EOQ Model For Items Research Articles

An EOQ Model for Items having Fuzzy Amelioration and Deterioration

An EOQ Model for Items having Fuzzy Amelioration and Deterioration

Efficient inventory control for imperfect quality items

In this paper, we present a general EOQ model for items that are subject to inspection for imperfect quality. Each lot that is delivered to the sorting facility undertakes a 100 per cent screening and the percentage of defective items per lot reduces according to a learning curve. The generality of the model is viewed as important both from an academic and practitioner perspective. The mathematical formulation considers arbitrary functions of time that allow the decision maker to assess the consequences of a diverse range of strategies by employing a single inventory model. A rigorous methodology is utilised to show that the solution is a unique and global optimal and a general step-by-step solution procedure is presented for continuous intra-cycle periodic review applications. The value of the temperature history and flow time through the supply chain is also used to determine an efficient policy. Furthermore, coordination mechanisms that may affect the supplier and the retailer are explored to improve inventory control at both echelons. The paper provides illustrative examples that demonstrate the application of the theoretical model in different settings and lead to the generation of interesting managerial insights.

An EOQ model for items with acceptable defective part and shortages

This paper investigates an EOQ model for items with imperfect quality and shortages backordered. It is assumed that the defective items of each lot are screened out by a 100% inspection process and then can be sold in a single batch by the end of the inspection process and that a portion of the defectives (called the acceptable defective part) can be utilized as perfect quality and hence affect the consumption of the remaining perfect quality items after the defectives are sold. By maximizing the expected profit per unit time, the optimal order quantity and the maximum backorder level are determined for the defective percentage being random. Besides, two properties of the optimal order quantity, the maximum backorder level, and the corresponding profit per unit time, are also given. Finally, a numerical example is provided to illustrate the proposed model.

Application of fuzzy sets theory in an EOQ model for items with imperfect quality and shortage backordering

This article investigates an inventory model for items received with imperfect quality and shortage backordering in the fuzzy sense, where, upon the arrival of order lot, 100% screening process is performed and the items of imperfect quality are sold as a single batch at a discounted price, prior to receiving the next shipment. The objective here is to determine the optimal order lot size and the optimal backordering quantity to maximise the annual total profit. Two fuzzy models have been proposed. We first propose a model with fuzzy defective rate. Then, the model with fuzzy defective rate and fuzzy annual demand is presented. For each case, we employ the signed distance, a ranking method for fuzzy numbers, to find the estimate of the total profit per unit time in the fuzzy sense, and then derive the corresponding optimal lot size and optimal backordering quantity. Numerical examples are provided to illustrate the results of proposed models.

EOQ Model for Items with Exponential Distribution Deterioration and Linear Trend Demand under Permissible Delay in Payments

EOQ Model for Items with Exponential Distribution Deterioration and Linear Trend Demand under Permissible Delay in Payments

AN EOQ MODEL FOR ITEMS WITH A FIXED SHELF-LIFE AND A DECLINING DEMAND RATE BASED ON TIME-TO-EXPIRY TECHNICAL NOTE

This work presents an extension of the classical EOQ model for items with a fixed shelf life and a declining demand rate due to a reduction in the quality of the item in the course of its shelf-life. The demand rate, reflecting consumer preference for fresh items, is a polynomial function of the remaining time until the expiry date of the item. A mathematical model is developed to maximize the average profit per unit time, subject to shelf-life and marginal profit limitations. We prove that based on these limitations the model has a unique optimal solution and suggest a procedure for finding the optimal cycle length. A numeric example, including a sensitivity analysis, illustrates the model.

A Note on EOQ Model for Items with Mixtures of Exponential Distribution Deterioration, Shortages and Time-varying Demand

An inventory model is considered in which inventory is depleted not only by demand, but also by deterioration. In this paper, we derive the EOQ model for inventory of items that deteriorates at a mixtures of exponential distributed rate, assuming the demand rate with a continuous function of time. Moreover, the proposed model cannot be solved directly in a closed form, thus we used the computer software IMSL MATH/LIBRARY (1989) to find the optimal reorder time Further, we also find that the optimal procedure is independent of the form of the demand rate. Finally, we also assume that the holding cost is a continuous, nonnegative and non-decreasing function of time in order to generalize EOQ model. Moreover, four numerical examples and sensitivity analyses are provided to assess the solution procedure.

An EOQ model for items with Weibull distribution deterioration, shortages and trended demand: An extension of Philip's model

The scope of the model lies in its applicability in the management of inventories of deteriorating items. It has been empirically observed that failure and life expectancy of many items can be expressed in terms of Weibull distribution. This empirical observation has prompted researchers to represent the time to deterioration of a product by a Weibull distribution. It is also seen that the demand of a consumer product usually varies with time and hence, the demand rate should be taken as time-dependent. Also there may be occasional shortages in inventory due to many reasons. Our purpose is to devise a mathematical model on inventory management taking all these factors into consideration. We, therefore, develop an economic order quantity model for the inventory of a deteriorating item, taking a time-variable demand rate and allowing shortages in inventory.This paper presents an inventory model for deteriorating items with instantaneous supply, linearly increasing demand and shortages in inventory. A three-parameter Weibull distribution is used to represent the distribution of the time to deterioration. The theory for finding the optimal solution of the problem is developed. Two numerical examples are then taken to illustrate the solution procedure.

EOQ model for items with Weibull distribution deterioration, shortages and trended demand

The present paper deals with an inventory model for deteriorating items with instantaneous supply, linearly increasing demand and shortages in inventory. A two-parameter Weibull distribution is taken to represent the time to deterioration. A theory is developed to obtain the optimal solution of the problem; it is then illustrated with the help of a numerical example. The sensitivity of the optimal solution towards changes in the values of different system parameters is also studied

An EOQ model for items with stock dependent consumption rate and exponential decay

In this paper an inventory model is developed for Initial Stock Dependent Consumption Rate and Exponential Decay Items, considering cost of the material lost due to deterioration in addition to ordering cost, carrying cost and material cost. Infinite replenishment rate is assumed and backlogging is not permitted. Expression for optimum ordering quantity has been obtained. The model is illustrated with a numerical example and the effects of various parameters on economic ordering quantity and total system cost have been analysed through sensitivity analysis.

A Generalized EOQ Model for Items with Weibull Distribution Deterioration

Abstract A generalized form of Covert and Philip's EOQ model with Weibull distribution deterioration is developed. Specifically, the 3-parameter Weibull distribution is used to represent the time to deterioration. It is shown that this model can be related to the previously developed simpler models. The solutions to two numerical examples are compared to Covert and Philip's solution.

An EOQ Model for Items with Weibull Distribution Deterioration

Abstract An inventory model is considered for deteriorating items with a variable rate of deterioration, where deterioration means decay, damage or spoilage such that the item cannot be used for its original purpose. Specifically, the Weibull distribution is used to represent the distribution of the time to deterioration. The EOQ formula is derived under conditions of constant demand, instantaneous delivery and no shortages, and it is shown that the results can be related to previously developed simpler models. A computer program is developed to provide the numerical solution and a numerical example is used to show the solution form and verify that the solution gives minimum total cost per unit time. An economic lot size model has been developed for situation in which the deterioration follows a Weibull distribution. The theoretical derivation was shown to reduce to the previous model found by Ghare and Schrader when the deterioration was exponential in nature and to a non deteriorating EOQ model when deterioration was made very small. A computer program was developed to provide a numerical solution and its use demonstrated on a numerical example. The computer program is available from the authors.