Chandra K. Jaggi

A joint approach for setting unit price and the length of the credit period for a seller when end demand is price sensitive

This paper considers the seller–buyer channel in which the end demand is price sensitive and the seller may offer trade credit to the buyer. The unit price seller charged by the seller and the length of the credit period offered by the seller to the buyer both influence the final demand for the product. Hence we consider both to be policy variables for the seller. We use the case of no credit as a benchmark in our analysis. The paper provides procedures for determiningthe seller’s and the buyer’s policies under non-cooperative as well as cooperative relationships. In the non-cooperative case, we determine for the seller the optimal unit price and the length of the credit period. For the cooperative structure, we provide a procedure for characterizingPareto efficient solutions. r 2002 Elsevier Science B.V. All rights reserved.

Retailer's optimal replenishment decisions with credit-linked demand under permissible delay in payments

Usually it is assumed that the supplier would offer a fixed credit period to the retailer but the retailer in turn would not offer any credit period to its customers, which is unrealistic, because in real practice retailer might offer a credit period to its customers in order to stimulate his own demand. Moreover, it is observed that credit period offered by the retailer to its customers has a positive impact on demand of an item but the impact of credit period on demand has received a very little attention by the researchers. To incorporate this phenomenon, we assume that demand is linked to credit period offered by the retailer to the customers. This paper incorporates the concept of credit-linked demand and develops a new inventory model under two levels of trade credit policy to reflect the real-life situations. An easy-to-use algorithm is developed to determine the optimal credit as well as replenishment policy jointly for the retailer. Finally, numerical example is presented to illustrate the theoretical results followed by the sensitivity of various parameters on the optimal solution.

Credit financing in economic ordering policies of deteriorating items

This paper presents the economic ordering policies of deteriorating items in the presence of trade credit using a discounted cash-flows (DCF) approach. A DCF approach permits a proper recognition of the financial implication of the opportunity cost and out-of-pocket costs in inventory analysis. It also permits an explicit recognition of the exact timing of cash-flows associated with an inventory system. A comprehensive sensitivity analysis has also been done.

A two-warehouse inventory model for deteriorating items under permissible delay in payment with partial backlogging

Abstract This paper deals with an inventory model for single deteriorating item with two separate warehouses (one is OW and other is RW) having different preserving facilities. Demand is assumed to be known and constant. Shortages are allowed and partially backlogged with a rate dependent on the duration of waiting time up to the arrival of next lot. Here, we have considered the permissible delay in payments. However, the model formulation is different rather than that of existing models. Accordingly, several realistic cases, sub cases and scenarios have been taken into account and the corresponding problems have been formulated as non-linear constrained optimization problems along with the solution procedure. Further, to illustrate the model and also to test the validity of the same, two numerical examples have been solved. Finally, considering first example, sensitivity analyses have been performed to study the effects of changes of different parameters, like demand, ordering cost and own warehouse capacity on optimal policies.

Credit financing in economic ordering policies for defective items with allowable shortages

In the classical inventory models, the common unrealistic assumption is that all the items produced are of good quality in nature. However, in realistic environment, it can be observed that there may be some defective items in an ordered lot. These items are usually picked up during the screening process and are sold as a single lot at the end of screening process. Further, it is tacitly assumed that the supplier must be paid for the items as soon as the items are received. Whereas, in today business transaction, it is common to see that the retailer is allowed some grace period before they settle the account with the supplier. Under this scenario, a new inventory model for imperfect quality items has been developed under permissible delay in payments. Shortages are allowed and fully backlogged, which are eliminated during screening process as it has been assumed that screening rate is greater than the demand rate. This model jointly optimizes the order quantity and shortages by maximizing the expected total profit. Results have been validated with the help of numerical example using Matlab 7.0.1. Comprehensive sensitivity analysis has also been presented.

Ordering policy for decaying inventory

The problem of finding the optimum price and production levels for an exponentially decaying product is dealt with, and a numerical example is included.

