Bi-objective location routing problem with M/M/c queue system: Application in waste collection problem

In this model, economic objective (opening cost of depots and treatment facility and transportation cost regard to loading time and waiting time) and societal objective function; that is, negative effect, of treatment facilities which are close to towns, for waste collection problem is considered under uncertainty noticing congestion in the treatment facilities. Each treatment facilities are modeled as an M/M/c queuing system. Then locate depots and treatment facilities and design the routes starting from depots to serve customers. Also modified weighted-sum approach and maximize minimum approach is used to validate the proposed model with GAMS.