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An exact algorithm for the Capacitated Total Quantity Discount Problem

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  • Manerba, Daniele
  • Mansini, Renata

Abstract

In this paper we analyze the procurement problem of a company that needs to purchase a number of products from a set of suppliers to satisfy demand. The suppliers offer total quantity discounts and the company aims at selecting a set of suppliers so to satisfy product demand at minimum purchasing cost. The problem, known as Total Quantity Discount Problem (TQDP), is strongly NP-hard. We study different families of valid inequalities and provide a branch-and-cut approach to solve the capacitated variant of the problem (Capacitated TQDP) where the quantity available for a product from a supplier is limited. A hybrid algorithm, called HELP (Heuristic Enhancement from LP), is used to provide an initial feasible solution to the exact approach. HELP exploits information provided by the continuous relaxation problem to construct neighborhoods optimally searched through the solution of mixed integer subproblems. A streamlined version of the proposed exact method can optimally solve in a reasonable amount of time instances with up to 100 suppliers and 500 products, and largely outperforms an existing approach available in the literature and CPLEX 12.2 that frequently runs out of memory before completing the search.

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  • Manerba, Daniele & Mansini, Renata, 2012. "An exact algorithm for the Capacitated Total Quantity Discount Problem," European Journal of Operational Research, Elsevier, vol. 222(2), pages 287-300.
    • Handle: RePEc:eee:ejores:v:222:y:2012:i:2:p:287-300
    DOI: 10.1016/j.ejor.2012.04.028
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    4. Kirschstein, Thomas & Meisel, Frank, 2019. "A multi-period multi-commodity lot-sizing problem with supplier selection, storage selection and discounts for the process industry," European Journal of Operational Research, Elsevier, vol. 279(2), pages 393-406.
    5. Nguyen, H.N. & Rainwater, C.E. & Mason, S.J. & Pohl, E.A., 2014. "Quantity discount with freight consolidation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 66(C), pages 66-82.
    6. Manerba, Daniele & Mansini, Renata & Perboli, Guido, 2018. "The Capacitated Supplier Selection problem with Total Quantity Discount policy and Activation Costs under uncertainty," International Journal of Production Economics, Elsevier, vol. 198(C), pages 119-132.
    7. Manerba, Daniele & Mansini, Renata & Riera-Ledesma, Jorge, 2017. "The Traveling Purchaser Problem and its variants," European Journal of Operational Research, Elsevier, vol. 259(1), pages 1-18.
    8. Li, Xin & Ventura, José A. & Venegas, Bárbara B. & Kweon, Sang Jin & Hwang, Seong Wook, 2018. "An integrated acquisition policy for supplier selection and lot sizing considering total quantity discounts and a quality constraint," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 119(C), pages 19-40.
    9. Chung, Wenming & Talluri, Srinivas & Narasimhan, Ram, 2015. "Optimal pricing and inventory strategies with multiple price markdowns over time," European Journal of Operational Research, Elsevier, vol. 243(1), pages 130-141.
    10. Maheswar Singh Mahapatra & Pravash Chandra Pradhan & J. K. Jha, 2022. "Sourcing decisions with order allocation under supply disruption risk considering quantitative and qualitative criteria," Operational Research, Springer, vol. 22(4), pages 3291-3333, September.
    11. Bianchessi, N. & Mansini, R. & Speranza, M.G., 2014. "The distance constrained multiple vehicle traveling purchaser problem," European Journal of Operational Research, Elsevier, vol. 235(1), pages 73-87.
    12. Aria Shahsavar & Nima Zoraghi & Babak Abbasi, 2018. "Integration of resource investment problem with quantity discount problem in material ordering for minimizing resource costs of projects," Operational Research, Springer, vol. 18(2), pages 315-342, July.
    13. Riccardo Giusti & Chiara Iorfida & Yuanyuan Li & Daniele Manerba & Stefano Musso & Guido Perboli & Roberto Tadei & Shuai Yuan, 2019. "Sustainable and De-Stressed International Supply-Chains Through the SYNCHRO-NET Approach," Sustainability, MDPI, vol. 11(4), pages 1-26, February.
    14. Song, Zhuzhu & Tang, Wansheng & Zhao, Ruiqing, 2019. "Encroachment and canvassing strategy in a sea-cargo service chain with empty container repositioning," European Journal of Operational Research, Elsevier, vol. 276(1), pages 175-186.

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