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Investigation of green production inventory problem with selling price and green level sensitive interval-valued demand via different metaheuristic algorithms

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Abstract

In real-life situation, different characteristics of an imperfect production inventory system, viz. demand, production, defectiveness and different costs may be imprecise. To represent the impreciseness of those parameters, several well-known approaches like interval, fuzzy, stochastic and fuzzy-stochastic approaches are applied. Among these approaches, interval approach is more realistic. This work deals with a green production model in interval environment. Due to consideration of interval-valued demand and defective rates, the corresponding differential equations of inventory levels of the proposed model are represented in interval form. With the help of parametric representation of interval, these differential equations are solved. The corresponding profit maximization problem is obtained in the interval form. To transform the said maximization problem into crisp form, interval order relations and centre-radius optimization technique are used and, the transformed problem is solved with the help of different metaheuristic algorithms. Then the proposed model is justified and validated with the help of a numerical example. Finally, the sensitivity analyses are performed to explore the effects of changes of different system parameters on the best found (optimal) policy.

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References

  • Alefeld G, Mayer G (2000) Interval analysis: theory and applications. J Comput Appl Math 121:421–464

    MathSciNet  MATH  Google Scholar 

  • Bhunia AK, Samanta SS (2014) A study of interval metric and its application in multi-objective optimization with interval objectives. Comput Ind Eng 74:169–178

    Google Scholar 

  • Bhunia AK, Shaikh AA (2016) Investigation of two-warehouse inventory problems in interval environment under inflation via particle swarm optimization. Math Comput Model Dyn Syst 22(2):160–179

    MathSciNet  MATH  Google Scholar 

  • Bhunia AK, Shaikh AA, Cárdenas-Barrón LE (2017) A partially integrated production-inventory model with interval valued inventory costs, variable demand and flexible reliability. Appl Soft Comput 55:491–502

    Google Scholar 

  • Cárdenas-Barrón LE (2001) The economic production quantity (EPQ) with shortage derived algebraically. Int J Prod Econ 70(3):289–292

    Google Scholar 

  • Chan RYK, Lau LBY (2002) Explaining green purchasing behavior: a cross cultural studies on American and Chinese consumers. J Int Consum 4(2–3):9–40

  • Cheah I, Phau I (2011) Attitudes towards environmentally friendly products. Mark Intell Plan

  • Coelho LS (2010) Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems. Expert Syst Appl 37(2):1676–1683

    Google Scholar 

  • da Costa TM, Chalco-Cano Y, Lodwick WA, Silva GN (2018) A new approach to linear interval differential equations as a first step toward solving fuzzy differential. Fuzzy Sets Syst 347:129–141

    MathSciNet  MATH  Google Scholar 

  • Duary A, Banerjee T, Shaikh AA, Niaki STA, Bhunia AK (2019) A Weibull distributed deteriorating inventory model with all-unit discount, advance payment and variable demand via different variants of PSO. Int J Logist Manag (In press)

  • Dye CY, Ouyang LY (2011) A particle swarm optimization for solving joint pricing and lot-sizing problem with fluctuating demand and trade credit financing. Comput Ind Eng 60(1):127–137

    Google Scholar 

  • Fankhauser S, Bowen A, Calel R, Dechezleprêtre A, Grover D, Rydge J, Sato M (2013) Who will win the green race? In search of environmental competitiveness and innovation. Glob Environ Change 23(5):902–913

    Google Scholar 

  • Gasilov NA, Emrah Amrahov S (2020) On differential equations with interval coefficients. Math Methods Appl Sci 43(4):1825–1837

    MathSciNet  MATH  Google Scholar 

  • Gavish B, Graves SC (1981) Production/inventory systems with a stochastic production rate under a continuous review policy. Comput Oper Res 8(3):169–183

    Google Scholar 

  • Ghosh D, Shah J (2015) Supply chain analysis under green sensitive consumer demand and cost sharing contract. Int J Prod Econ 164:319–329

    Google Scholar 

  • Goyal SK, Gunasekaran A (1995) An integrated production-inventory-marketing model for deteriorating items. Comput Ind Eng 28(4):755–762

    Google Scholar 

  • Goyal SK, Cárdenas-Barrón LE (2005) Economic production quantity with imperfect production system. Ind Eng 34(2):33–36

    Google Scholar 

  • Gupta RK, Bhunia AK, Goyal SK (2009) An application of genetic algorithm in solving an inventory model with advance payment and interval valued inventory costs. Math Comput Model 49(5–6):893–905

    MathSciNet  MATH  Google Scholar 

  • Hsieh CH (2002) Optimization of fuzzy production inventory models. Inf Sci 146(1–4):29–40

    MathSciNet  MATH  Google Scholar 

  • Jamali MB, Rasti-Barzoki M (2018) A game theoretic approach for green and non-green product pricing in chain-to-chain competitive sustainable and regular dual-channel supply chains. J Clean Prod 170:1029–1043

