Abstract
In this paper, an energy-aware Economic Production Quantity (EPQ) model is presented to determine optimum production run length and batch size with respect to variable energy cost. Here, variable unit production cost includes energy consumption charge which is a function of production time and time-of-use, and alternates between two prices during peak and off-peak hours. This paper addresses the above integration in order to minimize the overall cost of the system. In the first phase of this study, a new scenario-based framework is proposed to find the optimal value of production time. In the second phase, a general mixed integer nonlinear programming (MINLP) model is developed for the given framework. The energy cost defined by the framework and mathematical model depends on the number of peak periods during the production period and is calculated using floor functions. The MINLP is solved numerically and analytically, and a closed form solution is obtained for the production run length. The model is analyzed for different scenarios and the results are discussed.
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References
Ben-Daya M, Hariga M, Khursheed SN (2008) Economic production quantity model with a shifting production rate. Int Trans Oper Res 15(1):87–101
Chakraborty T, Giri BC (2014) Lot sizing in a deteriorating production system under inspections, imperfect maintenance and reworks. Oper Res Int J 14(1):29–50
Cheng J, Chu F, Xia W, Ding J, Ling X (2014) Bi-objective optimization for single-machine batch scheduling considering energy cost. In: IEEE international conference on control, decision and information technologies (CoDIT), pp 236–241
Fang K, Uhan N, Zhao F, Sutherland JW (2011) A new shop scheduling approach in support of sustainable manufacturing. In: Glocalized solutions for sustainability in manufacturing. Springer, Berlin, pp 305–310
Ghadimi P, Kara S, Kornfeld B (2015) Renewable energy integration into factories: real-time control of on-site energy systems. CIRP Ann Manuf Technol 64:443–446
Leung KNF (2007) A generalized geometric-programming solution to “An economic production quantity model with flexibility and reliability considerations”. Eur J Oper Res 176(1):240–251
Li D, Sun X (2006) Nonlinear integer programming. Springer, New York
Merkert L, Harjunkoski I, Isaksson A, Säynevirta S, Saarela A, Sand G (2015) Scheduling and energy-industrial challenges and opportunities. Comput Chem Eng 72:183–198
Nezami F, Yildirim B, Wang P (2012) Sustainable single-machine scheduling problem with reliability and energy consumption. In: 2012 Industrial and systems engineering research conference, 19–23 May 2012
Prabhu VV, Trentesaux D, Taisch M (2015) Energy-aware manufacturing operations. Int J Prod Res 53:6994–7004
Sana SS (2010) An economic production lot size model in an imperfect production system. Eur J Oper Res 201(1):158–170
Sana SS (2011) A production-inventory model of imperfect quality products in a three-layer supply chain. Decis Support Syst 50(2):539–547
Sarkar B (2012) An inventory model with reliability in an imperfect production process. Appl Math Comput 218(9):4881–4891
Shah NH, Patel DG, Shah DB (2016) EPQ model for returned/reworked inventories during imperfect production process under price-sensitive stock-dependent demand. Oper Res Int J. doi:10.1007/s12351-016-0267-4
Singh N, Vaish B, Singh S (2012) An economic production lot-size (EPLS) model with rework and flexibility under allowable shortages. Int J Proc Manag 5(1):104–122
Tan M, Duan B, Su Y (2016) Economic batch sizing and scheduling on parallel machines under time-of-use electricity pricing. Oper Res Int J. doi:10.1007/s12351-016-0256-7
Wan G, Qi X (2010) Scheduling with variable time slot costs. Nav Res Logist 57(2):159–171
Yildirim MB, Mouzon G (2012) Single-machine sustainable production planning to minimize total energy consumption and total completion time using a multiple objective genetic algorithm. IEEE Trans Eng Manag 59(4):585–597
Yildirim MB, Nezami FG (2014) Integrated maintenance and production planning with energy consumption and minimal repair. Int J Adv Manuf Technol 74(9):1419–1430
Zhang H, Zhao F, Fang K, Sutherland JW (2014a) Energy-conscious flow shop scheduling under time-of-use electricity tariffs. CIRP Ann Manuf Technol 63(1):37–40
Zhang H, Zhao F, Sutherland JW (2014b) Manufacturing scheduling for energy cost reduction in a smart grid scenario. In: ASME 2014 International Manufacturing Science and Engineering Conference collocated with the JSME 2014 International Conference on Materials and Processing and the 42nd North American Manufacturing Research Conference, American Society of Mechanical Engineers
Acknowledgements
We would like to thank Professor Ruben Hayrapetyan from the Department of Mathematics at Kettering University for his constructive comments and helpful guidance.
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Nezami, F.G., Heydar, M. Energy-aware Economic Production Quantity model with variable energy pricing. Oper Res Int J 19, 201–218 (2019). https://doi.org/10.1007/s12351-016-0284-3
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DOI: https://doi.org/10.1007/s12351-016-0284-3