Note on inventory model with a mixture of back orders and lost sales

Chu, Peter C.; Yang, Kuang-Yao; Liang, Shing-Ko; Niu, Thomas

doi:10.1016/s0377-2217(03)00416-8

Cited by 31 publications

(28 citation statements)

References 16 publications

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“…Therefore, in these cases, the proportion of customers willing to wait may not be a decreasing function with respect to the waiting time. The papers of Vrat (1990, 1995), Chu et al (2004), Ouyang et al (2003), Zhou et al (2003), Zhou (2003) and Dye et al (2006) follow this assumption. More concretely, the above authors consider that the fraction of backlogged demand depends linearly on the number of backlogging orders at that instant, i.e., on the net inventory level.…”

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confidence: 88%

An optimal replenishment policy for an EOQ model with partial backlogging

Sicilia

San-José²,

García-Laguna

2008

Ann Oper Res

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We study an inventory system where demand on the stockout period is partially backlogged. The backlogged demand ratio is a mixture of two exponential functions. The shortage cost has two significant costs: the unit backorder cost (which includes a fixed cost and a cost proportional to the length of time for which the backorder exists) and the cost of lost sales. A general procedure to determine the optimal policy and the minimum inventory cost for all the parameter values is developed. This model generalizes several inventory systems analyzed by different authors. Numerical examples are used to illustrate the theoretical results.Keywords Inventory systems · EOQ models · Partial backlogging Inventory models where demand is partially backlogged during the stockout period focus considerable attention in Inventory Control nowadays. This situation of partial backlogging has been modeled focusing on different aspects. Several authors model partial backlogging using the concept of impatience. This word was used by Hanssmann (1962) to model extreme shortage situations (complete backorder case and full lost sales case). Ten years later, Posner and Yansouni (1972) introduced the impatient customer concept. Later on, Abad (1996) was the first to introduce the supposition that the fraction of backlogged J. Sicilia ( )

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confidence: 88%

An optimal replenishment policy for an EOQ model with partial backlogging

Sicilia

San-José²,

García-Laguna

2008

Ann Oper Res

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“…In this model, the production rate was finite and in accordance with the time-dependent demand rate. Chu et al (2004) developed a paper with the aim of evaluating the inventory model presented by Padmanabhan and Vrat (1990) with a combination of lost sale costs and backlogging. They considered some criteria for optimal solution of the total cost function.…”

Section: Uniform Demandmentioning

confidence: 99%

“…Dye et al (2006) completed the model presented by Chu et al (2004) and Padmanabhan and Vrat (1990) by considering purchasing cost and lost sale cost and varied purchasing cost. It can be said that Chu et al (2004) presented the required conditions for the uniqueness of the optimal solution of Padmanabhan and Vrat (1990) study. Chern et al (2008) developed inventory control model with the shortage and inflation assumption.…”

Section: Times -Dependent Demandmentioning

confidence: 99%

Inventory control with deteriorating items: A state-of-the-art literature review

Khanlarzade¹,

Yegane²,

Kamalabadi³

et al. 2014

10.5267/j.ijiec

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The present study reviews different studies on inventory control of deteriorating items in chain supply published over the period 1963-2013. The study investigates supply chain of the items in terms of various perspectives. Finally, the summary of the studies is shown in two tables for oneechelon and multi-echelon supply chain including the main information and assumptions of each paper. In the mentioned tables, the papers were classified in terms of the type of demand rate, deterioration rate, solution procedure and findings. It can be said that no analysis on the results was done in the present study and it can be only used as a good reference in the study field for other researchers.

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“…Many researchers dealing with inventory models with varying costs for example, Chu et al [6] and Fergany [8] illustrated probabilistic multi-item inventory model with varying mixture shortage cost under restrictions. Fergany and El-Wakeel [10] illustrated probabilistic single item inventory problem with varying order cost under two linear constraints.…”

Section: Introductionmentioning

confidence: 99%

Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment

Ferganya

Hollahb²

2018

JAM

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This paper proposed a multi-item multi-source probabilistic periodic review inventory model under a varying holding cost constraint with zero lead time when: (1) the stock level decreases at a uniform rate over the cycle. (2) some costs are varying. (3) the demand is a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Rayleigh, Erlang distributions).The objective function under a constraint is imposed here in crisp and fuzzy environment. The objective is to find the optimal maximum inventory level for a given review time that minimize the expected annual total cost. Furthermore, a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations. The cost parameters in real inventory systems and other parameters such as price, marketing and service elasticity to demand are imprecise and uncertain in nature. Since the proposed model is in a fuzzy environment, a fuzzy decision should be made to meet the decision criteria, and the results should be fuzzy as well. Fuzzy sets introduced by many researchers as a mathematical way of representing impreciseness or vagueness in everyday life. Rong et al.[12] presented a multi-objective wholesaler-retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number. Sadjadi et al. [13] introduced fuzzy pricing and marketing planning model using a geometric programming approach.This paper is formulated a multi-item multi-source periodic review inventory problem with a varying holding cost constraint when the holding and backlogged costs are varying. Also, shortages are permitted but fully backlogged and the demand considered to be a random variable that follows some continuous distributions as (two-parameter exponential, Kumerswamy, Gamma, Beta, Erlang, Raylieph distributions) without lead time. Also, the cost parameters under a constraint is considered here in crisp and fuzzy environment. The problem has been solved by Lagrange multiplier technique. The objective is to find the optimal maximum inventory level for a given review time which minimize the expected annual total cost under a restriction. And a comparison between given distributions is made to find the optimal distribution that achieves the model under considerations The results of the numerical example are got by Mathematica program.

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Note on inventory model with a mixture of back orders and lost sales

Cited by 31 publications

References 16 publications

An optimal replenishment policy for an EOQ model with partial backlogging

An optimal replenishment policy for an EOQ model with partial backlogging

Inventory control with deteriorating items: A state-of-the-art literature review

Multi-Source Backlogged Probabilistic Inventory Model for Crisp and Fuzzy Environment

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