Advertisement

A light robust model for aggregate production planning with consideration of environmental impacts of machines

  • Donya RahmaniEmail author
  • Arash Zandi
  • Sara Behdad
  • Arezou Entezaminia
Original Paper
  • 23 Downloads

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.

Keywords

Aggregate production planning Environmental concerns Light robust optimization Uncertainty 

Notes

References

  1. 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):765–782Google Scholar
  2. 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):28–42Google Scholar
  3. Ben-Tal A, Nemirovski A (1998) Robust convex optimization. Math Oper Res 23(4):769–805Google Scholar
  4. Ben-Tal A, Nemirovski A (1999) Robust solutions of uncertain linear programs. Oper Res Lett 25:1–13Google Scholar
  5. Ben-Tal A, Nemirovski A (2000) Robust solutions of linear programming problems contaminated with uncertain data. Math Program 88:411–424Google Scholar
  6. Ben-Tal A, Nemirovski A (2002) Robust optimization, methodology and applications. Math Program 92(3):453–480Google Scholar
  7. Ben-Tal A, Nemirovski A, Roos C (2004) Robust solutions of uncertain quadratic and conic-quadratic problems. SIAM J Optim 13:535–560Google Scholar
  8. Bertsimas D, Sim M (2003) Robust discrete optimization and network flows. Math Program 98(1–3):49–71Google Scholar
  9. Bertsimas D, Sim M (2004) The Price of Robustness. Oper Res 52(1):35–53Google Scholar
  10. 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):289–306Google Scholar
  11. Chakrabortty RK, Akhtar Hasin MA, Sarker RA, Essam DL (2015) A possibilistic environment based particle swarm optimization for aggregate production planning. Comput Ind Eng 88:366–377Google Scholar
  12. 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):379–394Google Scholar
  13. 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 45:196–204Google Scholar
  14. David AG (1974) A goal programming approach to aggregate planning of production and work force. Manag Sci 20:1569–1575Google Scholar
  15. 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):148–156Google Scholar
  16. 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 40:63–75Google Scholar
  17. 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):543–577Google Scholar
  18. Fischetti M, Monaci M (2009) Light robustness. Springer, Berlin, pp 61–84Google Scholar
  19. 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 37:585–607Google Scholar
  20. 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):149–165Google Scholar
  21. 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):167–177Google Scholar
  22. Holt CC, Modigliani F, Simon HA (1955) A linear decision rule for production and employment scheduling. Manag Sci 2(1):1–30Google Scholar
  23. Iris C, Cevikcan E (2014) A fuzzy linear programming approach for aggregate production planning. Springer 313:355–374Google Scholar
  24. Jamalnia A, Soukhakian MA (2009) A hybrid fuzzy goal programming approach with different goal priorities to aggregate production planning. Comput Ind Eng 56(4):1474–1486Google Scholar
  25. 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):789–805Google Scholar
  26. José Alem D, Morabito R (2012) Production planning in furniture settings via robust optimization. Comput Oper Res 39(2):139–150Google Scholar
  27. 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):180–193Google Scholar
  28. Leung CHS, Wu Y (2004) A robust optimization model for stochastic aggregate production planning. Prod Plan Control 15(5):502–514Google Scholar
  29. Leung SCH, Wu Y, Lai KK (2006) A stochastic programming approach for multi-site aggregate production planning. J Oper Res Soc 57(2):123–132Google Scholar
  30. 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):224–238Google Scholar
  31. 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):3657–3668Google Scholar
  32. 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):593–603Google Scholar
  33. Masud ASM, Hwang CL (2007) An aggregate production planning model and application of three multiple objective decision methods. Int J Prod Res 18(6):741–752Google Scholar
  34. 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):26–41Google Scholar
  35. Mulvey JM, Vanderbei RJ, Zenios SA (1995) Robust optimization of large-scale systems. Oper Res 43:264–281Google Scholar
  36. Nam S-J, Logendran R (1992) Aggregate production planning - A survey of mdels and methodologies. Eur J Oper Res 61:255–272Google Scholar
  37. 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):623–634Google Scholar
  38. 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):2159–2163Google Scholar
  39. 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) Google Scholar
  40. 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):8957–8971Google Scholar
  41. Soyster AL (1973) Technical note—convex programming with set-inclusive constraints and applications to inexact linear programming. Oper Res 21(5):1154–1157Google Scholar
  42. 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):465–477Google Scholar
  43. Wang R-C, Fang H-H (2001) Aggregate production planning with multiple objectives in fuzzy environment. Eur J Oper Res 133:521–536Google Scholar
  44. Wang F, Lia X, Shi N (2011) A multi-objective optimization for green supply chain network design. Decis Support Syst 51:262–269Google Scholar
  45. 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):674–681Google Scholar
  46. 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):882–891Google Scholar
  47. Zanjani MK, Ait-Kadi D, Nourelfath M (2013). A stochastic programming approach for sawmill production planning. Int J Math Oper Res 5(1):1–8Google Scholar
  48. Zhang R, Zhang L, Xiao Y, Kaku I (2012) The activity-based aggregate production planning with capacity expansion in manufacturing systems. Comput Ind Eng 62:491–503Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  • Donya Rahmani
    • 1
    Email author
  • Arash Zandi
    • 1
  • Sara Behdad
    • 2
  • Arezou Entezaminia
    • 3
  1. 1.Department of Industrial EngineeringK. N. Toosi University of TechnologyTehranIran
  2. 2.Industrial and Systems Engineering DepartmentUniversity at BuffaloBuffaloUSA
  3. 3.Systems Engineering Department, Production System Design and Control LaboratoryUniversity of QuebecMontrealCanada

Personalised recommendations