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

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Název: Stochastic profit maximization and pricing in hub location problems with elastic demand: Mathematical formulations and exact algorithms.
Autoři: Tran, Dung1 (AUTHOR), Azizi, Nader1 (AUTHOR) nader.azizi@ed.ac.uk, Archibald, Thomas Welsh1 (AUTHOR)
Zdroj: European Journal of Operational Research. Mar2026, Vol. 329 Issue 2, p498-517. 20p.
Témata: *PROFIT maximization, *PRICES, *STOCHASTIC models, *ELASTICITY (Economics), LOCATION problems (Programming), OPTIMIZATION algorithms, RELAXATION methods (Mathematics), DECOMPOSITION method
Abstrakt: • Proposed two-stage stochastic programs for capacitated and uncapacitated (max)HLPs with elastic and uncertain demand. • Proposed a flexible approach to model and solve (max)HLPs with different degrees of price-demand correlation. • Proposed enhanced Lagrangian relaxation and Benders decomposition algorithms to solve large instance of the problems. • Presented comprehensive computational results and discussed managerial insights. 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. [ABSTRACT FROM AUTHOR]
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Abstrakt:• Proposed two-stage stochastic programs for capacitated and uncapacitated (max)HLPs with elastic and uncertain demand. • Proposed a flexible approach to model and solve (max)HLPs with different degrees of price-demand correlation. • Proposed enhanced Lagrangian relaxation and Benders decomposition algorithms to solve large instance of the problems. • Presented comprehensive computational results and discussed managerial insights. 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. [ABSTRACT FROM AUTHOR]
ISSN:03772217
DOI:10.1016/j.ejor.2025.08.007