Profit maximization in congested hub location problems: Demand models and service level constraints

Abstract

This study investigates a congested hub location problem with the aim of optimizing a service provider’s profit by determining hub locations, capacities, and prices for serving commodities. The study incorporates a price-dependent demand function with a general functional form and models hub operations as $M/G/1$ queueing systems to address congestion effects. The problem is initially formulated as a mixed-integer nonlinear program, which is subsequently transformed into a mixed-integer second-order cone program, demonstrating solvability with standard off-the-shelf solvers. Through numerical analysis, the study evaluates the influence of different demand functional forms and service time constraints on the optimal network configuration and the service provider’s profitability.