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An Inventory Policy and Payment Policy under Various Credits  [PDF]
Meng-Chang Lin,Yung-Fu Huang
Journal of Applied Sciences , 2005,
Abstract: This study tries to modify Huang and Chung to develop the retailer`s inventory model. We assume that the retailer can obtain the trade credit when the payment is paid within the trade credit period offered by the supplier. Otherwise, the retailer will just obtain a cash discount. In addition, we modify the assumption that the unit purchasing price and unit selling price were equal. Under these conditions, we want to investigate the retailer`s optimal ordering policy and optimal payment policy within the EOQ framework. Mathematical model has been derived for obtaining the optimal cycle time and optimal payment time for item so that the annual total relevant cost is minimized. Furthermore, numerical examples are given to illustrate the results developed in this study.
Two echelon partial trade credit financing in a supply chain derived algebraically  [PDF]
Jaggi Chandra K.,Verma Mona
Yugoslav Journal of Operations Research , 2012, DOI: 10.2298/yjor100108017j
Abstract: Trade credit financing has become a powerful tool to improve sales & profit in an industry. In general, a supplier/retailer frequently offers trade credit to its credit risk downstream member in order to stimulate their respective sales. This trade credit may either be full or partial depending upon the past profile of the downstream member. Partial trade credit may be offered by the supplier/retailer to their credit risk downstream member who must pay a portion of the purchase amount at the time of placing an order and then receives a permissible delay on the rest of the outstanding amount to avoid non-payment risks. The present study investigates the retailer’s inventory problem under partial trade credit financing for two echelon supply chain where the supplier, as well as the retailer, offers partial trade credit to the subsequent downstream member. An algebraic approach has been applied for finding the retailer’s optimal ordering policy under minimizing the annual total relevant cost. Results have been validated with the help of examples followed by comprehensive sensitivity analysis.
Retailer’s optimal ordering policies with cash discount and progressive payment scheme derived algebraically
Alok kumar,K K Kaanodiya,R R Pachauri
International Journal of Industrial Engineering Computations , 2011,
Abstract: This study presents optimal ordering policies for retailer when supplier offers cash discount and two progressive payment schemes for paying of purchasing cost. If the retailer pays the outstanding amount before or at first trade credit period M, the supplier provides r_1cash discount and does not charge any interest. If the retailer pays after M but before or at the second trade period N offered by the supplier, the supplier provides r_2 cash discount and charges interest on unpaid balance at the rate 〖Ic〗_1 . If retailer pays the balance after N, (N>M) then the supplier does not provide any cash discount but charges interest on unpaid balance at the rate 〖Ic〗_2. The primary objective of this paper is to minimize the total cost of inventory system. This paper develops an algebraic approach to determine the optimal cycle time, optimal order quantity and optimal relevant cost. Numerical example are also presented to illustrate the result of propose model and solution procedure developed.
Integrated Inventory Model for Deteriorating Items with Price-Dependent Demand under Quantity-Dependent Trade Credit  [PDF]
Karuppuchamy Annadurai
International Journal of Manufacturing Engineering , 2013, DOI: 10.1155/2013/439190
Abstract: This paper explores an integrated inventory model when the deterioration rate follows exponential distribution under trade credit. Here, it is assumed that demand rate is a function of selling price and the permissible delay in payment depends on the order quantity. In the model shortages are completely backlogged. The maximization of the total profit per unit of time is taken as the objective function to study the retailer’s optimal ordering policy. This paper also presents a practical application example where the proposed inventory model is utilized to support business decision making. Particularly, the model developed in the paper could be useful in the area of supply chain management. Finally, sensitivity analysis of the optimal solution with respect to major parameters is carried out. Our result illustrates that this model can be quite useful in determining the optimal ordering policy when the trade credit period is being analyzed. 