نوع مقاله : مقاله پژوهشی

نویسندگان

1 دانشجوی دکتری مهندسی صنایع و مکانیک، واحد قزوین، دانشگاه آزاد اسلامی، قزوین، ایران

2 دانشیار، دانشکده مهندسی صنایع و مکانیک، واحد قزوین، دانشگاه آزاد اسلامی، قزوین، ایران

چکیده

انتشار کربن مربوط به مصرف انرژی در صنایع تولیدی، بخش قابل‌توجهی از بار زیست‌محیطی است. در این مقاله، محدودیت انتشار کربن برای یک مدل اندازه انباشته اقتصادی جهت کاهش انتشار کربن ارائه شده است. هدف این مسئله برآورد تقاضای کالاهای مختلف در طول افق برنامه­ریزی باتوجه به کمینه کردن هزینه­های تولید، راه­اندازی، دوباره­کاری و نگهداری است. در این مسئله فرض شده است که فرآیند تولید کالا نامطلوب است و درحین فرآیند مقداری از کالاها باکیفیت نامطلوب تولید می­شوند. کالاهای معیوب پس از شناسایی با انجام فرآیند دوباره­کاری قابل‌استفاده می­شوند. در این مدل پیشنهادی از یک مسئله برنامه­ریزی غیرخطی محدب استفاده شده است؛ بنابراین، جواب بهینه این مدل پیشنهادی را می­توان با استفاده از روش مشتق­گیری به دست آورد. درنهایت، مثال عددی فرضی برای نشان دادن کارایی الگوریتم حل دقیق پیشنهادی حل شده است.

کلیدواژه‌ها

عنوان مقاله [English]

Presenting an economic lot-sizing scheduling problem considering maximum permissible carbon emissions

نویسندگان [English]

  • Amir Hossein Nobil 1
  • َAbolfazl Kazemi 2

1 PhD student in industrial and mechanical engineering, Qazvin branch, Islamic Azad University, Qazvin, Iran

2 Associate Professor, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

چکیده [English]

Carbon emissions related to energy consumptions from the manufacturing industry have become a substantial part of environmental burdens. Carbon emissions related to energy consumptions from the manufacturing industry have become a substantial part of environmental burdens. This study presents carbon emission constraint into the economic lot scheduling problem to reduce carbon emissions. The aim of this research to satisfy customer demand for various items over the planning horizon, with an objective to minimize total costs, includes setup, production, rework and holding costs. In this problem, it is assumed that the production process is defective, and during the process some of the goods are produced with undesirable quality. Defective products can be sold using a rework process. This proposed model has been proven to be a nonlinear convex programming problem. Hence, the optimal solution of this proposed model can be obtained using the derivative method. Finally, a hypothetical example is solved to demonstrate the performance of the proposed exact solution algorithm.

کلیدواژه‌ها [English]

