Abstract
In this paper, we investigated a multi-objective inventory model under both stock-dependent demand rate and holding cost rate with fuzzy random coefficients. Chance constrained fuzzy random multi-objective model and a traditional solution procedure based on an interactive fuzzy satisfying method are discussed. In addition, the technique of fuzzy random simulation is applied to deal with general fuzzy random objective functions and fuzzy random constraints which are usually difficult to converted into their crisp equivalents. The purposed of this study is to determine optimal order quantity and inventory level such that the total profit and wastage cost are maximized and minimize for the retailer respectively. Finally, illustrate example is given in order to show the application of the proposed model.
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Abbreviations
- Pos:
-
Possibility measure
- Nec:
-
Necessity measure
- Cr:
-
Credibility measure
- Pr:
-
Probability measure
- Ch:
-
Chance measure
- CCMOP:
-
Chance constrained multi-objective problem
- FISM:
-
Interactive fuzzy satisfied method
- \({\mathop {a}\limits ^{\simeq }}\) :
-
Fuzzy random variable
References
Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353
Ishii H, Konno T (1998) A stochastic inventory problem with fuzzy shortage cost. Eur J Oper Res 106:90–94
Zadeh LA (1978) Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets Syst 1:3–28
Dubois D, Prade H (1988) Possibility theory: an approach to computerized processing of uncertainty. Plenum, New York
Kwakernaak H (1978) Fuzzy random variables, definitions and theorems. Inf Sci 15:1–29
Liu B (2001) Fuzzy random chance-constrained programming. IEEE Trans Fuzzy Syst 9:713–720
Liu B (2001) Fuzzy random dependent-chance programming. IEEE Trans Fuzzy Syst 9:721–726
Luhandjula MK (2004) Optimisation under hybrid uncertainty. Fuzzy Sets Syst 146:187–203
Qiao Z, Wang G (1993) On solutions and distributions problems of the linear programming with fuzzy random variable coefficients. Fuzzy Sets Syst 58:155–170
Majumder S, Kar S, Pal T (2018) Mean-entropy model of uncertain portfolio selection problem. Springer, Singapore
Kar MB, Kar S, Guo S, Li X, Majumder S (2018) A new bi-objective fuzzy portfolio selection model and its solution through evolutionary algorithms. Soft Comput. https://doi.org/10.1007/s00500-018-3094-0
Garai T, Chakraborty D, Roy TK (2018) Possibility mean, variance and covariance of generalized intuitionistic fuzzy numbers and its application to multi-item inventory model with inventory level dependent demand. J Intell Fuzzy Syst 35:1021–1036
Mondal SP (2018) Interval valued intuitionistic fuzzy number and its application in differential equation. J Intell Fuzzy Syst 34:677–687
Salahshour S, Mahata A, Mondal SP, Alam S (2018) The behavior of logistic equation with alley effect in fuzzy environment: fuzzy differential equation approach. Int J Appl Comput Math 4:1–20
Dutta P, Chakraborty D, Roy AR (2005) A single-period inventory model with fuzzy random variable demand. Math Comput Model 41:915–922
Dey O, Chakraborty D (2011) A fuzzy random continuous review inventory system. Int J Prod Econ 132:101–106
Wang X (2011) Continuous review inventory model with variable lead time in a fuzzy random environment. Expert Syst Appl 38:11715–11721
Kumar RS, Goswami A (2015) A continuous review production-inventory system in fuzzy random environment: min–max distribution free procedure. Comput Ind Eng 79:65–75
Iltaf Hussain AS, Mandal UK, Mondal SP (2018) Decision maker priority index and degree of vagueness coupled decision making method: a synergistic approach. Int J Fuzzy Syst 20:1551–1566
Mondal SP (2016) Differential equation with interval valued fuzzy number and its applications. Int J Syst Assur Eng Manag 7:370–386
Balkhi ZT, Foul A (2009) A multi-item production lot size inventory model with cycle dependent parameters. Int J Math Model Methods Appl Sci 3:94–104