Two-warehouse partial backlogging inventory model for deteriorating items with linear trend in demand under inflationary conditions

In todays business transactions, there are various reasons, namely, bulk purchase discounts, re-ordering costs, seasonality of products, inflation induced demand, etc., which force the buyer to order more than the warehouse capacity. Such situations call for additional storage space to store the excess units purchased. This additional storage space is typically a rented warehouse. Inflation plays a very interesting and significant role here: It increases the cost of goods. To safeguard from the rising prices, during the inflation regime, the organisation prefers to keep a higher inventory, thereby increasing the aggregate demand. This additional inventory needs additional storage space, which is facilitated by a rented warehouse. Ignoring the effects of the time value of money and inflation might yield misleading results. In this study, a two-warehouse inventory model with linear trend in demand under inflationary conditions having different rates of deterioration has been developed. Shortages at the owned warehouse are also allowed subject to partial backlogging. The solution methodology provided in the model helps to decide on the feasibility of renting a warehouse. Finally, findings have been illustrated with the help of numerical examples. Comprehensive sensitivity analysis has also been provided.

Supply chain model for deteriorating items with stock-dependent consumption rate and shortages under inflation and permissible delay in payment

In todays world the financial decisions of any business/retail enterprise are very crucial, as from the financial standpoint, an inventory i.e., stock on display represents a capital investment and must compete with other assets for a firms limited capital funds. Moreover, rising inflation rate directly affects the financial situation of an organization. On the contrary, the todays market is totally customer oriented which forces the retailer to invest more on stock in order to attract more and more customers. Further, this situation becomes more challenging when the retailer is dealing with deteriorating items. Apart from all this, the trade credit also plays a vital role in the financial decision making, as it helps in reducing the costs of holding stock. Keeping such a scenario in mind, this paper develops an inventory model for deteriorating items with stock-dependent consumption rate and allowable shortages under inflation and permissible delay in payments. Finally the model has been validated through numerical examples.

Credit financing in economic ordering policies for non-instantaneous deteriorating items with price dependent demand and two storage facilities

The formulation of classical deteriorating inventory models is done with the common unrealistic assumption that all the items start deteriorating as soon as they arrive in the warehouse. On the contrary, in a realistic environment, it has been observed that there are several items that do not deteriorate immediately. Items such as dry fruits, potatoes, yams and even some fruits and vegetables have a shelf life and deteriorate only after a time lag. Apart from this, in today’s competitive business world, the supplier usually offers a trade credit period to his retailers to attract more sales and the retailer considers it as an alternative to price discount. The present research proposes a two warehouse inventory model for non-instantaneous deteriorating items under trade credit based on the above phenomena, where the demand rate is assumed to be a function of the selling price. Further, shortages are completely backlogged and the interest on shortages at the beginning of the cycle has also been considered. The objective of the study is to determine the retailer’s optimal replenishment policies that maximize the average profit per unit time. Conclusively, a numerical example is presented to illustrate the applicability of the proposed model. Sensitivity analysis on key parameters is provided to reveal the managerial insights.

Effect of deterioration on two-warehouse inventory model with imperfect quality

Two-warehouse inventory model for deteriorating items with imperfect quality.100% screening is conducted immediately after receiving the order.The screening rate is assumed to be greater than the demand rate (no shortages).Imperfect items are sold as a single batch at a discounted price.The proposed model is a general framework as it includes numerous previous models. The formulation of inventory models is often done with the presumption that all items produced are of perfect quality in nature. However, in real-life scenarios, the lot that arrives in inventory includes a fraction of imperfect quality items due to faulty production or mishandling of goods. It is also a misconception that the goods preserve their characteristics during their presence in the inventory. Thus, these assumptions need to be rectified in the planning/preparation of inventory models. In order to reduce the losses due to deterioration, at times, the retailer is forced to rent other warehouses (RW) with better preserving facilities, owing to the lack of facilities in his own warehouse (OW). The retailer may also rent warehouses voluntarily to store excessive goods that have been obtained at a discounted price or in order to avoid inflation rates. The present research paper is, thus, an attempt to incorporate the aforementioned concepts to develop a new inventory model with two warehouses: for goods that have a fraction of imperfect quality items and those that are deteriorating in nature. The study also states the developed mathematical model along with the solution procedure. Further, the sensitivity analysis of the optimal solution with respect to key parameters of the inventory system has also been performed to develop the managerial insights.