    Google Scholar 

  • 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

    Google Scholar 

  • Jorgensen S, Kort PM, Zaccour G (1999) Production, inventory, and pricing under cost and demand learning effects. Eur J Oper Res 117(2):382–395

    MATH  Google Scholar 

  • Khouja M (1995) The economic production lot size model under volume flexibility. Comput Oper Res 22(5):515–523

    MATH  Google Scholar 

  • Kumar N, Manna AK, Shaikh AA, Bhunia AK (2021) Application of hybrid binary tournament based quantum behaved particle swarm optimization on an imperfect production inventory problem. Soft Comput. https://doi.org/10.1007/s00500-021-05894-z

    Article  Google Scholar 

  • Lupulescu V (2013) Hukuhara differentiability of interval-valued functions and interval differential equations on time scales. Inf Sci 248:50–67

    MathSciNet  MATH  Google Scholar 

  • Malinowski MT (2011) Interval differential equations with a second type Hukuhara derivative. Appl Math Lett 24(12):2118–2123

    MathSciNet  MATH  Google Scholar 

  • Manna AK, Das B, Dey JK, Mondal SK (2016) An EPQ model with promotional demand in random planning horizon: population varying genetic algorithm approach. J Intell Manuf 29(7):1515–1531

    Google Scholar 

  • Manna AK, Dey JK, Mondal SK (2020) Effect of inspection errors on imperfect production inventory model with warranty and price discount dependent demand rate. RAIRO Oper Res 54:1189–1213

    MathSciNet  MATH  Google Scholar 

  • Manna AK, Banerjee T, Mandal SK, Shaikh AA, Bhunia AK (2021) Two-plant production model with customers demand dependent on warranty period of the product and carbon emission level of the manufacturer via different meta-heuristic algorithms. Neural Comput Appl. https://doi.org/10.1007/s00521-021-06073-9

    Article  Google Scholar 

  • Misra RB (1975) Optimum production lot size model for a system with deteriorating inventory. Int J Prod Res 13(5):495–505

    Google Scholar 

  • Mondal S, Maiti M (2003) Multi-item fuzzy EOQ models using genetic algorithm. Comput Ind Eng 44(1):105–117

    Google Scholar 

  • Mondal M, Maiti MK, Maiti M (2013) A two storage production-repairing model with fuzzy defective rate and displayed inventory dependent demand. Optim Eng 15(3):751–772

    MathSciNet  MATH  Google Scholar 

  • Mondal R, Shaikh AA, Bhunia AK (2019) Crisp and interval inventory models for ameliorating item with Weibull distributed amelioration and deterioration via different variants of quantum behaved particle swarm optimization-based techniques. Math Comput Model Dyn Syst 25(6):602–626

    MathSciNet  MATH  Google Scholar 

  • Moore RE (1962) Interval arithmetic and automatic error analysis in digital computing. Thesis, Stanford University, October 1962

  • Moore RE (1966) Interval Analysis. Prentice-Hall, Englewood Clis, p 1966

    Google Scholar 

  • Mousavi SM, Hajipour V, Niaki STA, Aalikar N (2014) A multi-product multi-period inventory control problem under inflation and discount: a parameter-tuned particle swarm optimization algorithm. Int J Adv Manuf Syst 70(9–12):1739–1756

    Google Scholar 

  • Naik A, Satapathy SC, Abraham A (2020) Modified Social Group Optimization-a metaheuristic algorithm to solve short-term hydrothermal scheduling. Appl Soft Comput 95:106524

    Google Scholar 

  • Neumaier A (1990) Interval methods for systems of equations. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  • Pal B, Sana SS, Chaudhuri K (2013) Two-echelon manufacturer-retailer supply chain strategies with price, quality, and promotional effort sensitive demand. Int Trans Oper Res 22(6):1071–1095

    MathSciNet  MATH  Google Scholar 

  • Panja S, Mondal SK (2019) Analyzing a four-layer green supply chain imperfect production inventory model for green products under type-2 fuzzy credit period. Comput Ind Eng 129:435–453

    Google Scholar 

  • Qu H, Ai XY, Wang L (2020) Optimizing an integrated inventory-routing system for multi-item joint replenishment and coordinated outbound delivery using differential evolution algorithm. Appl Soft Comput 86:105863

    Google Scholar 

  • Rahman MS, Manna AK, Shaikh AA, Bhunia AK (2020) An application of interval differential equation on a production inventory model with interval-valued demand via center-radius optimization technique and Particle Swarm Optimization. Int J Intell Syst 35(8):1280–1326

    Google Scholar 

  • Ramezanadeh M, Heidari M, Fard OS, Borzabadi AH (2015) On the interval differential equation: novel solution methodology. Adv Differ Equ 2015(1):1–23

