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Journal Article•DOI•

An inventory model for deteriorating items with time-dependent demand and time-varying holding cost under partial backlogging

Vinod Kumar Mishra, Lal Sahab Singh1, Rakesh Kumar1•
Dr. Ram Manohar Lohia Avadh University1
08 Apr 2013-Journal of Industrial Engineering, International (Springer Berlin Heidelberg)-Vol. 9, Iss: 1, pp 1-5
TL;DR: In this article, a deterministic inventory model with time-dependent demand and time-varying holding cost where deterioration is time proportional is considered, and the model is solved analytically by minimizing the total inventory cost.
Abstract: In this paper, we considered a deterministic inventory model with time-dependent demand and time-varying holding cost where deterioration is time proportional. The model considered here allows for shortages, and the demand is partially backlogged. The model is solved analytically by minimizing the total inventory cost. The result is illustrated with numerical example for the model. The model can be applied to optimize the total inventory cost for the business enterprises where both the holding cost and deterioration rate are time dependent.

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Citations
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Journal Article•DOI•
Literature review of deteriorating inventory models by key topics from 2012 to 2015

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Larissa Janssen1, Thorsten Claus2, Jürgen Sauer•
Jade University of Applied Sciences1, Dresden University of Technology2
01 Dec 2016-International Journal of Production Economics
TL;DR: An up-to-date review of perishable inventory models, but also of the joint key topics of publications from January 2012 until December 2015 in the research area of deteriorating inventory models is given.

206 citations

Journal Article•DOI•
Inventory and pricing model with price-dependent demand, time-varying holding cost, and quantity discounts

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Hesham K. Alfares1, Ahmed M. Ghaithan1•
King Fahd University of Petroleum and Minerals1
01 Apr 2016-Computers & Industrial Engineering
TL;DR: An inventory model is presented with a selling price-dependent demand rate, a storage time-dependent holding cost, and an order size-dependent purchase cost based on all-units quantity discount.

124 citations

Journal Article•DOI•
Analysis of inventory control model with shortage under time-dependent demand and time-varying holding cost including stochastic deterioration

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Magfura Pervin1, Sankar Kumar Roy1, Gerhard-Wilhelm Weber2•
Vidyasagar University1, Middle East Technical University2
01 Jan 2018-Annals of Operations Research
TL;DR: The main purpose of the paper is to investigate the optimal retailer’s replenishment decisions for deteriorating items including time-dependent demand for demonstrating more practical circumstances within economic-order quantity frameworks.
Abstract: In this paper, a deterministic inventory control model with deterioration is developed. Here, the deterioration rate follows stochastic deterioration, especially Weibull distribution deterioration. A time-dependent demand approach is introduced to show the applicability of our proposed model and to be up-to-date with respect to time. The main purpose of the paper is to investigate the optimal retailer’s replenishment decisions for deteriorating items including time-dependent demand for demonstrating more practical circumstances within economic-order quantity frameworks. Keeping in mind the criterion of modern era, we consider that the holding cost is totally dependent on time, and shortages are allowed for this model. Subject to the formulated model, we minimize the total inventory cost. The mathematical model is explored by numerical examples to validate the proposed model. A sensitivity analysis of the optimal solution with regard to important parameters is also carried out to elaborate the quality, e.g., stability, of our result and to possibly modify our model. The paper ends with a conclusion and an outlook to future studies.

91 citations

Cites background from "An inventory model for deterioratin..."

  • ...In a few inventory models like Giri et al. (1996) and Mishra et al. (2013), the holding cost as well as the demand function were considered as time dependent....

