A bi-objective incomplete hub location-routing problem with flow shipment scheduling

In this paper, we introduce a flow shipment scheduling and hub location-routing problem in which the hub network is not fully interconnected, with the aim of maximizing the total amount of flow delivered by a predetermined latest arrival time and minimizing total fixed and routing costs. We present integer programming models to solve this problem in deterministic and stochastic environments when flow arrivals follow a piecewise linear form. A set of valid inequalities and preprocessing is suggested. An ε-constraint-based method and normalized weighted sum method are proposed to solve bi-objective problems. Furthermore, a case study on inter-province postal delivery system for the Islamic Republic of Iran Post Company and well-known test instances are used to evaluate the proposed models. Computational results show the viability of the models under different scenarios.