    MathSciNet  MATH  Google Scholar 

  • Rao R (2016) Review of applications of TLBO algorithm and a tutorial for beginners to solve the unconstrained and constrained optimization problems. Decis Sci Lett 5(1):1–30

    Google Scholar 

  • Rao R (2020) Rao algorithms: three metaphor-less simple algorithms for solving optimization problems. Int J Ind Eng Comput 11(1):107–130

    Google Scholar 

  • Rosenblatt MJ, Lee HL (1986) Economic production cycles with imperfect production processes. IIE Trans 18(1):48–55

    Google Scholar 

  • Salameh MK, Jaber MY (2000) Economic production quantity model for items with imperfect quality. Int J Prod Econ 64(1–3):59–64

    Google Scholar 

  • Sana SS (2020) Price competition between green and non green products under corporate social responsible firm. J Retail Consum Serv 55:102118

    Google Scholar 

  • Sarkar B, Sana SS, Chaudhuri K (2011) An imperfect production process for time varying demand with inflation and time value of money—an EMQ model. Expert Syst Appl 38(11):13543–13548

    Google Scholar 

  • Shah NH (2015) Manufacturer-retailer inventory model for deteriorating items with price-sensitive credit-linked demand under two-level trade credit financing and profit sharing contract. Cogent Eng 2(1):1012989

    Google Scholar 

  • Shaikh AA, Cárdenas-Barrón LE, Tiwari S (2019) A two-warehouse inventory model for non-instantaneous deteriorating items with interval-valued inventory costs and stock-dependent demand under inflationary conditions. Neural Comput Appl 31(6):1931–1948

    Google Scholar 

  • Smith NR, Limón Robles J, Cárdenas-Barrón LE (2009) Optimal pricing and production master planning in a multi period horizon considering capacity and inventory constraints. Math Probl Eng 2009

  • Stefanini L, Bede B (2009) Generalized Hukuhara differentiability of interval-valued functions and interval differential equations. Nonlinear Anal Theory Methods Appl 71(3–4):1311–1328

    MathSciNet  MATH  Google Scholar 

  • Sunaga T (1958) Theory of interval algebra and its application to numerical analysis. RAAG Memoirs 1958:29–46

    MATH  Google Scholar 

  • Taleizadeh AA, Pourreza P, Moon I (2018) Hybrid for an imperfect production system considering product quality and returns under two warranty policies. Appl Soft Comput 75:333–348

    Google Scholar 

  • Wang L, He J, Wu D, Zeng YR (2012) A novel differential evolution algorithm for joint replenishment problem under interdependence and its application. Int J Prod Econ 135(1):190–198

    Google Scholar 

  • Xi M, Sun J, Xu W (2008) An improved quantum-behaved particle swarm optimization algorithm with weighted mean best position. Appl Math Comput 205(2):751–759

    MATH  Google Scholar 

  • Xu W, Sun J (2005) Adaptive parameter selection of quantum-behaved particle swarm optimization on global level. In: International conference on intelligent computing, Berlin, Heidelberg, pp 420–428

  • Yadav R, Pathak GS (2016) Young consumers’ intention towards buying green products in a developing nation: extending the theory of planned behavior. J Clean Prod 135:732–739

    Google Scholar 

  • Zhu Q, Sarkis J, Geng Y (2005) Green supply chain management in China: pressures, practices and performance. Int J Oper Prod Manag

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Acknowledgements

The authors express their sincere thanks to the editor and the anonymous reviewers for their valuable comments and suggestions which have led to a significant improvement of the manuscript. The first author would like to thank University Grants Commission providing the Dr. D. S. Kothari Post Doctoral Fellowship (DSKPDF) through The University of Burdwan for accomplish this research (Vide Research Grant No.F.4-2/2006 (BSR)/MA/18-19/0023). Also the second author would like to acknowledge the financial support provided by WBDST & BT, West Bengal, India for this research (Memo No: 429(Sanc.)/ST/P/S & T/16G-23/2018 dated 12/03/2019), and Department of Science and Technology, Govt. of India for FIST support (SR/FST/MSII/2017/10 (C)). Also, the authors would like to thank Md Akhtar (Research Scholar in the Department of Mathematics, The University of Burdwan) for his sincere help to improve the numerical experiment part.

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Authors and Affiliations

  1. Department of Mathematics, The University of Burdwan, Burdwan, 713104, India

    Amalesh Kumar Manna & Asoke Kumar Bhunia

  2. Department of Mathematics, C. V. Raman Global University, Bhubaneswar, 752054, India

    Amalesh Kumar Manna

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  1. Amalesh Kumar Manna
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Correspondence to Amalesh Kumar Manna.

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Manna, A.K., Bhunia, A.K. Investigation of green production inventory problem with selling price and green level sensitive interval-valued demand via different metaheuristic algorithms. Soft Comput 26, 10409–10421 (2022). https://doi.org/10.1007/s00500-022-06856-9

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