. The objective of the model is to maximise the present value of firm’ s net profit per unit time by jointly determining the optimal date-terms credit period and replenishment time. Numerical example and sensitivity analysis are presented to illustrate the effectiveness of proposed model and results are discussed. The model suggests that at high values of inventory carrying cost and accounts receivable carrying cost the firm should invest less in accounts receivables by following a tight credit policy.