1. Introduction Both in deterministic and probabilistic inventory models of classical type, it is observed that payments are made to the supplier immediately after receiving the items. In practice, the supplier will offer the retailer a delay period in payment for the amount of purchase to increase the demand known as trade credit period. Offering such a credit period to the retailer will encourage the supplier’s selling and reduce on-hand stock level. Simultaneously, without a primary payment the retailer can take the advantages of a credit period to reduce cost and increase profit. The customer does not have to pay any interest during the fixed period but if the payment gets delayed beyond the period interest will be charged by the supplier. This arrangement comes out to be very advantageous to the customer as he may delay the payment till the end of the permissible delay period. During this credit period the retailer can start to accumulate revenues on the sales and earn interest on that revenue. Thus, the delay in the payment offered by the supplier is a kind of price discount since paying later indirectly reduces the cost of holding and it encourages the retailers to increase their order quantity. Moreover, paying later indirectly reduces the cost of holding stock. Hence, trade credit can play an important role in inventory model for both the suppliers as well as the retailers in integrated inventory model. Goyal [1] first derived an EOQ model under the conditions of permissible delay in payments. Chung and Huang [2] extended Goyal’s [1] model to consider the case that the units are replenished at a finite rate
A Lot-Size Model for Deteriorating Items under Conditions of a One-Time Only Extended Credit Period  [PDF]
Nita H. Shah
International Journal of Mathematics and Mathematical Sciences , 2010, DOI: 10.1155/2010/137428
Abstract: Now-a-days, the offer of credit period to the customer for settling the account for the units purchased by the supplier is considered to be the most beneficial policy. In this article, an attempt is made to formulate the mathematical model for a customer to determine optimal special cycle time when the supplier offers the special extended credit period for one time only during a special period. A decision policy for a retailer is developed to find optimal special cycle time. The theoretical results and effects of various parameters are studied by appropriate dataset. 1. Introduction The most prevailing business strategy is adopted by the supplier to offer credit period of (say) 30 days to settle the account of the retailer. This strategy attracts new customers who consider it to be a type of discount strategy. The interest is not charged if the account is settled within the permissible credit period. However, if the payment is delayed beyond this period, the interest is charged for unsettled account. The retailer can earn the interest by putting generated revenue in an interest-bearing account. Thus, credit period reduces the amount of capital invested in stock, and thereby, reduces retailer’s holding cost of stock. When units in inventory are subject to deterioration, the cost of deterioration incurred by the retailer contributes to the total cost of an inventory system. Goyal [1] developed an economic order quantity (EOQ) model under conditions of permissible delay in payments. Shah [2] and Aggarwal and Jaggi [3] extended Goyal’s model for deteriorating items. Jamal et al. [4] generalized the model to allow for shortages. Teng [5] extended Goyal’s model by considering the difference between the selling price and the unit price and discussed closed-form solution to the problem analytically. Related research articles are by Shah [6, 7], Hwang and Shinn [8], Jamal et al. [9], Liao et al. [10], Chang et al. [11], Sarker et al. [12], Shah [13], Shah et al. [14], Teng et al. [15], Ouyang et al. [16], Shah [17], and many more. The abovementioned developments assumed that a supplier provides his customer a credit period (say) M for settling the account during the normal period. Soni and Shah [18] derived mathematical model under the assumption that the supplier offers one more credit period (say) to the retailer for settling the account of the purchased goods. In this paper, an attempt is made to extend the credit period only once during a specified period as a special marketing strategy to motivate the retailer to order larger than usual order quantities.
An Inventory Model under Conditional Trade Credits Depending on Payment Time  [PDF]
Chung-Li Chou,Yung-Fu Huang,Hung-Fu Huang
Journal of Applied Sciences , 2005,
Abstract: The present study investigate the retailer’s optimal cycle time and optimal payment time under supplier credits including conditionally permissible delay in payments and cash discount depending on retailer payment time. That is, the retailer can obtain fully permissible delay in payments and cash discount if the payment is paid before the period of full delay payments permitted by the supplier. Otherwise, the retailer will just obtain partially permissible delay in payments within the period of partial delay payments permitted by the supplier. The supplier uses this policy to attract retailer to pay the payment as soon as possible to shorten its collection period. Mathematical models have been derived for obtaining the optimal cycle time and optimal payment time for item so that the annual total relevant cost is minimized. One theorem is developed to efficiently determine the optimal replenishment and payment policy for the retailer.
