Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand

Chang, Hen‐Hong; Yao, Jing-Shing; Ouyang, Liang–Yuh

doi:10.1016/j.ejor.2004.04.044

Cited by 88 publications

(21 citation statements)

References 18 publications

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“…By our assumption, it is clear that min 06r6n i L ir ¼ L in i and max 06r6n i L ir ¼ L i0 , hence L in i 6 L i0 . Chang et al [19] already discussed that if L i 2 [L ir , L irÀ1 ], r = 1,2,. . .…”

Section: Model Formulation and Analysismentioning

confidence: 99%

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A multi-objective wholesaler–retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number

Rong

Mahapatra²,

Maiti

2008

Applied Mathematical Modelling

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This paper develops a single wholesaler and multi retailers mixture inventory distribution model for a single item involving controllable lead-time with backorder and lost sales. The retailers purchase their items from the wholesaler in lots at some intervals throughout the year to meet the customers' demand. Not to loose the demands, the retailers offer a price discount to the customers on the stock-out items. Here, it is assumed that the lead-time demands of retailers are uncertain in both stochastic and fuzzy sense, i.e., these are simultaneously random and imprecise. To implement this behavior of the lead-time demands, at first, these demands are assumed to be random, say following a normal distribution. With these random demands, the expected total cost for each retailer is obtained. Now, the mean lead-time demands (which are crisp ones) of the retailers are fuzzified. This fuzzy nature of the lead-time demands implies that the annual average demands of the retailers must be fuzzy numbers, suppose these are triangular fuzzy numbers. Using signed distance technique for defuzzification, the estimate of total costs for each retailer is derived. Therefore, the problem is reduced to optimize the crisp annual costs of wholesaler and retailers separately. The multi-objective model is solved using Global Criteria method. Numerical illustrations have been made with the help of an example taking two retailers into consideration. Mathematical analyses have been made for global pareto-optimal solutions of the multi-objective optimization problem. Sensitivity analyses have been made on backorder ratio and pareto-optimal solutions for wholesaler and different retailers are compared graphically.

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Section: Model Formulation and Analysismentioning

confidence: 99%

“…Moreover by our assumption each value of r i is obtain by the formula r i ¼ l Li þ SS i . As directed by Chang et al [19], we set reorder point as a fuzzy point with membership function…”

Section: Model Formulation and Analysismentioning

confidence: 99%

A multi-objective wholesaler–retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number

Rong

Mahapatra²,

Maiti

2008

Applied Mathematical Modelling

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“…Chang [2] introduced an EOQ model with imperfect quality item using fuzzy set theory. Also Chang et al [3] established a fuzzy mixture inventory model with fuzzy random lead time and fuzzy demand. Manna and Chaudhuri [10] presented an EOQ modelling with ramp time demand rate and time dependent deterioration rate.…”

Section: Introductionmentioning

confidence: 99%

Risk analysis in a production inventory model with fuzzy demand, variable production rate and production time dependent selling price

Patra

Mondal

2015

OPSEARCH

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In this paper a production inventory model of a single item with a variable production rate and production time dependent selling price has been introduced. Realistically it is seen that for any business concern, demand is always uncertain. Henceforth, in this model, demand of an item has been assumed to be fuzzy but its membership function is not known in prior. It is also considered that the production rate is a decreasing function of the inverse efficiency of the system. Under these circumstances, a profit function of the model has been formulated. As demand is fuzzy with unknown membership function, hence to get expected maximum profit, the diffusion method including possibility probability distribution has been used and the risk estimation values for failure to attain different profit levels have been evaluated. Finally the proposed model has been demonstrated taking a numerical example and a comparison among different types of demand such as crisp, fuzzy with triangular and trapezoidal membership value and fuzzy with unknown membership value have been shown.

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“…Another attempt to develop an inventory model in a fuzzy-stochastic environment is presented by Chang et al [6]. Their mixture inventory model with variable lead time takes back-ordering and lost sales into account.…”

Section: Genetic Algorithmsmentioning

confidence: 99%

Inventory management under uncertainty: A military application

Bean

Joubert

Luhandjula

2016

Computers & Industrial Engineering

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Fuzzy mixture inventory model involving fuzzy random variable lead time demand and fuzzy total demand

Cited by 88 publications

References 18 publications

A multi-objective wholesaler–retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number

A multi-objective wholesaler–retailers inventory-distribution model with controllable lead-time based on probabilistic fuzzy set and triangular fuzzy number

Risk analysis in a production inventory model with fuzzy demand, variable production rate and production time dependent selling price

Inventory management under uncertainty: A military application

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