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Journal Article•DOI•
Analysis of an EOQ inventory model with partial backordering and non-linear unit holding cost

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Luis A. San-José1, Joaquín Sicilia2, Juan García-Laguna1•
University of Valladolid1, University of La Laguna2
01 Jul 2015-Omega-international Journal of Management Science
TL;DR: In this article, an economic order quantity inventory model is analyzed, considering that the unit cumulative holding cost has two significant components: a fixed cost which represents the cost of accommodating the item in the warehouse and a variable cost given by a potential function of the length of time over which the item is held in stock.
Abstract: In this paper, an economic order quantity inventory model is analyzed, considering that the unit cumulative holding cost has two significant components: a fixed cost which represents the cost of accommodating the item in the warehouse and a variable cost given by a potential function of the length of time over which the item is held in stock. Shortages are allowed and, during the stockout period, only a fraction of demand is partially backordered. The backordering cost includes a fixed cost and a cost linearly dependent on the length of time for which backorder exists. A solution procedure is developed for determining the optimal inventory policy. Moreover, to illustrate the effects of some parameters on the optimal policy and the minimum total inventory cost, a numerical study is developed.

67 citations

Journal Article•DOI•
Multi-item EOQ model with nonlinear unit holding cost and partial backordering: moth-flame optimization algorithm

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Soheyl Khalilpourazari1, Seyed Hamid Reza Pasandideh1•
Kharazmi University1
02 Jan 2017-Journal of Industrial and Production Engineering
TL;DR: In this paper, a multi-item multi-constrained economic order quantity model with nonlinear unit holding cost and partial backordering is proposed, where different technical, physical, and strategic constraints are considered such as available budget, warehouse capacity, total permissible holding cost, and total permissible backordering cost constraints.
Abstract: In this paper, a multi-item multi-constrained Economic Order Quantity model with nonlinear unit holding cost and partial backordering is proposed. To develop an applicable model, different technical, physical, and strategic constraints are considered such as available budget, warehouse capacity, total permissible holding cost, and total permissible backordering cost constraints. The goal is to determine the lengths of inventory cycles, where the inventory level is positive and negative such that the total inventory costs are minimized. In addition, backordering rate during shortage period for each product is considered as a decision variable which can significantly reduce the total inventory costs. Due to complexity and nonlinearity of the proposed model, interior-point method and Moth-Flame optimization algorithm are utilized to solve the model in different sizes. At the end, the performance of the solution methods is compared statistically considering three measures to determine the superior sol...

55 citations

Cites methods from "An inventory model for deterioratin..."

  • ...[18] developed an EOQ model with partial backorders with linear and time-dependent holding cost for deteriorating items....

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References
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Journal Article•DOI•
Recent trends in modeling of deteriorating inventory

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Suresh Kumar Goyal1, Bibhas C. Giri2•
Concordia University Wisconsin1, Vivekananda College, Madhyamgram2
01 Oct 2001-European Journal of Operational Research
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

"An inventory model for deterioratin..." refers background in this paper

  • ...Goyal and Giri (2001) gave recent trends of modeling in deteriorating item inventory....

    [...]

A model for an exponentially decaying inventory

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P. M. Ghare
01 Jan 1963

710 citations

"An inventory model for deterioratin..." refers background in this paper

  • ...Ghare and Schrader (1963) developed a model for an exponentially decaying inventory....

    [...]

Journal Article•DOI•
(T, S i ) Policy Inventory Model for Deteriorating Items with Time Proportional Demand

[...]

Upendra Dave1, L. K. Patel1•
Gujarat University1
01 Feb 1981-Journal of the Operational Research Society
TL;DR: In this article, an EOQ model is reconsidered in which the demand rate is changing linearly with time and the deterioration is assumed to be a constant fraction of the onhand inventory.
Abstract: An EOQ model is reconsidered here in which the demand rate is changing linearly with time and the deterioration is assumed to be a constant fraction of the onhand inventory The planning horizon is finite and known and the replenishment periods are assumed to be constant The problem is to find the optimal number of replenishments, which are instantaneous When there is no deterioration, the model developed is related to the corresponding model for nondeteriorating items An example followed by sensitivity analysis is given to illustrate the derived results

424 citations

"An inventory model for deterioratin..." refers background in this paper

  • ...Dave and Patel (1981) were the first to study a deteriorating inventory with linear increasing demand when shortages are not allowed....

    [...]

