Abstract
In the present study, a multi-period multi-product aggregate production planning model is developed under uncertainty, considering some important aspects of real-world production systems. In order to apply environmental concerns and control the pollution arising from machines, environmental improvement planning is included as a periodic decision variable. Also, the pollution caused by the production is restricted to an allowable level. A light robust optimization approach is employed in which demands and processing times of operations are uncertain parameters. An illustrative example is presented to demonstrate the model validity and some test problems are designed to analyze the impact of uncertainty on the objective function. Several sensitivity analyses are carried out to provide useful managerial insights.
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References
Al-e-Hashem SMJM, Aryanezhad MB, Sadjadi SJ (2011a) An efficient algorithm to solve a multi-objective robust aggregate production planning in an uncertain environment. Int J Adv Manuf Technol 58(5–8):765–782
Al-e-hashem SMJM, Malekly H, Aryanezhad MB (2011b) A multi-objective robust optimization model for multi-product multi-site aggregate production planning in a supply chain under uncertainty. Int J Prod Econ 134(1):28–42
Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805
Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25:1–13
Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424
Ben-Tal A, Nemirovski A (2002) Robust optimization, methodology and applications. Math Program 92(3):453–480
Ben-Tal A, Nemirovski A, Roos C (2004) Robust solutions of uncertain quadratic and conic-quadratic problems. SIAM J Optim 13:535–560
Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program 98(1–3):49–71
Bertsimas D, Sim M (2004) The Price of Robustness. Oper Res 52(1):35–53
Bournaris T, Papathanasiou J, Manos B, Kazakis N, Voudouris K (2015) Support of irrigation water use and eco-friendly decision process in agricultural production planning. Oper Res 15(2):289–306
Chakrabortty RK, Akhtar Hasin MA, Sarker RA, Essam DL (2015) A possibilistic environment based particle swarm optimization for aggregate production planning. Comput Ind Eng 88:366–377
Choi YC, Xirouchakis P (2015) A holistic production planning approach in a reconfigurable manufacturing system with energy consumption and environmental effects. Int J Comput Integr Manuf 28(4):379–394
da Silva AF, Marins FAS (2014) A fuzzy goal programming model for solving aggregate production-planning problems under uncertainty: a case study in a Brazilian sugar mill. Energy Econ 45:196–204
David AG (1974) A goal programming approach to aggregate planning of production and work force. Manag Sci 20:1569–1575
de Oliveira Neto GC, Lucato WC (2016) Production planning and control as a tool for eco-efficency improvement and environmental impact reduction. Prod Plan Control 27(3):148–156
Entezaminia A, Heydari M, Rahmani D (2016) A multi-objective model for multi-product multi-site aggregate production planning in a green supply chain: considering collection and recycling centers. J Manuf Syst 40:63–75
Fang C, Liu X, Pei J, Fan W, Pardalos PM (2016) Optimal production planning in a hybrid manufacturing and recovering system based on the internet of things with closed loop supply chains. Oper Res 16(3):543–577
Fischetti M, Monaci M (2009) Light robustness. Springer, Berlin, pp 61–84
Gholamian N, Mahdavi I, Tavakkoli-Moghaddam R, Mahdavi-Amiri N (2015) A Comprehensive fuzzy multi-objective multi-product multi-site aggregate production planning decisions in a supply chain under uncertainty. Appl Soft Comput J 37:585–607
Gholamian N, Mahdavi I, Tavakkoli-Moghaddam R (2016) Multi-objective multi-product multi-site aggregate production planning in a supply chain under uncertainty: fuzzy multi-objective optimisation. Int J Comput Integr Manuf 29(2):149–165
Gomes da Silva C, Figueira J, Lisboa J, Barman S (2006) An interactive decision support system for an aggregate production planning model based on multiple criteria mixed integer linear programming. Omega 34(2):167–177
Holt CC, Modigliani F, Simon HA (1955) A linear decision rule for production and employment scheduling. Manag Sci 2(1):1–30
Iris C, Cevikcan E (2014) A fuzzy linear programming approach for aggregate production planning. Springer 313:355–374
