Stochastic Lot Sizing Problem with Carbon Emission Constraints

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.  

___

  • [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).