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Efficient formulation and heuristics for multi-item single source ordering problem with transportation cost

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  • Saravanan Venkatachalam
  • Arunachalam Narayanan

Abstract

Integrated inventory and transportation decisions are critical in the supply chain, providing significant gains for all parties. In this paper, we present a mathematical formulation for the dynamic demand multi-item single source replenishment problem with a piecewise linear transportation cost. Through an extensive experimental study, we find that the new formulation provides a tighter LP relaxation of the problem, while requiring fewer computational resources to optimally solve the problem when compared with existing model in the literature. We also present a new metaheuristic for this general class of coordinated capacitated replenishment problems. On average, the solutions from heuristics are within 1.23% of the optimal solution for the comprehensive set of test problems.

Suggested Citation

  • Saravanan Venkatachalam & Arunachalam Narayanan, 2016. "Efficient formulation and heuristics for multi-item single source ordering problem with transportation cost," International Journal of Production Research, Taylor & Francis Journals, vol. 54(14), pages 4087-4103, July.
  • Handle: RePEc:taf:tprsxx:v:54:y:2015:i:14:p:4087-4103
    DOI: 10.1080/00207543.2015.1088666
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    1. Sven Axsäter & Christian Howard & Johan Marklund, 2013. "A distribution inventory model with transshipments from a support warehouse," IISE Transactions, Taylor & Francis Journals, vol. 45(3), pages 309-322.
    2. Van Eijs, M. J. G., 1994. "Multi-item inventory systems with joint ordering and transportation decisions," International Journal of Production Economics, Elsevier, vol. 35(1-3), pages 285-292, June.
    3. Robinson, Powell & Narayanan, Arunachalam & Sahin, Funda, 2009. "Coordinated deterministic dynamic demand lot-sizing problem: A review of models and algorithms," Omega, Elsevier, vol. 37(1), pages 3-15, February.
    4. Lap Mui Ann Chan & Ana Muriel & Zuo-Jun Max Shen & David Simchi-Levi & Chung-Piaw Teo, 2002. "Effective Zero-Inventory-Ordering Policies for the Single-Warehouse Multiretailer Problem with Piecewise Linear Cost Structures," Management Science, INFORMS, vol. 48(11), pages 1446-1460, November.
    5. Wang, Lin & He, Jing & Wu, Desheng & Zeng, Yu-Rong, 2012. "A novel differential evolution algorithm for joint replenishment problem under interdependence and its application," International Journal of Production Economics, Elsevier, vol. 135(1), pages 190-198.
    6. Sıla Çetinkaya & Chung‐Yee Lee, 2002. "Optimal outbound dispatch policies: Modeling inventory and cargo capacity," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(6), pages 531-556, September.
    7. Ertogral, K. & Darwish, M. & Ben-Daya, M., 2007. "Production and shipment lot sizing in a vendor-buyer supply chain with transportation cost," European Journal of Operational Research, Elsevier, vol. 176(3), pages 1592-1606, February.
    8. Khouja, Moutaz & Goyal, Suresh, 2008. "A review of the joint replenishment problem literature: 1989-2005," European Journal of Operational Research, Elsevier, vol. 186(1), pages 1-16, April.
    9. Awi Federgruen & Joern Meissner & Michal Tzur, 2007. "Progressive Interval Heuristics for Multi-Item Capacitated Lot-Sizing Problems," Operations Research, INFORMS, vol. 55(3), pages 490-502, June.
    10. Konur, Dinçer & Toptal, Ayşegül, 2012. "Analysis and applications of replenishment problems under stepwise transportation costs and generalized wholesale prices," International Journal of Production Economics, Elsevier, vol. 140(1), pages 521-529.
    11. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    12. Amiya K. Chakravarty, 1984. "Joint Inventory Replenishments with Group Discounts Based on Invoice Value," Management Science, INFORMS, vol. 30(9), pages 1105-1112, September.
    13. Meltem Denizel & S. Selcuk Erenguc & Hanif D. Sherali, 1996. "Convex envelope results and strong formulations for a class of mixed‐integer programs," Naval Research Logistics (NRL), John Wiley & Sons, vol. 43(4), pages 503-518, June.
    14. Rieksts, Brian Q. & Ventura, Jose A., 2008. "Optimal inventory policies with two modes of freight transportation," European Journal of Operational Research, Elsevier, vol. 186(2), pages 576-585, April.
    15. Ertogral, Kadir, 2008. "Multi-item single source ordering problem with transportation cost: A Lagrangian decomposition approach," European Journal of Operational Research, Elsevier, vol. 191(1), pages 156-165, November.
    16. van Norden, Linda & van de Velde, Steef, 2005. "Multi-product lot-sizing with a transportation capacity reservation contract," European Journal of Operational Research, Elsevier, vol. 165(1), pages 127-138, August.
    17. Porras, Eric & Dekker, Rommert, 2006. "An efficient optimal solution method for the joint replenishment problem with minimum order quantities," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1595-1615, November.
    18. Mansini, Renata & Savelsbergh, Martin W.P. & Tocchella, Barbara, 2012. "The supplier selection problem with quantity discounts and truckload shipping," Omega, Elsevier, vol. 40(4), pages 445-455.
    19. Rizk, Nafee & Martel, Alain & Ramudhin, Amar, 2006. "A Lagrangean relaxation algorithm for multi-item lot-sizing problems with joint piecewise linear resource costs," International Journal of Production Economics, Elsevier, vol. 102(2), pages 344-357, August.
    20. Swenseth, Scott R. & Godfrey, Michael R., 2002. "Incorporating transportation costs into inventory replenishment decisions," International Journal of Production Economics, Elsevier, vol. 77(2), pages 113-130, May.
    21. Lee, Woon-Seek & Han, Jong-Han & Cho, Sung-Jin, 2005. "A heuristic algorithm for a multi-product dynamic lot-sizing and shipping problem," International Journal of Production Economics, Elsevier, vol. 98(2), pages 204-214, November.
    22. Narayanan, Arunachalam & Robinson, Powell, 2010. "Efficient and effective heuristics for the coordinated capacitated lot-size problem," European Journal of Operational Research, Elsevier, vol. 203(3), pages 583-592, June.
    23. E P Robinson & A Narayanan & L-L Gao, 2007. "Effective heuristics for the dynamic demand joint replenishment problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 58(6), pages 808-815, June.
    24. Chung-Yee Lee & Sila Çetinkaya & Wikrom Jaruphongsa, 2003. "A Dynamic Model for Inventory Lot Sizing and Outbound Shipment Scheduling at a Third-Party Warehouse," Operations Research, INFORMS, vol. 51(5), pages 735-747, October.
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    3. Zhang, Ren-Qian & Yi, Meng & Wang, Qi-Qi & Xiang, Chen, 2018. "Polynomial algorithm of inventory model with complete backordering and correlated demand caused by cross-selling," International Journal of Production Economics, Elsevier, vol. 199(C), pages 193-198.

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