1- Corresponding Author 1 Modeling and solving Bi-objective Periodic location routing problem with soft time window

This paper for the first time reflects on bi-objective periodic Location-routing problem with multi and capacitated depots based on soft time window (PLRPSTW). In bi-objective PLRPSTW demand meeting in each costumer is numerous times in given planning horizon instead of once and only in one day. Second objective function wants to minimize maximum summation of traveling time and service time for supplying service level and increasing system effectiveness. In addition, each costumer has to be served in pre-specified time interval, which is contemplated by them. Periodic feature beside of the bi-objective specific causes previously condition is closed to the real world and it can be used in the practical context of logistic and supply chain management. The existing research advises mixed integer linear programming model for bi-objective PLRPSTW with capacitated depots. For solving some optimality instances, augmented ε-constraint approach in the GAMS is used.