Jamalnia A, Soukhakian MA (2009) A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning. Comput Ind Eng 56(4):1474–1486
Jayaraman R, Colapinto C, Liuzzi D, La Torre D (2017) Planning sustainable development through a scenario-based stochastic goal programming model. Oper Res 17(3):789–805
José Alem D, Morabito R (2012) Production planning in furniture settings via robust optimization. Comput Oper Res 39(2):139–150
Kazemi A, Fazel Zarandi MH, Moattar Husseini SM (2009) A multi-agent system to solve the production–distribution planning problem for a supply chain: a genetic algorithm approach. Int J Adv Manuf Technol 44(1–2):180–193
Leung CHS, Wu Y (2004) A robust optimization model for stochastic aggregate production planning. Prod Plan Control 15(5):502–514
Leung SCH, Wu Y, Lai KK (2006) A stochastic programming approach for multi-site aggregate production planning. J Oper Res Soc 57(2):123–132
Leung CH, Tsang SOS, Ng WL, Wu Y (2007) A robust optimization model for multi-site production planning problem in an uncertain environment. Eur J Oper Res 181(1):224–238
Li C, Liu F, Cao H, Wang Q (2009) A stochastic dynamic programming based model for uncertain production planning of re-manufacturing system. Int J Prod Res 47(13):3657–3668
Lim SJ, Jeong SJ, Kim KS, Park MW (2005) A simulation approach for production-distribution planning with consideration given to replenishment policies. Int J Adv Manuf Technol 27(5–6):593–603
Masud ASM, Hwang CL (2007) An aggregate production planning model and application of three multiple objective decision methods. Int J Prod Res 18(6):741–752
Mirzapour Al-e-hashem SMJ, Baboli A, Sazvar Z (2013) A stochastic aggregate production planning model in a green supply chain: considering flexible lead times, nonlinear purchase and shortage cost functions. Eur J Oper Res 230(1):26–41
Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43:264–281
Nam S-J, Logendran R (1992) Aggregate production planning - A survey of mdels and methodologies. Eur J Oper Res 61:255–272
Niknamfar AH, Niaki STA, Pasandideh SHR (2014) Robust optimization approach for an aggregate production—distribution planning in a three-level. Int J Adv Manuf Technol 76(1–4):623–634
Orcun S, Uzsoy R, Kempf KG (2009) An integrated production planning model with load-dependent lead-times and safety stocks. Comput Chem Eng 33(12):2159–2163
Porkar S, Mahdavi I, Vishkaei BM, Hematian M (2018) Green supply chain flow analysis with multi-attribute demand in a multi-period product development environment. Oper Res, pp 1–31 (in press)
Rahmani D, Ramezanian R, Fattahi P, Heydari M (2013) A robust optimization model for multi-product two-stage capacitated production planning under uncertainty. Appl Math Model 37(20–21):8957–8971
Soyster AL (1973) Technical note—convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21(5):1154–1157
Tien-Fu Liang H-WC, Chen Ping-Yen, Shen Kuan-Hsinung (2011) Application of fuzzy sets to aggregate production planningwith multiproducts and multitime periods. IEEE Transl Fuzzy Syst 19(3):465–477
Wang R-C, Fang H-H (2001) Aggregate production planning with multiple objectives in fuzzy environment. Eur J Oper Res 133:521–536
Wang F, Lia X, Shi N (2011) A multi-objective optimization for green supply chain network design. Decis Support Syst 51:262–269
Xue G, Felix Offodile O, Zhou H, Troutt MD (2011) Integrated production planning with sequence-dependent family setup times. Int J Prod Econ 131(2):674–681
Zanjani MK, Ait-Kadi D, Nourelfath M (2010) Robust production planning in a manufacturing environment with random yield: a case in sawmill production planning. Eur J Oper Res 201(3):882–891
Zanjani MK, Ait-Kadi D, Nourelfath M (2013). A stochastic programming approach for sawmill production planning. Int J Math Oper Res 5(1):1–8
Zhang R, Zhang L, Xiao Y, Kaku I (2012) The activity-based aggregate production planning with capacity expansion in manufacturing systems. Comput Ind Eng 62:491–503
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Rahmani, D., Zandi, A., Behdad, S. et al. A light robust model for aggregate production planning with consideration of environmental impacts of machines. Oper Res Int J 21, 273–297 (2021). https://doi.org/10.1007/s12351-019-00451-x
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DOI: https://doi.org/10.1007/s12351-019-00451-x