Retailer’s optimal ordering policy for deteriorating items with maximum lifetime under supplier’s trade credit financing (original) (raw)
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International Journal of Strategic Decision Sciences, 2011
This paper investigates the economic order quantity inventory model for a retailer under two levels of trade credit to reflect the supply chain management situation. It is assumed that the retailer maintains a powerful position and can obtain full trade credit offered by supplier, yet the retailer just offers the partial trade credit to customers. Under these conditions, the retailer can obtain the most benefits. This study also investigates the retailer’s inventory policy for deteriorating items in a supply chain management situation as a cost minimization problem. The present study shows that the annual total variable cost for the retailer is convex, that is, a unique solution exists. Mathematical theorems and algorithms are developed to efficiently determine the optimal inventory policy for the retailer. The results in this paper generalize some already published results. Finally, numerical examples are given to illustrate the theorems and obtain managerial phenomena.
2018
In this paper, an inventory model for deteriorating items with selling price and credit period sensitive demand is developed. The inventory system deals with products which have a fixed expiry date after which the product cannot be sold. Here, a permissible delay period is allowed by the supplier to the retailer to pay all his dues, but if the retailer doesn't pay the entire amount at the end of the delay period, an interest will be charged on the remaining dues. The shortages are also allowed and partially backlogged. This paper provides a procedure to develop the total retailer's profit function per unit time of the system and optimal ordering quantity per cycle for the retailer. Finally, the model is illustrated with numerical examples.
2017
The present paper deals with development of an optimal inventory policy for deteriorating products with variable carrying cost.In this paper, the demand of the product is a multivariate function which depends on the stock level and selling price of the product. A permissible delay period is allowed to the retailer to pay all his dues, but if the retailer doesn’t pay the entire amount at the end of delay period, an interest will be charged on the remaining dues. The shortages are allowed and partially backlogged. With the help of Mathematical formulation, the total profit of the retailer per unit time and order quantity are calculated numerically. A sensitivity analysis of the decision variables is also carried out to check the effect of changes in the values of the parameters and affect of these changes on the optimal policy of inventory.
Journal of Mathematical Modelling and Algorithms in Operations Research, 2015
In a supplier-retailer-customer supply chain, a credit-worthy retailer frequently receives a permissible delay on the entire purchase amount without collateral deposits from his/her supplier (i.e., an upstream full trade credit). By contrast, a retailer usually requests his/her credit-risk customers to pay a fraction of the purchase amount at the time of placing an order, and then grants a permissible delay on the remaining balance (i.e., a downstream partial trade credit). Also, in selecting an item for use, the selling price of that item is one of the decisive factors to the customers. It is well known that the higher selling price of item decreases the demand rate of that item where the lesser price has the reverse effect. Hence, the demand rate of an item is dependent on the selling price of that item. In addition, 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 to allow for: (a) the strategy that supplier offers retailer a full trade credit policy whereas the retailer offers their customers a partial trade credit policy, (b) selling price dependent demand rate, (c) a profit maximization objective and (d) deteriorating items not only deteriorate continuously but also have their expiration dates. For the 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.
RAIRO - Operations Research, 2019
In this study one obtained the optimal decision of a retailer for the replenishment rate with selling-price and credit-period dependent demand to maximize the profit. A time-varying deterioration rate was considered for those products. A credit-period was offered by the retailer to the end customer to settle the whole payments. The aim of the model was to obtain the maximum profit for the retailer based model. A solution methodology with an algorithm was used to obtain the global optimum profit. An illustrative numerical example was given to test the practical applicability of the model. Numerical study indicated that the profit was at a maximum when the permissible delay-period for payment offered by the suppliers was lies between the permissible delay-time, and the cycle time, offered by the retailer.
International Journal of Systems Science, 2001
This paper proposes, a Fuzzy economic order quantity based Inventory model for Non-Instantaneous deteriorating items under trade credit period. This model aids in minimizing the Fuzzy total inventory cost by finding an optimal replenishment policy. In this model, shortages are allowed and partially backlogged. The backlogging rate varies inversely as the waiting time for the next replenishment. All the inventory costs involved here are taken as pentagonal Fuzzy numbers. Graded mean representation method is used to defuzzify the model. The model is illustrated with the help of numerical examples. Sensitivity analysis of the optimal solution with respect to various parameters of the system is carried out and the results are discussed in detail.
International Journal of Applied Industrial Engineering (IJAIE), 2012
While developing the inventory model with shortages under permissible delay in payments, it has been observed in the literature, the researchers have not considered the fact that the retailer can earn interest on the revenue generated after fulfilling the outstanding demand as soon as he receives the new consignment at the start of the cycle. Owing to this fact, the present paper investigates the impact of interest earned from revenue generated after fulfilling the stock out at the start of the cycle on a single commodity inventory model with shortages for deteriorating item, in which the whole lot goes through an inspection on arrival before entering into inventory system, under the conditions of permissible delay in payments. The results have been demonstrated with the help of a numerical example using the tools of Matlab7.0.1.
International Journal of Production Economics, 2013
Soni 2013. Int. J. Prod. Econ., 146 (1), 259-268 proposed optimal replenishment policies for noninstantaneous deteriorating items (i.e., the product starts deteriorating after a period of no-deterioration) with price and stock sensitive demand. With a stock-dependent demand, it is desirable to have non-zero ending inventory due to potential profit resulting from the increased demand. However, Soni 2013. Int. J. Prod. Econ., 146 (1), 259-268 treated those ending inventory as fresh stocks to go through another period of non-deterioration again. Additionally, he assumed for simplicity that the replenishment cycle time T must be longer than the period of non-deterioration t d (i.e., T 4 t d ). In reality, one should consider all possible replenishment cycle time to maximize the profit. In this note, we complement the shortcomings of his model by (i) selling those ending inventory as salvages, and (ii) considering all possible replenishment cycle time, which may be shorter than the period of non-deterioration. With these modifications the repeatability of the replenishment cycle is ensured and the applicability of Soni 0 s model is strengthened. The numerical examples indicate that the global optimal solution is indeed possible in the case of T r t d .
RAIRO - Operations Research, 2019
In this study one obtained the optimal decision of a retailer for the replenishment rate with selling-price and credit-period dependent demand to maximize the profit. A time-varying deterioration rate was considered for those products. A credit-period was offered by the retailer to the end customer to settle the whole payments. The aim of the model was to obtain the maximum profit for the retailer based model. A solution methodology with an algorithm was used to obtain the global optimum profit. An illustrative numerical example was given to test the practical applicability of the model. Numerical study indicated that the profit was at a maximum when the permissible delay-period for payment offered by the suppliers was lies between the permissible delay-time, and the cycle time, offered by the retailer.
Mathematical Problems in Engineering, 2009
An inventory system for non-instantaneous deteriorating items with price-dependent demand is formulated and solved. A model is developed in which shortages are allowed and partially backlogged, where the backlogging rate is variable and dependent on the waiting time for the next replenishment. The major objective is to determine the optimal selling price, the length of time in which there is no inventory shortage, and the replenishment cycle time simultaneously such that the total profit per unit time has a maximum value. An algorithm is developed to find the optimal solution, and numerical examples are provided to illustrate the theoretical results. A sensitivity analysis of the optimal solution with respect to major parameters is also carried out.