Chandra K. Jaggi

Bio: Chandra K. Jaggi is an academic researcher from University of Delhi. The author has contributed to research in topics: Trade credit & Supply chain. The author has an hindex of 25, co-authored 127 publications receiving 3066 citations.

Ordering Policies of Deteriorating Items under Permissible Delay in Payments

Abstract: In developing mathematical models in inventory control it is assumed that payment will be made to the supplier for the goods immediately after receiving the consignment. However, in practice, it is found that the supplier allows a certain fixed period to settle the account. During this fixed period no interest is charged by the supplier, but beyond this period interest is charged under the terms and conditions agreed upon and, moreover, interest can be earned on the revenue received during the credit period. In this paper an attempt has been made to obtain the optimum order quantity of deteriorating items under a permissible delay in payments. A numerical example is also given. Over the last two decades a lot of work has been published for controlling the inventory of deteriorating items. The analysis of decaying inventory problems began with Ghare and Schrader1, who developed a simple economic order quantity model with a constant rate of decay. Covert and Philip2 extended Ghare and Schrader's model and obtained an economic order quantity model for a variable rate of deterioration by assuming a two-parameter Weibull distribution. Misra3 developed the first production lot size model in which both a constant and variable rate of deterioration were considered and obtained approximate expressions for the production lot size with no backlogging. Furthermore, while developing a mathematical model in inventory control, it is assumed that the payment will be made to the suppliers for the goods immediately after receiving the consignment. However, in day-to-day dealing, it is found that a supplier allows a certain fixed period to settle the account. During this fixed period no interest is charged by the supplier, but beyond this period interest is charged by the supplier under the terms and conditions agreed upon, since inventories are usually financed through debt or equity. In case of debt financing, it is often a short-term financing. Thus, interest paid here is nothing but the cost of capital or opportunity cost. Also, short-term loans can be thought of as having been taken from the suppliers on the expiry of the credit period. However, before the account has to be settled, the customer can sell the goods and continues to accumulate revenue and earn interest instead of paying the overdraft that is necessary if the supplier requires settlement of the account after replenishment. Interest earned can be thought of as a return on investment since the money generated through revenue can be ploughed back into the business. Therefore, it makes economic sense for the customer to delay the settlement of the replenishment account up to the last day of the credit period allowed by the supplier. If the credit period is less than the cycle length, the customer continues to accumulate revenue and earn interest on it for the rest of the period in the cycle, from the stock remaining beyond the credit period. This point was not considered by Goyal4. The primary benefit of taking trade credit is that one can have savings in purchase cost and opportunity cost, which become quite relevant for deteriorating items. In such cases one has to procure more units than required in the given cycle to account for the deteriorating effect. In particular, when the unit purchase cost is high and decay is continuous, the saving due to delayed payment appears to be more significant than when the decay is continuous but

An ordering policy for deteriorating items with allowable shortage and permissible delay in payment

Abstract: In many inventory situations, the purchaser is allowed a permissible period to pay back the cost of goods bought without paying any interest. Depending on the length of that payment period, the purchaser can earn interest on the sales of the inventory. This paper develops a model to determine an optimal ordering policy for deteriorating items under permissible delay of payment and allowable shortage. Different facets of the permissible delays in payment are discussed, and this generalized model exhibits a set of solutions that reduces to an existing model. Results are discussed and demonstrated with an illustrative example.

Applied Mathematics and Computation

Abstract: The work is giving estimations of the discrepancy between solutions of the initial and the homogenized problems for a one{dimensional second order elliptic operators with random coeecients satisfying strong or uniform mixing conditions. We obtain several sharp estimates in terms of the corresponding mixing coeecient. Abstract. In the theory of homogenisation it is of particular interest to determine the classes of problems which are stable on taking the homogenisation limits. A notable situation where the limit enlarges the class of original problems is known as memory (nonlocal) eeects. A number of results in that direction has been obtained for linear problems. Tartar (1990) innitiated the study of the eeective equation corresponding to nonlinear equation: @ t u n + a n u 2 n = f: Signiicant progress has been hampered by the complexity of required computations needed in order to obtain the terms in power{series expansion. We propose a method which overcomes that diiculty by introducing graphs representing the domain of integration of the integrals in each term. The graphs are relatively simple, it is easy to calculate with them and they give us a clear image of the form of each term. The method allows us to discuss the form of the eeective equation and the convergence of power{series expansions. The feasibility of our method for other types of nonlinearities will be discussed as well.

Financing the Newsvendor: Supplier vs. Bank, and the Structure of Optimal Trade Credit Contracts

Abstract: We consider a supply chain with a retailer and a supplier: A newsvendor-like retailer has a single opportunity to order a product from a supplier to satisfy future uncertain demand. Both the retailer and supplier are capital constrained and in need of short-term financing. In the presence of bankruptcy risks for both the retailer and supplier, we model their strategic interaction as a Stackelberg game with the supplier as the leader. We use the supplier early payment discount scheme as a decision framework to analyze all decisions involved in optimally structuring the trade credit contract (discounted wholesale price if paying early, financing rate if delaying payment) from the supplier's perspective. Under mild assumptions we conclude that a risk-neutral supplier should always finance the retailer at rates less than or equal to the risk-free rate. The retailer, if offered an optimally structured trade credit contract, will always prefer supplier financing to bank financing. Furthermore, under optimal trade credit contracts, both the supplier's profit and supply chain efficiency improve, and the retailer might improve his profits relative to under bank financing (or equivalently, a rich retailer under wholesale price contracts), depending on his current “wealth” (working capital and collateral).