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Research Article

Improved Lagrangian-relaxation based approaches for multi-period multi-stage fixed charge transportation problem

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Article: 2224511 | Received 20 Dec 2022, Accepted 31 May 2023, Published online: 21 Jun 2023

References

  • Adlakha, V., & Kowalski, K. (2003). A simple heuristic for solving small fixed-charge transportation problems. Omega, 31(3), 205–211. https://doi.org/10.1016/S0305-0483(03)00025-2
  • Adlakha, V., Kowalski, K., Vemuganti, R., & Lev, B. (2007). More-for-less algorithm for fixed-charge transportation problems. Omega, 35(1), 116–127. https://doi.org/10.1016/j.omega.2006.03.001
  • Adlakha, V., Kowalski, K., Wang, S., Lev, B., & Shen, W. (2014). On approximation of the fixed charge transportation problem. Omega, 43, 64–70. https://doi.org/10.1016/j.omega.2013.06.005
  • Akbari, M., Molla-Alizadeh-Zavardehi, S., & Niroomand, S. (2020). Meta-heuristic approaches for fixed-charge solid transportation problem in two-stage supply chain network. Operational Research, 20(1), 447–471. https://doi.org/10.1007/s12351-017-0332-7
  • Alam, S. T., Ahmed, S., Ali, S. M., Sarker, S., & Kabir, G. (2021). Challenges to COVID-19 vaccine supply chain: Implications for sustainable development goals. International Journal of Production Economics, 239, 108193. https://doi.org/10.1016/j.ijpe.2021.108193
  • Balaji, A. N., Mukund Nilakantan, J., Nielsen, I., Jawahar, N., & Ponnambalam, S. G. (2019). Solving fixed charge transportation problem with truck load constraint using metaheuristics. Annals of Operations Research, 273(1-2), 207–236. https://doi.org/10.1007/s10479-017-2692-z
  • Balinski, M. L. (1961). Fixed-cost transportation problems. Naval Research Logistics, 8(1), 41–54. https://doi.org/10.1002/(ISSN)1931-9193
  • Barbarosoğlu, G., & Özgür, D. (1999). Hierarchical design of an integrated production and 2-echelon distribution system. European Journal of Operational Research, 118(3), 464–484. https://doi.org/10.1016/S0377-2217(98)00317-8
  • Barr, R. S., Glover, F., & Klingman, D. (1981). A new optimization method for large scale fixed charge transportation problems. Operations Research, 29(3), 448–463. https://doi.org/10.1287/opre.29.3.448
  • Cabot, A. V., & Erenguc, S. S. (1984). Some branch-and-bound procedures for fixed-cost transportation problems. Naval Research Logistics, 31(1), 145–154. https://doi.org/10.1002/(ISSN)1931-9193
  • Calvete, H. I., Galé, C., Iranzo, J. A., & Toth, P. (2018). A matheuristic for the two-stage fixed-charge transportation problem. Computers & Operations Research, 95, 113–122. https://doi.org/10.1016/j.cor.2018.03.007
  • Chandra, P., & Fisher, M. L. (1994). Coordination of production and distribution planning. European Journal of Operational Research, 72(3), 503–517. https://doi.org/10.1016/0377-2217(94)90419-7
  • Chowdhury, P., Paul, S. K., Kaisar, S., & Moktadir, M. A. (2021). COVID-19 pandemic related supply chain studies: A systematic review. Transportation Research Part E: Logistics and Transportation Review, 148, 102271. https://doi.org/10.1016/j.tre.2021.102271
  • Chun, F., & Yi, Z. (2009). A genetic algorithm of two-stage supply chain distribution problem associated with fixed charge and multiple transportation modes. Natural Computation. In ICNC'09. Fifth International Conference on (Vol. 4) IEEE.
  • Eckert, C., & Gottlieb, J. (2002). Direct representation and variation operators for the fixed charge transportation problem. In International Conference on Parallel Problem Solving from Nature (pp. 77–87) Springer.
  • Ezhil, S. A., & Rajendran, C. (2017). Lagrangian-Relaxation based bounding approaches and fast deterministic heuristics for a class of multi-stage fixed-charge transportation problems. In 7th International Conference on Industrial Engineering and Systems Management (pp. 604–609). Industrial Engineering and Systems Management (IESM)
