Research Article
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Year 2021, Volume: 34 Issue: 1, 148 - 160, 01.03.2021
https://doi.org/10.35378/gujs.598772

Abstract

References

  • [1] Burke, M., Davis, W.M., Diffenbaugh, N.S., "Large potential reduction in economic damages under UN mitigation targets", Nature, 557, 7706:549 , (2018).
  • [2] Internet: Global Climate Change, https://climate.nasa.gov.tr (July, 2019).
  • [3] Wagner, H.M., Whitin, T.M., "Dynamic version of the economic lot size model", Management Science, 5, 1: 89-96, (1958).
  • [4] Pochet, Y., Wolsey, L.A., “Production planning by mixed integer programming”, Springer Science & Business Media, (2006).
  • [5] Benjafaar, S., Li, Y., Daskin, M., "Carbon footprint and the management of supply chains: Insights from simple models", IEEE Transactions on Automation Science and Engineering, 10, 1: 99-116, (2012).
  • [6] Absi, N., Dauzère-Pérès, S., Kedad-Sidhoum, S., Penz, B., Rapine, C., "Lot sizing with carbon emission constraints", European Journal of Operational Research, 227, 1: 55-61, (2013).
  • [7] Helmrich, M.J.R., Jans, R., Van den Heuvel, W., Wagelmans, A.P., "The economic lot-sizing problem with an emission capacity constraint", European Journal of Operational Research, 241, 1: 50-62, (2015).
  • [8] Akbalik, A., Rapine, C., "Single-item lot sizing problem with carbon emission under the cap-and-trade policy", 2014 International Conference on Control, Decision and Information Technologies (CoDIT), IEEE, (2014).
  • [9] Romeijn, H.E., Morales, D.R., Van den Heuvel, W., "Computational complexity of finding Pareto efficient outcomes for biobjective lot‐sizing models", Naval Research Logistics (NRL), 61, 5: 386-402, (2014).
  • [10] Absi, N., Dauzère-Pérès, S., Kedad-Sidhoum, S., Penz, B., Rapine, C., "The single-item green lot-sizing problem with fixed carbon emissions", European Journal of Operational Research, 248, 3: 849-855, (2016).
  • [11] Hong, Z., Chu, C., Yu, Y., "Dual-mode production planning for manufacturing with emission constraints", European Journal of Operational Research, 251, 1: 96-106, (2016).
  • [12] Silver, E., "Inventory control under a probabilistic time-varying, demand pattern", AIIE Transactions, 10, 4: 371-379, (1978).
  • [13] Lasserre, J.B., Bes, C., Roubellat, F., "The stochastic discrete dynamic lot size problem: an open-loop solution", Operations Research, 33, 3: 684-689, (1985).
  • [14] Bookbinder, J.H., Tan, J.-Y., "Strategies for the probabilistic lot-sizing problem with service-level constraints", Management Science, 34, 9: 1096-1108, (1988).
  • [15] Tunc, H., Kilic, O.A., Tarim, S.A., Eksioglu, B., "A simple approach for assessing the cost of system nervousness", International Journal of Production Economics, 141, 2: 619-625, (2013).
  • [16] Tunc, H., Kilic, O.A., Tarim, S.A., Eksioglu, B., "A reformulation for the stochastic lot sizing problem with service-level constraints", Operations Research Letters, 42, 2: 161-165, (2014).
  • [17] Nahmias, S., Cheng, Y., “Production and operations analysis”, Vol. 6. New York: McGraw-Hill, (2005).
  • [18] Chen, F.Y., Krass, D., "Inventory models with minimal service level constraints", European Journal of Operational Research, 134, 1: 120-140, (2001).
  • [19] Purohit, A. K., Choudhary, D., Shankar R., "Inventory lot-sizing under dynamic stochastic demand with carbon emission constraints", Procedia-Social and Behavioral Sciences, 189: 193-197, (2015).
  • [20] Ghosh, A., Jha, J.K., Sarmah, S.P., “Optimal lot-sizing under strict carbon cap policy considering stochastic demand”, Applied Mathematical Modelling, 44: 688-704, (2017).
  • [21] Qiao, A., Choi, S.H., Wang, X.J., Zhao, Y.C., “Stochastic lot-sizing under carbon emission control for profit optimisation in MTO manufacturing”, In MATEC Web of Conferences, 95: 18003, EDP Sciences, (2017).
  • [22] Charnes, A., Cooper, W.W., “Deterministic equivalents for optimizing and satisficing under chance constraints”, Operations Research, 11: 18-39, (1963).
  • [23] Prekopa, A., “Handbooks in operations research and management science”, Vol 10, Chapter Probabilistic Programming, Elsevier, Amsterdam, Editors: A. Ruszczynski and A. Shapiro, (2003).
  • [24] Dentcheva, D., “Probabilistic and randomized methods for design under uncertainty”, Chapter Optimization Models with Probabilistic Constraints, Springer-Verlag, London, Editors: G. Calafiore and F. Dabbene, (2006).
  • [25] Shapiro, A., Dentcheva, D., Ruszczynski, A., “Lectures on stochastic programming: modeling and theory”, The Society for Industrial and Applied Mathematics and The Mathematical Programming Society, Philadelphia, USA, (2009).
  • [26] Koca, E, Yaman, H., Aktürk, M.S., "Stochastic lot sizing problem with controllable processing times", Omega, 53: 1-10, (2015).

