Periodic vehicle routing problem and time dependent vehicle routing problem are among the most practical logistic problems. Periodic vehicle routing problem is specially observed in urban logistics, since sometimes the customers require fulfilling their needs along a significant time period, not at one time together. On the other hand, in spite of the time being an inseparable part of urban traortation system, an appropriate model for the combination of the two mentioned problems has not been proposed and the existing problem solutions for periodic routing are utilized without their time-dependence taken into consideration so far. The present study aims to combine the two periodic vehicle routing and time dependent vehicle routing problems. Since these two problems are not combined in the available literature, the mathematical model presented in this paper is the first model for this problem. Due to the considered problem being NP-hard, three meta-heuristic TabuSA, VNSRRT, and TabuRRT are for solving the mathematical model. After the mathematical model is solved, it is revealed that which visiting days are selected for each customer and how the vehicles are designated to existing routes during those days. The utilized data for solving the presented mathematical model via proposed algorithms are the existing standard periodic vehicle routing problem’s data. Finally, the numerical results of utilized data are compared with each other and the acquired results are investigated and analyzed. It was revealed from numerical results investigation that the two meta-heuristic TabuSA and VNSRRT algorithms are more efficient than TabuRRT algorithm.