  • Fisher, M. L. (1981). The Lagrangian relaxation method for solving integer programming problems. Management Science, 27(1), 1–18. https://doi.org/10.1287/mnsc.27.1.1
  • Godwin, T., Gopalan, R., & Narendran, T. T. (2015). Estimating order delivery times and fleet capacity in freight rail networks: Part I-simulation modelling. International Journal of Operational Research, 24(3), 329–355. https://doi.org/10.1504/IJOR.2015.072232
  • Gopalan, R. (2015). Computational complexity of convoy movement planning problems. Mathematical Methods of Operations Research, 82(1), 31–60. https://doi.org/10.1007/s00186-015-0503-3
  • Gray, P. (1971). Exact solution of the fixed-charge transportation problem. Operations Research, 19(6), 1529–1538. https://doi.org/10.1287/opre.19.6.1529
  • Haq, A. N., Vrat, P., & Kanda, A. (1991). An integrated production-inventory-distribution model for manufacture of urea: A case. International Journal of Production Economics, 25(1-3), 39–49. https://doi.org/10.1016/0925-5273(91)90129-H
  • Hirsch, W. M., & Dantzig, G. B. (1968). The fixed charge problem. Naval Research Logistics, 15(3), 413–424. https://doi.org/10.1002/nav.3800150306
  • Hultberg, T. H., & Cardoso, D. M. (1997). The teacher assignment problem: A special case of the fixed charge transportation problem. European Journal of Operational Research, 101(3), 463–473. https://doi.org/10.1016/S0377-2217(96)00082-3
  • Jawahar, N., & Balaji, A. (2009). A genetic algorithm for the two-stage supply chain distribution problem associated with a fixed charge. European Journal of Operational Research, 194(2), 496–537. https://doi.org/10.1016/j.ejor.2007.12.005
  • Jawahar, N., & Balaji, N. (2010). Constructive heuristics to the multi-period fixed charge transportation problem. International Journal of Business Performance and Supply Chain Modelling, 2(2), 97–111. https://doi.org/10.1504/IJBPSCM.2010.036163
  • Jawahar, N., Gunasekaran, A., & Balaji, N. (2012). A simulated annealing algorithm to the multi-period fixed charge distribution problem associated with backorder and inventory. International Journal of Production Research, 50(9), 2533–2554. https://doi.org/10.1080/00207543.2011.581013
  • Kennington, J., & Unger, E. (1976). A new branch-and-bound algorithm for the fixed-charge transportation problem. Management Science, 22(10), 1116–1126. https://doi.org/10.1287/mnsc.22.10.1116
  • Lin, Q., Zhao, Q., & Lev, B. (2020). Cold chain transportation decision in the vaccine supply chain. European Journal of Operational Research, 283(1), 182–195. https://doi.org/10.1016/j.ejor.2019.11.005
  • McKeown, P. G. (1981). A branch-and-bound algorithm for solving fixed charge problems. Naval Research Logistics, 28(4), 607–617. https://doi.org/10.1002/(ISSN)1931-9193
  • MD Logistics (2021). White paper: Extending the life sciences and pharmaceutical supply chain. https://www.mdlogistics.com/wp-content/uploads/2021/02/White-Paper_Extending-the-Life-Sciences-and-Pharmaceutical-Supply-Chain.pdf
  • Mogale, D., Kumar, S. K., Márquez, F. P. G., & Tiwari, M. K. (2017). Bulk wheat transportation and storage problem of public distribution system. Computers & Industrial Engineering, 104, 80–97. https://doi.org/10.1016/j.cie.2016.12.027
  • Murty, K. G. (1968). Solving the fixed charge problem by ranking the extreme points. Operations Research, 16(2), 268–279. https://doi.org/10.1287/opre.16.2.268
  • Palekar, U. S., Karwan, M. H., & Zionts, S. (1990). A branch-and-bound method for the fixed charge transportation problem. Management Science, 36(9), 1092–1105. https://doi.org/10.1287/mnsc.36.9.1092
  • Panicker, V. V., Vanga, R., & Sridharan, R. (2013). Ant colony optimisation algorithm for distribution-allocation problem in a two-stage supply chain with a fixed transportation charge. International Journal of Production Research, 51(3), 698–717. https://doi.org/10.1080/00207543.2012.658118
