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An overview of Stackelberg pricing in networks

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  • van Hoesel, Stan

Abstract

The Stackelberg pricing problem has two levels of decision making: tariff setting by an operator, and then selection of the cheapest alternative by customers. In the network version, an operator determines tariffs on a subset of the arcs that he owns. Customers, who wish to connect two vertices with a path of a certain capacity, select the cheapest path. The revenue for the operator is determined by the tariff and the amount of usage of his arcs. The most natural model for the problem is a (bilinear) bilevel program, where the upper level problem is the pricing problem of the operator, and the lower level problem is a shortest path problem for each of the customers. This paper contains a compilation of theoretical and algorithmic results on the network Stackelberg pricing problem. The description of the theory and algorithms is generally informal and intuitive. We redefine the underlying network of the problem, to obtain a compact representation. Then we describe a basic branch-and-bound enumeration procedure. Both concepts are used for complexity issues and for the development of algorithms: establishing NP-hardness, approximability, special cases solvable in polynomial time, and an efficient exact branch-and-bound algorithm.

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  • van Hoesel, Stan, 2008. "An overview of Stackelberg pricing in networks," European Journal of Operational Research, Elsevier, vol. 189(3), pages 1393-1402, September.
    • Handle: RePEc:eee:ejores:v:189:y:2008:i:3:p:1393-1402
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    Cited by:

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    2. Martine Labbé & Alessia Violin, 2016. "Bilevel programming and price setting problems," Annals of Operations Research, Springer, vol. 240(1), pages 141-169, May.
    3. Dong, Baomin & Guo, Guixia & Wang, Yuntong, 2012. "Highway toll pricing," European Journal of Operational Research, Elsevier, vol. 220(3), pages 744-751.
    4. Tawfik, Christine & Gendron, Bernard & Limbourg, Sabine, 2022. "An iterative two-stage heuristic algorithm for a bilevel service network design and pricing model," European Journal of Operational Research, Elsevier, vol. 300(2), pages 512-526.
    5. François Gilbert & Patrice Marcotte & Gilles Savard, 2015. "A Numerical Study of the Logit Network Pricing Problem," Transportation Science, INFORMS, vol. 49(3), pages 706-719, August.
    6. Juan M. C. Larrosa, 2014. "Non cooperative Stackelberg network formation," Revista Cuadernos de Economia, Universidad Nacional de Colombia, FCE, CID, August.
    7. Yang, Dong & Jiao, Jianxin (Roger) & Ji, Yangjian & Du, Gang & Helo, Petri & Valente, Anna, 2015. "Joint optimization for coordinated configuration of product families and supply chains by a leader-follower Stackelberg game," European Journal of Operational Research, Elsevier, vol. 246(1), pages 263-280.
    8. Ivan Eryganov & Radovan Šomplák & Dušan Hrabec & Josef Jadrný, 2023. "Bilevel programming methods in waste-to-energy plants' price-setting game," Operational Research, Springer, vol. 23(2), pages 1-37, June.
    9. Christine Tawfik & Sabine Limbourg, 2018. "Pricing Problems in Intermodal Freight Transport: Research Overview and Prospects," Sustainability, MDPI, vol. 10(9), pages 1-22, September.
    10. Pferschy, Ulrich & Nicosia, Gaia & Pacifici, Andrea & Schauer, Joachim, 2021. "On the Stackelberg knapsack game," European Journal of Operational Research, Elsevier, vol. 291(1), pages 18-31.
    11. Eltoukhy, Abdelrahman E.E. & Wang, Z.X. & Chan, Felix T.S. & Fu, X., 2019. "Data analytics in managing aircraft routing and maintenance staffing with price competition by a Stackelberg-Nash game model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 122(C), pages 143-168.
    12. Shuang Ma & Gang Du & Jianxin (Roger) Jiao & Ruchuan Zhang, 2016. "Hierarchical game joint optimization for product family-driven modular design," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 67(12), pages 1496-1509, December.

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