Virtualization is a core 5G network technology which helps telecom companies significantly reduce capital expenditure and operating expenses by deploying multiple services on the same hardware infrastructure. However, providing QoS-guaranteed services for multi-tenants poses a significant challenge due to multi-tenant service diversity. Network slicing has been proposed as a means of addressing this problem by isolating computing and communication resources for the different tenants of different services. However, optimizing the allocation of the network and computation resources across multiple network slices is a critical but extremely difficult problem. Accordingly, this study proposes two heuristic algorithms, namely Minimum Cost Resource Allocation (MCRA) and Fast Latency Decrease Resource Allocation (FLDRA), to perform dynamic path routing and resource allocation for multi-tenant network slices in a two-tier architecture. The simulation results show that both algorithms significantly outperform the Upper-tier First with Latency-bounded Overprovisioning Prevention (UFLOP) algorithm proposed in previous work. Furthermore, the MCRA algorithm achieves a higher resource utilization than the FLDRA algorithm.