  • Pramanik, S., Jana, D. K., & Maiti, M. (2016). Bi-criteria solid transportation problem with substitutable and damageable items in disaster response operations on fuzzy rough environment. Socio-Economic Planning Sciences, 55, 1–13. https://doi.org/10.1016/j.seps.2016.04.002
  • Pramanik, S., Jana, D. K., Mondal, S. K., & Maiti, M. (2015). A fixed-charge transportation problem in two-stage supply chain network in Gaussian type-2 fuzzy environments. Information Sciences, 325, 190–214. https://doi.org/10.1016/j.ins.2015.07.012
  • Raj, K. A. A. D, & Rajendran, C. (2009). Fast heuristic algorithms to solve a single-stage fixed-charge transportation problem. International Journal of Operational Research, 6(3), 304–329. https://doi.org/10.1504/IJOR.2009.026936
  • Raj, K. A. A. D., & Rajendran, C. (2011). A hybrid genetic algorithm for solving single-stage fixed-charge transportation problems. Technology Operation Management, 2(1), 1–15. https://doi.org/10.1007/s13727-012-0001-2
  • Raj, K. A. A. D., & Rajendran, C. (2012). A genetic algorithm for solving the fixed-charge transportation model: Two-stage problem. Computers & Operations Research, 39(9), 2016–2032. https://doi.org/10.1016/j.cor.2011.09.020
  • Reeves, C. R. (1995). Modern heuristic techniques for combinatorial problems. Advanced topics in computer science. In Modern heuristic techniques for combinatorial problems: Advanced topics in computer science. John Wiley & Sons, Inc
  • Robers, P., & Cooper, L. (1976). A study of the fixed charge transportation problem. Computers & Mathematics with Applications, 2(2), 125–135. https://doi.org/10.1016/0898-1221(76)90024-9
  • Sadagopan, S., & Ravindran, A. (1982). A vertex ranking algorithm for the fixed-charge transportation problem. Journal of Optimization Theory and Applications, 37(2), 221–230. https://doi.org/10.1007/BF00934768
  • Sahoo, P., Jana, D. K., Pramanik, S., & Panigrahi, G. (2023). Implement an uncertain vector approach to solve entropy-based four-dimensional transportation problems with discounted costs. International Journal of Machine Learning and Cybernetics, 14(1), 3–31. https://doi.org/10.1007/s13042-021-01457-8
  • Schaffer, J. R., & O'Leary, D. E. (1989). Use of penalties in a branch and bound procedure for the fixed charge transportation problem. European Journal of Operational Research, 43(3), 305–312. https://doi.org/10.1016/0377-2217(89)90229-4
  • Schrenk, S., Finke, G., & Cung, V. (2011). Two classical transportation problems revisited: Pure constant fixed charges and the paradox. Mathematical and Computer Modelling, 54( 9-10), 2306–2315. https://doi.org/10.1016/j.mcm.2011.05.039
  • Sharma, V., Dahiya, K., & Verma, V. (2010). Capacitated two-stage time minimization transportation problem. Asia-Pacific Journal of Operational Research, 27(04), 457–476. https://doi.org/10.1142/S021759591000279X
  • Sun, M., Aronson, J. E., McKeown, P. G., & Drinka, D. (1998). A tabu search heuristic procedure for the fixed charge transportation problem. European Journal of Operational Research, 106(2-3), 441–456. https://doi.org/10.1016/S0377-2217(97)00284-1
  • UNICEF (2006). Solid and liquid waste management in rural areas: A technical note. Government of India, Ministry of Rural Development, Department of Drinking Water Supply, New Delhi. https://swachhbharatmission.gov.in/sbmcms/writereaddata/images/pdf/technical-notes-manuals/SLWM-in-Rural-Areas-Technical-Note.pdf
  • Vinay, V., & Sridharan, R. (2012). Development and analysis of heuristic algorithms for a two-stage supply chain allocation problem with a fixed transportation cost. International Journal of Services and Operations Management, 12(2), 244–268. https://doi.org/10.1504/IJSOM.2012.047107

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