Stochastic Lot Sizing Problem with Carbon Emission Constraints

Year 2021, Volume: 34 Issue: 1, 148 - 160, 01.03.2021
https://doi.org/10.35378/gujs.598772

Abstract

In
this paper, we study the stochastic lot sizing problem with probabilistic
carbon emission constraints. To the best of our knowledge, this is the first
study that considers this problem. We study the problem under static
uncertainty strategy and α service level constraints. We consider both the
periodic and global carbon emission constraints and use chance constraints to
ensure that the carbon emission constraints are satisfied with the desired
probabilities. We formulate the problems as mixed integer program and solve
them by a commercial solver. Our computational experiments show that the
formulations can be
solved for quite large problem instances
in reasonable times. We compare the probabilistic global and periodic emission
constraints according to their effects on the total cost and carbon
emissions.  

References

  • [1] Burke, M., Davis, W.M., Diffenbaugh, N.S., "Large potential reduction in economic damages under UN mitigation targets", Nature, 557, 7706:549 , (2018).
  • [2] Internet: Global Climate Change, https://climate.nasa.gov.tr (July, 2019).
  • [3] Wagner, H.M., Whitin, T.M., "Dynamic version of the economic lot size model", Management Science, 5, 1: 89-96, (1958).
  • [4] Pochet, Y., Wolsey, L.A., “Production planning by mixed integer programming”, Springer Science & Business Media, (2006).
  • [5] Benjafaar, S., Li, Y., Daskin, M., "Carbon footprint and the management of supply chains: Insights from simple models", IEEE Transactions on Automation Science and Engineering, 10, 1: 99-116, (2012).
  • [6] Absi, N., Dauzère-Pérès, S., Kedad-Sidhoum, S., Penz, B., Rapine, C., "Lot sizing with carbon emission constraints", European Journal of Operational Research, 227, 1: 55-61, (2013).
  • [7] Helmrich, M.J.R., Jans, R., Van den Heuvel, W., Wagelmans, A.P., "The economic lot-sizing problem with an emission capacity constraint", European Journal of Operational Research, 241, 1: 50-62, (2015).
  • [8] Akbalik, A., Rapine, C., "Single-item lot sizing problem with carbon emission under the cap-and-trade policy", 2014 International Conference on Control, Decision and Information Technologies (CoDIT), IEEE, (2014).
  • [9] Romeijn, H.E., Morales, D.R., Van den Heuvel, W., "Computational complexity of finding Pareto efficient outcomes for biobjective lot‐sizing models", Naval Research Logistics (NRL), 61, 5: 386-402, (2014).
  • [10] Absi, N., Dauzère-Pérès, S., Kedad-Sidhoum, S., Penz, B., Rapine, C., "The single-item green lot-sizing problem with fixed carbon emissions", European Journal of Operational Research, 248, 3: 849-855, (2016).
  • [11] Hong, Z., Chu, C., Yu, Y., "Dual-mode production planning for manufacturing with emission constraints", European Journal of Operational Research, 251, 1: 96-106, (2016).
  • [12] Silver, E., "Inventory control under a probabilistic time-varying, demand pattern", AIIE Transactions, 10, 4: 371-379, (1978).
  • [13] Lasserre, J.B., Bes, C., Roubellat, F., "The stochastic discrete dynamic lot size problem: an open-loop solution", Operations Research, 33, 3: 684-689, (1985).
  • [14] Bookbinder, J.H., Tan, J.-Y., "Strategies for the probabilistic lot-sizing problem with service-level constraints", Management Science, 34, 9: 1096-1108, (1988).
  • [15] Tunc, H., Kilic, O.A., Tarim, S.A., Eksioglu, B., "A simple approach for assessing the cost of system nervousness", International Journal of Production Economics, 141, 2: 619-625, (2013).
  • [16] Tunc, H., Kilic, O.A., Tarim, S.A., Eksioglu, B., "A reformulation for the stochastic lot sizing problem with service-level constraints", Operations Research Letters, 42, 2: 161-165, (2014).
  • [17] Nahmias, S., Cheng, Y., “Production and operations analysis”, Vol. 6. New York: McGraw-Hill, (2005).
  • [18] Chen, F.Y., Krass, D., "Inventory models with minimal service level constraints", European Journal of Operational Research, 134, 1: 120-140, (2001).
  • [19] Purohit, A. K., Choudhary, D., Shankar R., "Inventory lot-sizing under dynamic stochastic demand with carbon emission constraints", Procedia-Social and Behavioral Sciences, 189: 193-197, (2015).
  • [20] Ghosh, A., Jha, J.K., Sarmah, S.P., “Optimal lot-sizing under strict carbon cap policy considering stochastic demand”, Applied Mathematical Modelling, 44: 688-704, (2017).
  • [21] Qiao, A., Choi, S.H., Wang, X.J., Zhao, Y.C., “Stochastic lot-sizing under carbon emission control for profit optimisation in MTO manufacturing”, In MATEC Web of Conferences, 95: 18003, EDP Sciences, (2017).
  • [22] Charnes, A., Cooper, W.W., “Deterministic equivalents for optimizing and satisficing under chance constraints”, Operations Research, 11: 18-39, (1963).
  • [23] Prekopa, A., “Handbooks in operations research and management science”, Vol 10, Chapter Probabilistic Programming, Elsevier, Amsterdam, Editors: A. Ruszczynski and A. Shapiro, (2003).
  • [24] Dentcheva, D., “Probabilistic and randomized methods for design under uncertainty”, Chapter Optimization Models with Probabilistic Constraints, Springer-Verlag, London, Editors: G. Calafiore and F. Dabbene, (2006).
  • [25] Shapiro, A., Dentcheva, D., Ruszczynski, A., “Lectures on stochastic programming: modeling and theory”, The Society for Industrial and Applied Mathematics and The Mathematical Programming Society, Philadelphia, USA, (2009).
  • [26] Koca, E, Yaman, H., Aktürk, M.S., "Stochastic lot sizing problem with controllable processing times", Omega, 53: 1-10, (2015).
There are 26 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Industrial Engineering
Authors

