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Multi-item single source ordering problem with transportation cost: A Lagrangian decomposition approach

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  • Ertogral, Kadir

Abstract

As a part of supply chain management literature and practice, it has been recognized that there can be significant gains in integrating inventory and transportation decisions. The problem we tackle here is a common one both in retail and production sectors where several items have to be ordered from a single supplier. We assume that there is a finite planning horizon to make the ordering decisions for the items, and in this finite horizon the retailer or the producer knows the demand of each item in each period. In addition to the inventory holding cost, an item-base fixed cost associated with each item included in the order, and a piecewise linear transportation cost are incurred. We suggest a Lagrangean decomposition based solution procedure for the problem and carry out numerical experiments to analyze the value of integrating inventory and transportation decisions under different scenarios.

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  • 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.
    • Handle: RePEc:eee:ejores:v:191:y:2008:i:1:p:156-165
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    1. 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.
    2. 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.
    3. 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.
    4. Burwell, Timothy H. & Dave, Dinesh S. & Fitzpatrick, Kathy E. & Roy, Melvin R., 1997. "Economic lot size model for price-dependent demand under quantity and freight discounts," International Journal of Production Economics, Elsevier, vol. 48(2), pages 141-155, January.
    5. 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.
    6. Panayotis Afentakis & Bezalel Gavish, 1986. "Optimal Lot-Sizing Algorithms for Complex Product Structures," Operations Research, INFORMS, vol. 34(2), pages 237-249, April.
    7. E. Powell Robinson, Jr. & Li-Lian Gao, 1996. "A Dual Ascent Procedure for Multiproduct Dynamic Demand Coordinated Replenishment with Backlogging," Management Science, INFORMS, vol. 42(11), pages 1556-1564, November.
    8. 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.
    9. W. J. Baumol & H. D. Vinod, 1970. "An Inventory Theoretic Model of Freight Transport Demand," Management Science, INFORMS, vol. 16(7), pages 413-421, March.
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    3. Tamssaouet, Karim & Engebrethsen, Erna & Dauzère-Pérès, Stéphane, 2023. "Multi-item dynamic lot sizing with multiple transportation modes and item fragmentation," International Journal of Production Economics, Elsevier, vol. 265(C).
    4. Mou, Shandong & Robb, David J. & DeHoratius, Nicole, 2018. "Retail store operations: Literature review and research directions," European Journal of Operational Research, Elsevier, vol. 265(2), pages 399-422.
    5. 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.
    6. Hua, Guowei & Wang, Shouyang & Cheng, T.C.E., 2012. "Optimal pricing and order quantity for the newsvendor problem with free shipping," International Journal of Production Economics, Elsevier, vol. 135(1), pages 162-169.
    7. Sadia Samar Ali & Haripriya Barman & Rajbir Kaur & Hana Tomaskova & Sankar Kumar Roy, 2021. "Multi-Product Multi Echelon Measurements of Perishable Supply Chain: Fuzzy Non-Linear Programming Approach," Mathematics, MDPI, vol. 9(17), pages 1-27, August.
    8. Lai, Minghui & Cai, Xiaoqiang & Li, Xiang, 2017. "Mechanism design for collaborative production-distribution planning with shipment consolidation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 106(C), pages 137-159.
    9. Sancak, Emre & Salman, F. Sibel, 2011. "Multi-item dynamic lot-sizing with delayed transportation policy," International Journal of Production Economics, Elsevier, vol. 131(2), pages 595-603, June.
    10. Chiu, Yuan-Shyi Peter & Huang, Chao-Chih & Wu, Mei-Fang & Chang, Huei-Hsin, 2013. "Joint determination of rotation cycle time and number of shipments for a multi-item EPQ model with random defective rate," Economic Modelling, Elsevier, vol. 35(C), pages 112-117.

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