*Periodicity.:*

**March - April 2020***e-ISSN......:*

**2236-269X**### Multi-item a supply chain production inventory model of time dependent production rate and demand rate under space constraint in fuzzy environment

#### Abstract

In this paper, we have developed an integrated production inventory model for two echelon supply chain consisting of one vendor and one retailer. Production rate and demand rate of retailer and customer are time dependent. Idle time cost of the vendor has been considered. Multi-item inventory has been considered. In integrated inventory model average cost has been calculated under limitation on stroge space. Two echelon supply chain fuzzy inventory model has been solved by various techniques like as Fuzzy programming technique with hyperbolic membership functions (FPTHMF), Fuzzy non-linear programming technique (FNLP) and Fuzzy additive goal programming technique (FAGP), weighted Fuzzy non-linear programming technique (WFNLP) and weighted Fuzzy additive goal programming technique (WFAGP). A numerical example is illustrated to test the model. Finally to make the model more realistic, sensitivity analysis has been shown.

#### Keywords

#### References

CARDENAS-BARRON, L. E; SANA, S. S. (2014) A Production Inventory Model for a two echelon Supply Chain when demand is dependent on sales teams’ initiatives. Int. J. Production Economics, http://dx.doi.org/10.1016/j.ijpe.2014.03.007

CARDENAS-BARRON, L. E; SANA, S. S. (2015) Multi-item EOQ inventory model in a two-layer supply chain while demand varies with promotional effort, Appl. Math. Modell.http://dx.doi.org/10.1016/j.apm.2015.02.004

CHUNG, K. J.; TING, P. S. (1994) On replenishment schedule for deteriorating items with time-proportional demand, Production Planning & Control, n. 5, p. 392–396

DAVE, U.; PATEL, L. K. (1981) policy inventory for deteriorating items with time proportional demand. J. Oper. Res. n. 32, p. 137–142

ISLAM, S.; ROY,T. K. (2006) A fuzzy EPQ model with flexibility and reliability consideration and demand depended unit Production cost under a space constraint: A fuzzy geometric programming approach, Applied Mathematics and Computation, v. 176, n. 2, p. 531-544

ISLAM S. (2008) Multi-objective marketing planning inventory model, A geometric programming approach, Appl. Math. Comput, n. 205, p. 238-246.

ISLAM, S.; ROY, T. K. (2010) Multi-Objective Geometric-Programming Problem and its Application, Yugoslav Journal of Operations Research, n. 20, p. 213-227.

ISLAM, S.; MANDAL, W. A. (2017) A Fuzzy Inventory Model with Unit Production Cost, Time Depended Holding Cost, with-out Shortages under A Space Constraint: A Parametric Geometric Programming Approach, The Journal of Fuzzy Mathematics, v. 25, n. 3, p. 517-532.

ISLAM, S.; MANDAL, W. A. (2019) Fuzzy geometric programming techniques and applications, Forum for Interdisciplinary Mathematics: Springer.

LEE, C. C; MA, C. Y. (2000) Optimal inventory policy for deteriorating items with two-warehouse and time-dependent demands, Production Planning & Control, n. 11, p. 689–696.

LEE, H. T.; WU, J. C. (2006) A study on inventory replenishment policies in a two-echelon supply chain system, Computers & Industrial Engineering, n. 5, p. 257–263

SANA, S.; CHAUDHURI, K. S. (2004) On a volume flexible production policy for a deteriorating item with time dependent demand and shortage. Adv. Model. Opt., n. 6, p. 57–74

SANA, S. S. (2010) A Collaborating inventory model in a supply chain. Economic Modeling, n. 29, p. 2016-2023.

SILVER, E. A.; MEAL, H. C. (1969) A simple modification of the EOQ for the case of a varying demand rate, Production and Inventory Management, v. 10, n. 4, p. 52–65.

THANGAM, A.; UTHAYAKUMAR, R. (2009) Two-echelon trade credit financing for perishable items in a supply chain when demand depends on both selling price and credit period, Computers & Industrial Engineering, n. 57, p. 773–786.

TRIPATHI, R. P.; KAUR, M.; PAREEK, S. (2016) Inventory Model with Exponential Time-Dependent Demand Rate, Variable Deterioration, Shortages and Production Cost, Int. J. Appl. Comput. Math, DOI 10.1007/s40819-016-0185-4

TRIPATHI, R. P.; KAUR, M. (2018)A linear time-dependent deteriorating inventory model with linearly time-dependent demand rate and inflation, Int. J. Computing Science and Mathematics, v. 9, n. 4, p.352–364.

WANG, J.; SHU, Y. F. (2005) Fuzzy decision modelling for supply chain management. Fuzzy Sets Syst. n.150, p.107–127.

YANG, M. F. (2006) A Two-echelon inventory model with fuzzy annual demand in a supply chain, Journal of Information and Optimization Science, https://doi.org/10.1080/02522667.2006.10699709.

ZADEH, L. A. (1965) Fuzzy sets, Information and Control, n. 8, p. 338-353.

ZIMMERMANN, H. J. (1985) Application of fuzzy set theory to mathematical programming, Information Science, n. 36, p. 29-58.

DOI: http://dx.doi.org/10.14807/ijmp.v11i2.1037

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