Journal Article•DOI•
Optimal pricing and lot-sizing under conditions of perishability and partial backordering

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Prakash L. Abad1•
McMaster University1
01 Aug 1996-Management Science
TL;DR: In this article, a generalized model of dynamic pricing and lot-sizing by a reseller who sells a perishable good is formulated, where when it is economic to backlog demand, the reseller can plan for periods of shortage during which demand can be partially backordered.
Abstract: We formulate a generalized model of dynamic pricing and lot-sizing by a reseller who sells a perishable good. We assume that when it is economic to backlog demand, the reseller can plan for periods of shortage during which demand can be partially backordered. When the good is highly perishable, the reseller may need to backlog demand in order to market the good at a reasonable price. We present a simple solution procedure for solving the optimization problem. The procedure entails solving first a single nonlinear equation and then, if required, two nonlinear equations.

407 citations

"An inventory model for deterioratin..." refers background or methods in this paper

  • ...They made the work of Abad (1996, 2001) more realistic and applicable in practice. Mandal (2010) gave an EOQ inventory model for Weibull-distributed deteriorating items under ramp-type demand and shortages. Mishra and Singh (2011a, b) gave an inventory model for ramp-type demand, time-dependent deteriorating items with salvage value and shortages and deteriorating inventory model for time-dependent demand and holding cost with partial backlogging. Hung (2011) gave an inventory model with generalized-type demand, deterioration, and backorder rates....

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  • ...They made the work of Abad (1996, 2001) more realistic and applicable in practice....

    [...]

  • ...They made the work of Abad (1996, 2001) more realistic and applicable in practice. Mandal (2010) gave an EOQ inventory model for Weibull-distributed deteriorating items under ramp-type demand and shortages. Mishra and Singh (2011a, b) gave an inventory model for ramp-type demand, time-dependent deteriorating items with salvage value and shortages and deteriorating inventory model for time-dependent demand and holding cost with partial backlogging. Hung (2011) gave an inventory model with generalized-type demand, deterioration, and backorder rates. In classical inventory models, the demand rate and holding cost is assumed to be constant. In reality, the demand and holding cost for physical goods may be time dependent. Time also plays an important role in the inventory system; therefore, in this inventory system, we consider that demand and holding cost are time dependent. In this paper, we made the work of Roy (2008) more realistic by considering demand rate and holding cost as linear functions of time and developed an inventory model for deteriorating items where deterioration rate is expressed as a linearly increasing function of time....

    [...]

  • ...They made the work of Abad (1996, 2001) more realistic and applicable in practice. Mandal (2010) gave an EOQ inventory model for Weibull-distributed deteriorating items under ramp-type demand and shortages....

    [...]

Journal Article•DOI•
An EOQ model for deteriorating items with time varying demand and partial backlogging

[...]

Horng-Jinh Chang1, Chung-Yuan Dye1•
Tamkang University1
17 Nov 1999-Journal of the Operational Research Society
TL;DR: This paper focuses on the effect of the backlogging rate on the economic order quantity decision and Numerical examples are presented to illustrate the model.
Abstract: In the classical economic order quantity model, it is often assumed that the shortages are either completely backlogged or completely lost. However, in some inventory systems, it is more reasonable to assume that the backlogging rate is dependent on the length of the waiting time for the next replenishment. The longer the waiting time is, the smaller the backlogging rate would be. In this paper, we focus on the effect of the backlogging rate on the economic order quantity decision. Numerical examples are presented to illustrate the model.

299 citations

Related Papers (5)
A model for an exponentially decaying inventory

[...]

01 Jan 1963
P. M. Ghare
(T, S i ) Policy Inventory Model for Deteriorating Items with Time Proportional Demand

[...]

01 Feb 1981-Journal of the Operational Research Society
Upendra Dave, L. K. Patel
An EOQ Model for Items with Weibull Distribution Deterioration

[...]

01 Dec 1973-Iie Transactions
Richard P. Covert, George C. Philip
Recent trends in modeling of deteriorating inventory

[...]

01 Oct 2001-European Journal of Operational Research
Suresh Kumar Goyal, Bibhas C. Giri
An inventory model for deteriorating items under stock-dependent demand and controllable deterioration rate

[...]

01 Sep 2012-Computers & Industrial Engineering
Yu-Ping Lee, Chung-Yuan Dye