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A Mixed-Integer Optimization Formulation for Buyers Formation

Authors: Dávila-Gálvez, Sebastián; Labbé, Martine; Marianov, Vladimir; Ordónẽz, Fernando; Semet, Frédéric;

A Mixed-Integer Optimization Formulation for Buyers Formation

Abstract

Companies frequently offer wholesale prices for their products that decrease with the number of purchased items. However, single buyers may not be willing or able to purchase large quantities of a single item. Nevertheless, consumers can form groups to purchase at wholesale prices, obtaining bargaining power. This practice can be extended from single products to bundles. We propose a mathematical model to create groups of buyers wishing to purchase product bundles optimally. Mixed-integer programming formulations are presented for the cases of non-increasing price and step price functions. A Benders decomposition formulation is proposed for step price functions to solve large instances. Computational experiments show the performance of the method for synthetic instances.

Country
France
Keywords

Coalition formation, Benders decomposition, Coalition formation MIP Benders decomposition, [INFO] Computer Science [cs], MIP

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    popularity
    This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
    Average
    influence
    This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
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    impulse
    This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
1
Average
Average
Average
Green