A Bi-Objective Robust Model for Location-Routing and Capacity Sharing in Districting Regions under Uncertainty

One of the most important approaches that can lead to the creation of various advantages for enterprises is the districting regions into the service offering locations and the demand units, which causes the increase in level of customers’ access to get the service. On the other hand, if vehicle routing is carried out in districting regions in order to deliver products to customers, the planning of customer service can be improved. However, in none of the research conducted in the area of design supply chain, vehicle routing in districting regions has been not investigated. Therefore, in the current study, a bi-objective mathematical model is presented to simultaneously focus on districting regions, facility location–allocation, service sharing, intra-district service transfer and vehicle routing. The first objective function is to minimize the total cost of designing the CLSC network, which includes costs of opening facility and vehicle routing. The second objective function is to minimize the maximum volume of surplus demand from service providers in order to achieve an appropriate balance in demand volume across all regions. Moreover, a robust optimization approach is used to take into account uncertainty in some parameters of the proposed model. In addition, the validity of the proposed mathematical model and the proposed solution on a real case study in the oil and gas industry has been investigated.