Stochastic profit maximization and pricing in hub location problems with elastic demand: Mathematical formulations and exact algorithms

Dung Tran, Nader Azizi and Thomas Welsh Archibald

European Journal of Operational Research, 2026, vol. 329, issue 2, 498-517

Abstract: This paper addresses profit maximization and pricing in capacitated and uncapacitated single allocation hub location problems taking into account the uncertain and price-elastic demand. We formulate the problem as a two-stage stochastic program in which a finite set of discrete price values are used to derive the demand. The models aim to determine simultaneously the location of hubs, the allocation of nodes to the hubs, the pricing decisions and the routing of demand within the network in order to maximize profit. The mathematical formulations for small uncapacitated and capacitated problems can be solved to optimality by commercial solvers. To solve large instances, we develop a Benders decomposition algorithm and an enhanced Lagrangian relaxation technique. We conduct extensive computational experiments using two well-known hub location datasets and present numerical results and analysis along with managerial insights.

Keywords: Location; Profit maximisation in hub location problem; Two-stage stochastic programming; Benders decomposition; Lagrangian relaxation (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:329:y:2026:i:2:p:498-517

DOI: 10.1016/j.ejor.2025.08.007

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