Esra Koca 0000-0002-7478-1220

Publication Date March 1, 2021
Published in Issue Year 2021 Volume: 34 Issue: 1

Cite

APA Koca, E. (2021). Stochastic Lot Sizing Problem with Carbon Emission Constraints. Gazi University Journal of Science, 34(1), 148-160. https://doi.org/10.35378/gujs.598772
AMA Koca E. Stochastic Lot Sizing Problem with Carbon Emission Constraints. Gazi University Journal of Science. March 2021;34(1):148-160. doi:10.35378/gujs.598772
Chicago Koca, Esra. “Stochastic Lot Sizing Problem With Carbon Emission Constraints”. Gazi University Journal of Science 34, no. 1 (March 2021): 148-60. https://doi.org/10.35378/gujs.598772.
EndNote Koca E (March 1, 2021) Stochastic Lot Sizing Problem with Carbon Emission Constraints. Gazi University Journal of Science 34 1 148–160.
IEEE E. Koca, “Stochastic Lot Sizing Problem with Carbon Emission Constraints”, Gazi University Journal of Science, vol. 34, no. 1, pp. 148–160, 2021, doi: 10.35378/gujs.598772.
ISNAD Koca, Esra. “Stochastic Lot Sizing Problem With Carbon Emission Constraints”. Gazi University Journal of Science 34/1 (March 2021), 148-160. https://doi.org/10.35378/gujs.598772.
JAMA Koca E. Stochastic Lot Sizing Problem with Carbon Emission Constraints. Gazi University Journal of Science. 2021;34:148–160.
MLA Koca, Esra. “Stochastic Lot Sizing Problem With Carbon Emission Constraints”. Gazi University Journal of Science, vol. 34, no. 1, 2021, pp. 148-60, doi:10.35378/gujs.598772.
Vancouver Koca E. Stochastic Lot Sizing Problem with Carbon Emission Constraints. Gazi University Journal of Science. 2021;34(1):148-60.