Algorithms for min-buying in networks

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Bibliographic Details
Main Authors:	Bhardwaj, Aaditya, Black, Ben, Dokka, Trivikram, Kirkbride, Christopher
Format:	Preprint
Published:	2025
Subjects:	Optimization and Control
Online Access:	Acceder al recurso
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author	Bhardwaj, Aaditya Black, Ben Dokka, Trivikram Kirkbride, Christopher
author_facet	Bhardwaj, Aaditya Black, Ben Dokka, Trivikram Kirkbride, Christopher
contents	The paper is motivated by pricing decisions faced by forecourt fuel retailers across their outlets on a road network. Through our modelling approach we are able adapt the network structure to a bipartite graph with demand nodes representing volumes of fuel from customers using a specific route that connects to the seller's outlet nodes that intersect that route on the network. Customers may have their demand satisfied at the lowest priced competitor on their route. However, the seller can satisfy some or all of this demand by matching or beating this price via one of their outlets intersecting the route. We give a practical extension to min-pricing by considering a binary logit variant for buyers evaluating the choice between two sellers. We derive two MIP formulations for min-buying in the case of general demand. We also propose several constructive heuristics, based on insertion and selection operations, suitable for problem instances beyond the scope of the exact methods. The performance of models and algorithms are evaluated in a numerical study and develop insights from the results. Importantly, we are able to highlight the value of price-matching decisions under buyer demand sensitivity.
format	Preprint
id	arxiv_https___arxiv_org_abs_2502_14459
institution	arXiv
publishDate	2025
record_format	arxiv
spellingShingle	Algorithms for min-buying in networks Bhardwaj, Aaditya Black, Ben Dokka, Trivikram Kirkbride, Christopher Optimization and Control The paper is motivated by pricing decisions faced by forecourt fuel retailers across their outlets on a road network. Through our modelling approach we are able adapt the network structure to a bipartite graph with demand nodes representing volumes of fuel from customers using a specific route that connects to the seller's outlet nodes that intersect that route on the network. Customers may have their demand satisfied at the lowest priced competitor on their route. However, the seller can satisfy some or all of this demand by matching or beating this price via one of their outlets intersecting the route. We give a practical extension to min-pricing by considering a binary logit variant for buyers evaluating the choice between two sellers. We derive two MIP formulations for min-buying in the case of general demand. We also propose several constructive heuristics, based on insertion and selection operations, suitable for problem instances beyond the scope of the exact methods. The performance of models and algorithms are evaluated in a numerical study and develop insights from the results. Importantly, we are able to highlight the value of price-matching decisions under buyer demand sensitivity.
title	Algorithms for min-buying in networks
topic	Optimization and Control
url	https://arxiv.org/abs/2502.14459

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