Kar MB, Kundu P, Kar S, Pal T (2018) A multi-objective multi-item solid transportation problem with vehicle cost, volume and weight capacity under fuzzy environment. J Intell Fuzzy Syst 35:1991–1995
Majumder S, Kundu P, Kar S, Pal T (2018) Uncertain multi-objective multi-item fixed charge solid transportation problem with budget constraint. Soft Comput. https://doi.org/10.1007/s00500-017-2987-7
Kundu P, Kar S, Maiti M (2014) Multi-objective solid transportation problems with budget constraint in uncertain environment. Int J Syst Sci 45:1668–1682
Taleizadeh AA, Sadjadi SJ, Niaki STA (2011) Multi-product EPQ model with single machine, back-ordering and immediate rework process. Eur J Ind Eng 5:388–411
Garai T, Chakraborty D, Roy TK (2018) A multi-objective multi-item inventory model with both stock-dependent demand rate and holding cost rate under fuzzy rough environment. J Granul Comput 3:1–18
Wu KS, Ouyang LY, Yang CT (2006) An optimal replenishment policy for non-instantaneous deteriorating items with stock-dependent demand and partial backlogging. Int J Prod Econ 101:369–384
Avinadav T, Herbon A, Spiegel U (2013) Optimal inventory policy for a perishable item with demand function sensitive to price and time. Int J Prod Econ 144:497–506
Garai T, Chakraborty D, Roy TK (2018) Expected value of exponential fuzzy number and its application to multi-item deterministic inventory model for deteriorating items. J Uncertain Anal Appl. https://doi.org/10.1186/s40467-017-0062-7
Min J, Zhou YW, Liu GQ, Wang SD (2012) An EPQ model for deteriorating items with inventory level dependent demand and permissible delay in payments. Int Syst Sci 43:1039–1053
Taleizadeh AA, Wee MH, Jolai F (2013) Revisiting a fuzzy rough economic order quantity model for deteriorating items considering quantity discount and prepayment. Math Comput Model 57:1466–1479
Jana DK, Das B, Maiti M (2014) Multi-item partial backlogging inventory models over random planning horizon in random fuzzy environment. Appl Soft Comput 21:12–27
Chakraborty D, Jana D k, Roy TK (2015) Multi-item integrated supply chain model for deteriorating items with stock dependent demand under fuzzy random and bi-fuzzy environments. Comput Ind Eng 88:166–180
Chakraborty D, Jana KD, Roy KT (2017) A new approach to solve intuitionistic fuzzy optimization problem using possibility, necessity and credibility measures. Int J Eng Math 1:1–12
Xu J, Zaho L (2008) A class of fuzzy rough expected value multi-objective decision making model and its application to inventory problems. Computers Math Appl 56:2107–2119
Pando V, Garcia-Lagunaa J, San-Jose LA, Sicilia J (2012) Maximizing profits in an inventory model with both demand rate and holding cost per unit time dependent on the stock level. Comput Ind Eng 62:599–608
Tripaathi EP (2013) Inventory model with different demand rate and different holding cost. Int J Ind Eng Comput 4:437–446
Pando V, San-jose LA, Garcia-Laguna J, Sicilia J (2013) An economic lot-size model with non-linear holding cost hinging on time quantity. Int J Prod Econ 145:294–303
Roy A (2008) An inventory model for deteriorating items with price dependent demand and time varying holding cost. Adv Model Optim 10:25–37
Liu YK, Liu B (2003) Fuzzy random variables: a scalar expected value operator. Fuzzy Optim Decis Mak 2:143–160
Li J, Xu J, Gen MA (2006) class of multi-objective linear programming model with fuzzy random coefficients. Math Comput Model 44:1097–1113
Xu J, Yao L (2009) A class of multi-objective linear programming models with random rough coefficients. Math Comput model 49:189–206
Liu B (2002) Theory and practice of uncertain programming. Physica-Verlag, Heidelberg
Sakawa K (1993) Fuzzy sets an interactive multi-objective optimization. Plenum, New York
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Garai, T., Chakraborty, D. & Roy, T.K. Multi-objective Inventory Model with Both Stock-Dependent Demand Rate and Holding Cost Rate Under Fuzzy Random Environment. Ann. Data. Sci. 6, 61–81 (2019). https://doi.org/10.1007/s40745-018-00186-0
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DOI: https://doi.org/10.1007/s40745-018-00186-0