Price Dependent Demand Rate Research Articles

An Optimum Inventory Policy for Exponentially Deteriorating Items, Considering Multi Variate Consumption Rate with Partial Backlogging

Customer purchasing deeds may be affected by factors such as selling price and inventory level instead of demand which is considered either constant or function of a single variable which is not feasible. Consequently, in the present study, we have considered the demand rate as a function of stock-level and selling price both. In the present study, in order to develop this model, it has been assumed that items are exponentially decaying and shortages are partially backlogged and the most realistic backlogging rate is considered. In this research, we proposed a partial backlogging inventory model for exponentially decaying items considering stock and selling price dependent demand rate in fuzzy environment. In developing the model demand rate, ordering cost, purchasing cost, holding cost, back ordering cost and opportunity cost are considered as triangular fuzzy numbers. Graded mean integration representation method is used for defuzzification. A numerical example is provided to illustrate the problem. Sensitivity analysis of the optimal solution with respect to the changes in the value of system parameters is also discussed.

A fuzzy framework for coordinating pricing and inventory policies for deteriorating items under retailer partial trade credit financing

In this paper, we proposed a generalized economic order quantity (EOQ) – based inventory model using a trade credit policy in a fuzzy sense. The trade credit policy adopted here is a two-level trade credit policy in which the supplier offers the retailer a permissible delay period M, and the retailer, in turn, partially provides customers a permissible delay period N. This study considers fuzzy EOQ model to allow for: (1) selling price dependent demand rate which is imprecise in nature, (2) a profit maximization objective and (3) an imprecise holding cost, ordering cost, purchasing cost, interest earned and interest charged rate. Besides, the cases N⩽M and N⩾M are explored thoroughly. The objective function for the retailer in fuzzy sense is defuzzified using Modified Graded Mean Integration Representation Method. For the defuzzified 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.

An Inventory Model for Decaying Items, considering Multi Variate Consumption Rate with Partial Backlogging

In most of the research articles, demand is considered either constant or a function of single variable which is not practical; customers' purchasing deeds may be affected by factors such as selling price and inventory level consequently in the present study we have considered demand rate as a function of stock-level and selling price both. Various researchers considered the situation in which shortages are either completely backlogged or completely lost which is not realistic therefore in development of this model it is assumed that shortages are partially backlogged and the most realistic backlogging rate is considered. In this research, we proposed a partial backlogging inventory model for decaying items considering stock and selling price dependent demand rate in fuzzy environment. In developing the model demand rate, ordering cost, purchasing cost, holding cost, backordering cost and opportunity cost are considered as triangular fuzzy numbers. Graded mean integration representation method is used for defuzzification. A numerical example is provided to illustrate the problem. Sensitivity analysis of the optimal solution with respect to the changes in the value of system parameters is also discussed.

Coordinating a manufacturer–retailer chain under time and price dependent demand rate

This paper deals with the coordination of a supply chain that consists of a manufacturer and a price setting retailer. The manufacturer offers a single product to the retailer, who faces time and price sensitive demand. Under explicit cost information, optimal quantity–price pairs are derived for an integrated scenario and a decentralized scenario by considering the manufacturer as the Stackelberg leader. It is shown that a conventional revenue sharing contract does not coordinate the chain. Then a coordination contract is used – with a fraction of the retailer's generated revenue, the manufacturer also shares a fraction of the retailer's cost and it is shown that the coordination contract cuts out channel conflict and leads to a win–win result. The revenue sharing fraction, wholesale price and range of cost sharing fraction, within which a win–win result is possible, are determined in exact form. A numerical example is presented to explain the proposed model.

An EOQ Model for Weibull Deteriorating Items With Price Dependent Demand

In the present paper we developed an economic order quantity model for Weibull deteriorating items with price dependent demand rate together with a replenishment policy for profit maximization. The demand rate is a continuous and differentiable function of price. The variable items deteriorate with time shortages are allowed and completely back-ordered. Further it is illustrated with the help of numerical examples.

