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Linearization technique with superior expressions for centralized planning problem with discount policy

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  • Yang, Fang
  • Huang, Yao-Huei

Abstract

This paper studies a centralized planning problem (CPP), which is a variant of the winner determination problem (WDP) in transportation service procurement. The WDP contains one shipper with multiple depots, and multiple carriers. Traditionally, the shipper solves the WDP to obtain winning carriers for serving lanes. In this paper, the shipper specifically considers J possible locations, and then only p locations can be selected as depots. These carriers provided the best quantity discount are able to obtain the best chance of being winners for serving lanes. This study proposes a mixed-integer nonlinear programming (MINP) model for the CPP. The non-convex property of the MINP makes the model difficult to find an exact global optimal solution efficiently and effectively. To overcome the difficulty, the MINP model can be converted into a mixed-integer linear programming (MILP) model to obtain an optimal solution by utilizing the proposed linearization technique with superior expressions. Numerical experiments also show the usefulness of the proposed model, and indicate that moderately sized realistic instances can be solved efficiently and effectively.

Suggested Citation

  • Yang, Fang & Huang, Yao-Huei, 2020. "Linearization technique with superior expressions for centralized planning problem with discount policy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    • Handle: RePEc:eee:phsmap:v:542:y:2020:i:c:s0378437119315614
    DOI: 10.1016/j.physa.2019.122746
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    References listed on IDEAS

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    1. Richard Li-Yang Chen & Shervin AhmadBeygi & Amy Cohn & Damian R. Beil & Amitabh Sinha, 2009. "Solving Truckload Procurement Auctions Over an Exponential Number of Bundles," Transportation Science, INFORMS, vol. 43(4), pages 493-510, November.
    2. Gianfranco Guastaroba & Renata Mansini & M Grazia Speranza, 2009. "Modeling the Pre Auction Stage The Truckload Case," Lecture Notes in Economics and Mathematical Systems, in: Jo A.E.E. Nunen & M. Grazia Speranza & Luca Bertazzi (ed.), Innovations in Distribution Logistics, chapter 11, pages 219-233, Springer.
    3. Martins, Ricardo Silveira & Xavier, Wescley Silva & De Souza Filho, Osmar Vieira & Martins, Guilherme Silveira, 2010. "Transport management in small and medium-sized enterprises in Brazil," Journal of Operations and Supply Chain Management (JOSCM), Fundação Getulio Vargas, Escola de Administração de Empresas de São Paulo (FGV EAESP), vol. 3(1), June.
    4. Triki, Chefi & Oprea, Simona & Beraldi, Patriza & Crainic, Teodor Gabriel, 2014. "The stochastic bid generation problem in combinatorial transportation auctions," European Journal of Operational Research, Elsevier, vol. 236(3), pages 991-999.
    5. Chang, Tsung-Sheng, 2009. "Decision support for truckload carriers in one-shot combinatorial auctions," Transportation Research Part B: Methodological, Elsevier, vol. 43(5), pages 522-541, June.
    6. Lee, Chi-Guhn & Kwon, Roy H. & Ma, Zhong, 2007. "A carrier's optimal bid generation problem in combinatorial auctions for transportation procurement," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 43(2), pages 173-191, March.
    7. Andrew Lim & Brian Rodrigues & Zhou Xu, 2008. "Transportation Procurement with Seasonally Varying Shipper Demand and Volume Guarantees," Operations Research, INFORMS, vol. 56(3), pages 758-771, June.
    8. Han-Lin Li & Hao-Chun Lu, 2009. "Global Optimization for Generalized Geometric Programs with Mixed Free-Sign Variables," Operations Research, INFORMS, vol. 57(3), pages 701-713, June.
    9. Zhang, Bo & Yao, Tao & Friesz, Terry L. & Sun, Yuqi, 2015. "A tractable two-stage robust winner determination model for truckload service procurement via combinatorial auctions," Transportation Research Part B: Methodological, Elsevier, vol. 78(C), pages 16-31.
    10. Bo Zhang & Hongwei Ding & Hongbo Li & Wei Wang & Tao Yao, 2014. "A Sampling-Based Stochastic Winner Determination Model for Truckload Service Procurement," Networks and Spatial Economics, Springer, vol. 14(2), pages 159-181, June.
    11. Yossi Sheffi, 2004. "Combinatorial Auctions in the Procurement of Transportation Services," Interfaces, INFORMS, vol. 34(4), pages 245-252, August.
    12. John O. Ledyard & Mark Olson & David Porter & Joseph A. Swanson & David P. Torma, 2002. "The First Use of a Combined-Value Auction for Transportation Services," Interfaces, INFORMS, vol. 32(5), pages 4-12, October.
    13. Goossens, D.R. & Maas, A.J.T. & Spieksma, F.C.R. & van de Klundert, J.J., 2007. "Exact algorithms for procurement problems under a total quantity discount structure," European Journal of Operational Research, Elsevier, vol. 178(2), pages 603-626, April.
    14. S. L. Hakimi, 1964. "Optimum Locations of Switching Centers and the Absolute Centers and Medians of a Graph," Operations Research, INFORMS, vol. 12(3), pages 450-459, June.
    15. Ma, Zhong & Kwon, Roy H. & Lee, Chi-Guhn, 2010. "A stochastic programming winner determination model for truckload procurement under shipment uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 46(1), pages 49-60, January.
    16. Tsao, Yu-Chung & Lu, Jye-Chyi, 2012. "A supply chain network design considering transportation cost discounts," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(2), pages 401-414.
    17. Gail Hohner & John Rich & Ed Ng & Grant Reid & Andrew J. Davenport & Jayant R. Kalagnanam & Ho Soo Lee & Chae An, 2003. "Combinatorial and Quantity-Discount Procurement Auctions Benefit Mars, Incorporated and Its Suppliers," Interfaces, INFORMS, vol. 33(1), pages 23-35, February.
    18. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2017. "Linear Reformulation of Polynomial Discrete Programming for Fast Computation," INFORMS Journal on Computing, INFORMS, vol. 29(1), pages 108-122, February.
    19. Corberán, Ángel & Landete, Mercedes & Peiró, Juanjo & Saldanha-da-Gama, Francisco, 2019. "Improved polyhedral descriptions and exact procedures for a broad class of uncapacitated p-hub median problems," Transportation Research Part B: Methodological, Elsevier, vol. 123(C), pages 38-63.
    20. Han-Lin Li & Yao-Huei Huang & Shu-Cherng Fang, 2013. "A Logarithmic Method for Reducing Binary Variables and Inequality Constraints in Solving Task Assignment Problems," INFORMS Journal on Computing, INFORMS, vol. 25(4), pages 643-653, November.
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    Cited by:

    1. Fang Yang & Yao-Huei Huang, 2021. "An optimization approach for winner determination problem considering transportation cost discounts," Journal of Global Optimization, Springer, vol. 80(3), pages 711-728, July.
    2. Aghdas Badiee & Hamed Kalantari & Chefi Triki, 2023. "Leader-based diffusion optimization model in transportation service procurement under heterogeneous drivers’ collaboration networks," Annals of Operations Research, Springer, vol. 322(1), pages 345-383, March.

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