A continuous review production–inventory system in fuzzy random environment: Minmax distribution free procedure

Kumar, Ravi Shankar; Goswami, Adrijit

doi:10.1016/j.cie.2014.10.022

Cited by 36 publications

(13 citation statements)

References 32 publications

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“…Datta et al [21,22] already developed EOQ and Production inventory model under fuzzy stochastic environment but they took lead-time as constant but did not control it. Here we consider lead-time is a decision variable and control it by paying an extra crashing cost.…”

Section: Mathematical Modeling and Analysismentioning

confidence: 98%

On an EOQ model with service level constraint under fuzzy-stochastic demand and variable lead-time

Rong

Maiti

2015

Applied Mathematical Modelling

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a b s t r a c tThis study deals with an EOQ inventory model with fuzzy stochastic demand and controllable lead-time by relaxing the assumption that demand during lead-time follows a specific probability distribution. Here considering the unsatisfied demands to be partially backordered, both lead-time and order quantity are considered as the decision variables. Instead of having a stockout term in the objective function, a service level constraint, which implies that the stockout level per cycle is bounded, is added to the model. This study, we provide an elegant methodology to determine the optimal order quantity and reorder point such that total expected annual cost in fuzzy sense has a minimum value. Finally the proposed model is illustrated by a numerical example.

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Section: Mathematical Modeling and Analysismentioning

confidence: 98%

On an EOQ model with service level constraint under fuzzy-stochastic demand and variable lead-time

Rong

Maiti

2015

Applied Mathematical Modelling

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“…Mostly, the researchers considered constant demand by considering a distribution-free approach for lead-time demand. However, several researchers consider fuzzy demand (see for reference Sarkar and Mahapatra [53], Kumar and Goswami [54], Soni et al [55], and Tayyab et al [56]) with the distribution-free approach. Demand in existing literature is considered to be a triangular fuzzy number, so for this we are assuming it is a triangular number [56][57][58].…”

Section: Fuzzificationmentioning

confidence: 99%

Coordinating Supply-Chain Management under Stochastic Fuzzy Environment and Lead-Time Reduction

Malik

Sarkar

2019

Mathematics

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In this paper, a supply-chain (SC) coordination method based on the lead-time crashing is proposed for a seller–buyer system. By considering different transportation modes, we control the lead-time (LT) variability. For the first time, we have attempted to determine the impact of the reliable and unreliable seller in a continuous-review supply-chain model under the stochastic environment. The authors discussed two reliability cases for the seller. First, we consider the seller is unreliable and in the second case, the seller is reliable. In addition, the demand during the lead time is stochastic with the known mean and variance. The proposed approach tries to find an optimal solution that performs well without a specific probability distribution. Besides, a discrete investment is made to reduce the setup cost, which will indirectly help supply-chain members to increase the total profit of the system. In the proposed model, the seller motivates the buyer by reducing lead time to take part in coordinating decision-making for the system’s profit optimization. We derive the coordination conditions for both members, the seller and the buyer, under which they are convinced to take part in the cooperative decision-making plan. Therefore, lead-time crashing is the proposed incentive mechanism for collaborative supply-chain management. We use a fixed-charge step function to calculate the lead-time crashing cost for slow and fast shipping mode. We give two numerical examples to validate the proposed models and demonstrate the service-level enhancement under the collaborative supply-chain management in case of an unreliable seller. Concluding remarks and future extensions are discussed at the end.

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“…(a) The construction of new inventory models: Qi et al [2],Şen and Talebian [3], Wang et al [4], Kumar and Goswami [5], Sarkar et al [6], Yu and Zhai [7], Qin and Kar [8], Yu and Zhen [9], Moon et al [10], Tajbakhsh [11], Gallego andŞAhin [12], Perakis and Roeis [13], Ahmed et al [14], Levin et al [15], Mostard et al [16], Alfares and Elmorra [17], Lin [18], Hariga and Ben-Daya [19], Talluri and Van Ryzin [20], and Gallego [21]. (b) The development of new solution procedures: Fu et al [22], Postek et al [23], Zhou et al [24], Wu and Warsing [25], Popescu [26], Gallego et al [27], Chung et al [28], Puerto and Fernández [29], Tyworth and O'Neill [30], Moon and Choi [31], Moon and Yun [32], and Baganha et al [33].…”

Section: Introductionmentioning

confidence: 99%

The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models

Hung

Yang

2019

Mathematics

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For inventory models with unknown distribution demand, during shortages, researchers used the first and the second moments to derive an upper bound for the worst case, that is the min-max distribution-free procedure for inventory models. They applied an iterative method to generate a sequence to obtain the optimal order quantity. A researcher developed a three-sequence proof for the convergence of the order quantity sequence. We directly provide proof for the original order quantity sequence. Under our proof, we can construct an increasing sequence and a decreasing sequence that both converge to the optimal order quantity such that we can obtain the optimal solution within the predesigned threshold value.

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A continuous review production–inventory system in fuzzy random environment: Minmax distribution free procedure

Cited by 36 publications

References 32 publications

On an EOQ model with service level constraint under fuzzy-stochastic demand and variable lead-time

On an EOQ model with service level constraint under fuzzy-stochastic demand and variable lead-time

Coordinating Supply-Chain Management under Stochastic Fuzzy Environment and Lead-Time Reduction

The Convergence of Gallego’s Iterative Method for Distribution-Free Inventory Models

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