Policy Decisions for a Price Dependent Demand Rate Inventory Model with Progressive Payments Scheme

Problem statement: In this proposed research, we developed an inventory model to formulate an optimal ordering policies for supplier who offers progressive permissible delay periods to the retailer to settle his/her account. We assumed that the annual demand rate as a decreasing function of price with constant rate of deterioration and time-varying holding cost. Shortages in inventory are allowed which is completely backlogged. Approach: The main objective of this study to frame an inventory model in real life situations. In this study, we introduced a new idea of trade credits, namely, the supplier charges the retailer progressive interest rates if the retailer prolongs its unpaid balance. By offering progressive interest rates to the retailers, a supplier, can secure competitive market advantage over the competitors and possibly improve market share profit. This study has two main purposes, first the mathematical model of an inventory system are establish under the above conditions and second demonstrate that the optimal solution not only exists but also feasible. We developed theoretical results to obtain the optimal replenishment interval by examine the explicit condition. An algorithm is given to find the flow of optimal ordering policy. Results: The results is illustrated with the help of numerical example using Mathematica software and the optimal solution of the problem is Z (p, T1) = 76.8586 at (p, T1) = (0.952656, 0.128844). Conclusion: We proposed an algorithm to find the optimal ordering policy. A numerical study has been performed to observe the sensitivity of the effect of demand parameter changes.

An EOQ model for perishable item with stock and price dependent demand rate

This paper deals with a single-item economic order quantity model where the vendor is in a position to influence demand of customers by its stock display and pricing decision. In general, most of the merchandise have a certain life time after which deterioration starts. In this situation, a good management decides to boost the sales of their products at reduced price to avoid more losses due to deterioration. Consequently, the demand of deteriorating items is an increasing function of reduction rate on selling price. It is thus confronted with simultaneous reduction on selling price and replenishment quantity decisions, which would jointly maximise the expected average profit over an infinite planning horizon. Computational aspects of the proposed model are discussed, and formulation is shown to give successful results on test problems. The sensitivity of the optimal solution to changes in the values of different parameters is also examined.

COORDINATED PRICING AND BASE-STOCK POLICIES FOR AN ITEM WITH PRICE AND STOCK-DEPENDENT DEMAND SUBJECT TO DECAY AND FIXED LIFETIME

ABSTRACT We consider a firm who sells a perishable item that is subject to effects of decay and fixed shelf lifetime, facing a price and stock-level dependent demand rate. We assume the firm adopts the base-stock replenishment and the first-in-first-out issuing policies. Our model is a generalized version of the previous work by considering the retail price as a decision variable and taking into account the effect of decay. The objective of the model is to jointly determine the optimal selling price, base-stock level, and inventory cycle over an infinite planning horizon so that the net profit per time unit is maximized. The profit-maximizing problem is formulated as a multivariate optimization model, solved by an iterative search process combined with an enumeration scheme. An intensive numerical study shows that the pricing scheme can be an effective mechanism in profit improvement.

Joint pricing and ordering policy for a deteriorating inventory

An inventory model is developed for a deteriorating item with a price-dependent demand rate. The rate of deterioration is taken to be time-proportional and a power law form of the price-dependence of demand is considered. The model is solved analytically and is illustrated with a numerical example.

An inventory system of ameliorating items for price dependent demand rate

This study is concerned with the development of inventory model for ameliorating items. These items include the fast growing animals like duck, pigs, broiler, etc. in poultry farm, high breed fishes in bhery (pond), etc. When these items stay at farm or bhery or in the sales counter or distribution centre, the stock increases due to growth and decreases also due to death. As a result, both amelioration and deterioration effect are seen simultaneously for this type of inventory system. In this paper, we have developed an instantaneous replenishment inventory model of these ameliorating items for prescribed time period. The rate of amelioration follows the Weibull distribution and the demand rate is assumed to be a function of selling price of an item. Shortages are not allowed. The salvage values of deteriorated units due to death of such items and the cost for feeding the life stocks are taken into account. The model is numerically illustrated with the demand rate dependent linearly on the selling price of the item. Finally, the effect of amelioration as well as the deterioration on an inventory policy has been studied. The sensitivity of the average profit with respect to the amelioration parameters has also been presented with the help of Analysis of Variance method.