A multi-modal competitive hub location pricing problem with customer loyalty and elastic demand

• Published in: Computers & operations research 2020-11, Vol.123, p.105048, Article 105048
• Main Authors: Mahmoodjanloo, Mehdi, Tavakkoli-Moghaddam, Reza, Baboli, Armand, Jamiri, Atefeh
• Format: Article
• Language: English
• Subjects: Brand loyalty; Computer Science; Customer loyalty; Customer services; Customers; Decisions; Elastic demand; Hub location; Integer programming; Logit models; Lower bounds; Mixed integer; Multi-modal transportation; Operations Research; Postal services; Pricing; Search algorithms; Solution space; Transportation services; Transportation systems
• ISSN: 0305-0548; 0305-0548; 1873-765X
• DOI: 10.1016/j.cor.2020.105048

[Display omitted] •Considering elastic demands and customer loyalty in a hub location-pricing problem.•Deriving a closed-form expression for the pricing problem with inelastic demands.•Deriving the upper and lower bounds of the prices when the demands are elastic.•Decomposing the proposed model to a hub location problem and a pricing problem.•Proposing two nested evolutionary algorithms to tackle the bi-level structure. This paper develops a multi-modal competitive hub location pricing problem whose target is the design of a transportation system for a company that plans to enter into a market with elastic demand, in which an existing transportation company operates its hub-and-spoke network. The entrant company aims to attract customers in the market by convenient locations for its hubs and proper pricing of its transportation services, while customer loyalty is different in the nodes. Hence, mixed-integer programming based on a multi-nominal logit model is proposed. Thereafter, to solve the single allocation hub-and-spoke model, it is decomposed into a bi-level model. In the new structure, the master problem is associated with hub location and assignment decisions, and the sub-problem is associated with pricing decisions. Moreover, upper and lower bounds are calculated to determine the price of transportation routes. Finally, based on a nested approach, a scatter search algorithm is used to search the solution space of the master problem, and a matheuristic method is designed to solve the pricing problem interactively. The proposed approach is employed to solve a case study in the postal service industry of Iran.