A Note on Retailer`s Ordering Policy and Payment Policy under Trade Credit and Cash Discount  [PDF]
Yung-Fu Huang
Journal of Applied Sciences , 2004,
Abstract: In present study, the model of Huang has been modified and discussed with retailer`s ordering policy under conditions of cash discount and trade credit. Mathematical model has been modified for obtaining the optimal cycle time and optimal payment policy for item under cash discount and trade credit so that the annual total cost is minimized. Then, a theorem is provided to efficiently determine the optimal cycle time and optimal payment policy. Finally, a numerical example is solved to illustrate the results obtained.
An Inventory Model for Ramp-Type Demand with Two-Level Trade Credit Financing Linked to Order Quantity  [PDF]
Hui-Ling Yang
Open Journal of Business and Management (OJBM) , 2019, DOI: 10.4236/ojbm.2019.72029
Abstract: 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.
An Inventory Model with Finite Replenishment Rate, Trade Credit Policy and Price-Discount Offer  [PDF]
Biswajit Sarkar,Shib Sankar Sana,Kripasindhu Chaudhuri
Journal of Industrial Engineering , 2013, DOI: 10.1155/2013/672504
Abstract: When some suppliers offer trade credit periods and price discounts to retailers in order to increase the demand of their products, retailers have to face different types of discount offers and credits within which they have to take a decision which is the best offer for them to make more profit. The retailers try to buy perfect-quality items at a reasonable price, and also they try to invest returns obtained by selling those items in such a manner that their business is not hampered. In this point of view, we consider an economic order quantity (EOQ) model for various types of time-dependent demand when delay in payment and price discount are permitted by suppliers to retailers. The models of various demand patterns are discussed analytically. Some numerical examples and graphical representations are considered to illustrate the model. 1. Introduction Many classical inventory models assume that demand is constant. In present marketing environment, few items follow constant demand. Many product’s demands follow variable time-varying demand. The recent trend of the marketing system is to provide more buy opportunities to the retailer by the supplier by offering different discounts. To take the discount opportunity, retailers prefer to buy more beyond their capacity of buying. As a result, the supplier has the opportunity to sell more for better earning. This is the benefit of the supplier. The classical inventory model does not consider the delay time concept or variable demand. The proposed model considers time-varying demand and delay in payments along with finite replenishment rate. The basic well-known square root formula for the EOQ of the item was formulated by Harris [1] based on constant demand. Donaldson [2] extended the constant demand to linear time-dependent demand model analytically with finite time horizon. Following Donaldson [2], significant contribution in this direction came out from researchers like Goyal [3], Goswami and Chaudhuri [4], Goyal et al. [5], and others. Hariga and Benkherouf [6] discussed an optimal and heuristic replenishment model for deteriorating items with an exponentially time-varying demand. Wee [7] studied a deterministic lot size inventory model for deteriorating items with shortage and decline market. Khanra and Chaudhuri [8] extended an inventory model with quadratic increasing demand over a finite time horizon and shortages. Sana and Chaudhuri [9] studied an inventory model with linear trend demand incorporating shortages. Cárdenas-Barrón [10] discussed the derivation of inventory models by using analytic
Optimal Ordering policy in demand declining market under inflation when supplier credits linked to order quantity  [cached]
Nita H. Shah,Kunal T. Shukla
Electronic Journal of Applied Statistical Analysis , 2011,
Abstract: In this research paper, a lot–size model is proposed when supplier offers the retailer a credit period to settle the account if the retailer orders a large quantity. The proposed study is meant for demand declining market. Here, the retailer needs to arrive at a static decision when demand of a product is decreasing and on the other side the supplier offer the credit period if the retailer orders for more than pre – specified quantity. Shortages are not allowed and the effect of inflation is incorporated. The objective to minimize the total cost in demand declining market under inflation when the supplier offers a credit period to the retailer if the ordered quantity is greater than or equal to pre – specified quantity. An easy – to – use flow chart is given to find the optimal replenishment time and the order quantity. The mathematical formulation is supported by a numerical example. The sensitivity analysis of parameters on the optimal solution is carried out.
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