  • Carbon emission constraint
  • nonlinear programming
  • exact solution algorithm
  • sustainable environment
  • lot-sizing problem
امیری. مقصود، نایبی. محمدامین، زرآبادی­پور. اویس (1393)، توسعه مدل­های کنترل موجودی (r,Q) و (R,T)، فصلنامه علمی-پژوهشی مطالعات مدیریت صنعتی، سال دوازدهم، شماره 33، ص 125-150.
نایبی. محمدامین، پناهی. مزرعتی (1390)، توسعه یک مدل موجودی چند هدفه احتمالی فازی، فصلنامه علمی-پژوهشی مطالعات مدیریت صنعتی، سال نهم، شماره 22، ص 209-235.
طالعی­زاده. عطااله، نوبیل. امیرحسین (1396)، کنترل موجودی: سیستم­های سفارش­دهی و خرده­فروشی، جلد اول، چاپ اول، تهران، موسسه انتشارات علمی دانشگاه صنعتی شریف.
Akrami, B. Karimi, B., and Hosseini, S.M. (2006). Two metaheuristic methods for the common cycle economic lot sizing and scheduling in flexible flow shops with limited intermediate buffers: The finite horizon case. Applied Mathematics and Computation, No. 183(1), PP: 634-645.
Alle, A., Pinto, J.M., and Papageorgiou, L.G. (2004). The economic lot scheduling problem under performance decay. Industrial and engineering chemistry research, No. 43(20), PP: 6463-6475.
Banerjee, A. (2009). Simultaneous determination of multiproduct batch and full truckload shipment schedules. International Journal of Production Economics, 118(1), PP: 111-117.
Ben-Daya, M., and Hariga, M. (2000). Economic lot scheduling problem with imperfect production processes. Journal of the Operational Research Society, No. 51(7), PP: 875-881.
Bourland, K.E., and Yano, C.A. (1997). A comparison of solution approaches for the fixed-sequence economic lot scheduling problem. IIE transactions, No. 29(2), PP: 103-108.
Brander, P., and Forsberg, R. (2005). Cyclic lot scheduling with sequence-dependent set-ups: a heuristic for disassembly processes. International Journal of Production Research, No. 43(2), PP: 295-310.
Chan, H. K., Chung, S.H., and Lim, M.K. (2013). Recent research trend of economic-lot scheduling problems. Journal of Manufacturing Technology Management, No. 24(3), PP: 465-482.
Chiu, S.W., Tseng, C.T., Wu, M.F., and Sung, P.C. (2014). Multi-item EPQ model with scrap, rework and multi-delivery using common cycle policy. Journal of applied research and technology, No. 12(3), PP: 615-622.
Eilon, S. (1957). Scheduling for batch production. Journal of Institute of Production Engineering, No. 36, PP: 549-570 and 582. 
Eynan, A. (2003). The benefits of flexible production rates in the economic lot scheduling problem. IIE Transactions, No. 35(11), PP: 1057-1064.
Haji, R., and Mansuri, M. (1995). Optimum common cycle for scheduling a single-machine multiproduct system with a budgetary constraint. Production Planning and Control, No. 6(2), PP: 151-156.
Haji, R., and Haji, B. (2010). Optimal batch production for a single machine system with accumulated defectives and random rate of rework. Journal of Industrial and Systems Engineering, No. 3(4), PP: 243-256.
Hanssman F. 1962. Operations research in production and inventory control (10nd ed)", John Wiley and Sons, New York.
Hariga, M.A. (1998). Economic production-ordering quantity models with limited production capacity. Production Planning and Control, No. 9(7), PP: 671-674.
He P., Zhang W., Xu X. and Bian Y. (2015). Production lot-sizing and carbon emissions under cap-and-trade and carbon tax regulations. Journal of Cleaner Production, Vol. 103, PP: 241-248.
Hennet, J.C. (2001). A common cycle approach to lot-scheduling in multistage manufacturing systems. Production Planning and Control, No. 12(4), PP: 362-371.
Jodlbauer, H., and Reitner, S. (2012). Optimizing service-level and relevant cost for a stochastic multi-item cyclic production system. International Journal of Production Economics, No. 136(2), PP: 306-317.
Johnson, L.A., and Montgomery, D.C. (1974). Operations Research in Production Planning, Scheduling, and Inventory Control (17nd ed)", John Wileyand Sons. Inc. USA.
Kim, D., Mabert, V.A., and Pinto, P.A. (1993). Integrative cycle scheduling approach for a capacitated flexible assembly system. Decision Sciences, No. 24(1), PP: 126-147.
Khouja M. 1999. A note on' deliberately slowing down output in a family production context'. International Journal of Production Research, PP: 4067-4077.
Mohammadi M. (2020). Designing an integrated reliable model for stochastic lot-sizing and scheduling problem in hazardous materials supply chain under disruption and demand uncertainty. Journal of Cleaner Production, Vol. 274, PP: 125-139.
Moon, I., Gallego, G., and Simchi-Levi, D. (1991). Controllable production rates in a family production context. The International Journal of Production Research, No. 29(12), PP: 2459-2470.
Moon I. (1994). Multiproduct economic lot size models with investment costs for setup reduction and quality improvement: review and extensions. International Journal of Production Research, No. 32, PP: 2795-2801.
Nobil, A.H., and Sedigh, A.H.A. (2017). An economic production quantity inventory model with a defective production system and uncertain uptime. International Journal of Inventory Research, No. 4(2-3), PP: 132-147.
Nobil, A.H., Sedigh, A.H.A., and Cárdenas-Barrón, L.E. (2017). A multiproduct single machine economic production quantity (EPQ) inventory model with discrete delivery order, joint production policy and budget constraints. Annals of Operations Research, PP: 1-37 (In Press).
Nobil, A.H., Afshar Sedigh, A.H., Tiwari, S., and Wee, H.M. (2018). An imperfect multi-item single machine production system with shortage, rework, and scrapped considering inspection, dissimilar deficiency levels, and non-zero setup times. Scientia Iranica (In Press).
Öner, S., and Bilgiç, T. (2008). Economic lot scheduling with uncontrolled co-production. European Journal of Operational Research, No. 188(3), PP: 793-810.
Pasandideh, S.H.R., Niaki, S.T.A., Nobil, A.H., and Cárdenas-Barrón, L.E. (2015). A multiproduct single machine economic production quantity model for an imperfect production system under warehouse construction cost. International Journal of Production Economics, No. 169, PP: 203-214.
Ramani, S., and Narayanan, N. (1992). Single facility, multi-item lot sizing under Just-in-Time and “cyclic scheduling for improvement”. International Journal of Production Economics, No. 26(1-3), PP: 333-339.
Rogers, J. (1958). A computational approach to the economic lot scheduling problem. Management science, No. 4(3), PP: 264-291.
Shirodkar, V.A., Sridharan, R., and Pillai, V. M. (2011). Effective allocation of idle time in the group technology economic lot scheduling problem. International Journal of Production Research, No. 49(24), PP: 7493-7513.
Silver, E.A. (1990). Deliberately slowing down output in a family production context. The International Journal of Production Research, No. 28(1), PP: 17-27.
Taft, E.W. (1918). The most economical production lot. Iron Age, No. 101, PP: 1410-1412.
Taleizadeh, A.A., Wee, H.M., and Jalali-Naini, S.G. (2013). Economic production quantity model with repair failure and limited capacity. Applied Mathematical Modelling, No. 37(5), PP: 2765-2774.
Taleizadeh, A.A. (2018). A constrained integrated imperfect manufacturing-inventory system with preventive maintenance and partial backordering. Annals of Operations Research, No. 261(1-2), PP: 303-337.
Vaez P., Sabouhi F. and Jabalameli M.S. (2019). Sustainability in a lot-sizing and scheduling problem with delivery time window and sequence-dependent setup cost consideration. Sustainable Cities and Society, Vol. 51, PP: 1-9.
Vemuganti, R.R., Dianich, D., Oblak, M., and Dabbaghi, H. (1990). Constrained Optimal Production Lot Sizes for Several Products. American Journal of Mathematical and Management Sciences, No. 10(3-4), PP: 199-228.
Viswanathan, S., and Goyal, S. K. (2002). On' Manufacturing batch size and ordering policy for products with shelf lives'. International Journal of Production Research, No. 40(8), PP: 1965-1970.
Wu T., Xiao F., Zhang C., He Y. and Liang Z. (2018). The green capacitated multi-item lot sizing problem with parallel machines. Computers & Operations Research, Vol. 98, PP: 149-164.