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Present Value Formulation of Economic Lot-Size Model for Inventory System with Variable Deteriorating Rate of Items

TL;DR: In this article, an alternative numerical analysis is described to examine the present value of the discounted costs over an infinite horizon, where the deterioration rate is a continuou s random variable and follows a two parameter weibull distribution.
Abstract: The analysis of the deterministic economic order quantity problem for time dependent deterioration of units seeks to minimize the average cost of inventory systems. An alternative numerical analysis is described in this paper to examine the present value of the discounted costs over an infinite horizon. The deterioration rate is a continuou s random variable and follows a two parameter weibull distribution. Also a sensitivity analysis is studied by some numerical illustrations. Comparison of two solutions is also discussed.

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Citations
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01 Jan 2009
TL;DR: In this paper, a mathematical model is developed to obtain optimal ordering policy of time dependent deteriorating item when demand rate is dependent on displayed stock level and frequency of advertisement through media, the objective is to minimize total cost.
Abstract: In this study, a mathematical model is developed to obtain optimal ordering policy of time dependent deteriorating item when demand rate is dependent on displayed stock level and frequency of advertisement through media. Shortages are not allowed. The objective is to minimize total cost. The significant features and the results are studied with the help of a numerical example. The effect of changes in the demand parameter, deterioration rate ( α -constant deterioration, β- time dependent deterioration), rate of frequency of advertisements, stock dependent parameter and salvage parameter for deteriorated items on total cycle time, total cost and on procurement quantity is studied numerically. Keyword⎯Lot-size, Time dependent deterioration, Advertisement frequency, Procurement quantity and total cost.

7 citations

Journal Article
TL;DR: In this article, the effects of the inflation rate on purchase price, ordering price and inventory holding price, time dependent deterioration of units and permissible delay in payment are discussed, and an inventory model under a situation in which the supplier offers the purchaser some credit period if the purchaser orders a large quantity.
Abstract: This article deals with an inventory model under a situation in which the supplier offers the purchaser some credit period if the purchaser orders a large quantity. Shortages are not allowed. The effects of the inflation rate on purchase price, ordering price and inventory holding price, time dependent deterioration of units and permissible delay in payment are discussed. A mathemat- ical model is developed when units in inventory are subject to time dependent deterioration under inflation when the supplier offers a permissible delay to the purchaser if the order quantity is greater than or equal to a pre-specified quantity. Optimal solution is ob- tained and algorithm is given to find the optimal order quantity and replenishment time, which minimizes the total cost of an inventory system in different scenarios. The paper concludes with a numerical example to illustrate the theoretical results and interdependence of parameters is studied for the optimal solutions.

1 citations

References
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Journal ArticleDOI
TL;DR: The motivations, extensions and generalizations of various models in each sub-class have been discussed in brief to bring out pertinent information regarding model developments in the last decade.

1,247 citations


"Present Value Formulation of Econom..." refers background in this paper

  • ...Raafat (1991), Shah and Shah (2000), and Goyal and Giri (2001) gave up-to-date survey of literature for inventory models when units in inventory are subject to deterioration....

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  • ...Hence, relation (6) is minimum for the obtained value of T....

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Journal ArticleDOI
TL;DR: A complete and up-to-date survey of published inventory literature for the deteriorating (decaying) inventory models and a classification scheme is presented along with suggestions for future research.
Abstract: This paper presents a complete and up-to-date survey of published inventory literature for the deteriorating (decaying) inventory models. More specifically, those papers are addressed that consider the effect of deterioration as a function of the on-hand level of inventory. The basic features, extensions and generalization of various models are discussed. A classification scheme is presented along with suggestions for future research.

812 citations


"Present Value Formulation of Econom..." refers background in this paper

  • ...Raafat (1991), Shah and Shah (2000), and Goyal and Giri (2001) gave up-to-date survey of literature for inventory models when units in inventory are subject to deterioration....

    [...]

Journal ArticleDOI
TL;DR: In this paper, 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.
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 det...

705 citations

Journal ArticleDOI
TL;DR: An inventory model for deteriorating items with instantaneous supply, linearly increasing demand and shortages in inventory is presented and the theory for finding the optimal solution of the problem is developed.

180 citations


"Present Value Formulation of Econom..." refers background in this paper

  • ...Chakrabarty et al (1998) derived model for deteriorating items with instantaneous supply, trended demand and shortages in inventory....

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  • ..., R Q(t) (t) t d Q(t) d − = +θ T t 0 ≤ ≤ (1)...

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Journal ArticleDOI
TL;DR: In this paper, the authors examined the present value of discounted costs over an infinite horizon, and discussed the differences in the solutions and implications of errors using the two methodologies, and proposed an alternative approach described in this paper.
Abstract: The usual analysis of the deterministic economic order quantity problem seeks to minimize the average cost of inventory ordering and holding costs per unit time. An alternative approach described in this paper examines the present value of discounted costs over an infinite horizon. Differences in the solutions and implications of errors using the two methodologies are discussed.

109 citations


"Present Value Formulation of Econom..." refers methods in this paper

  • ...Trippi and Lewin (1974) gave the discounted cash-flows (DCF)/(Net Present Value (NPV)) approach for the analysis of the basic EOQ model....

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