In this paper, we describe and compare serial, parallel, and distributed solver implementations for large batches of Traveling Salesman Problems using the Lin-Kernighan Heuristic (LKH) and the Concorde exact TSP Solver. Parallel and distributed solver implementations are useful when many medium to large size TSP instances must be solved simultaneously. These implementations are found to be straightforward and highly efficient compared to serial implementations. Our results indicate that parallel computing using hyper-threading for solving 150- and 200-city TSPs can increase the overall utilization of computer resources up to 25 percent compared to single thread computing. The resulting speed-up/physical core ratios are as much as ten times better than a parallel and concurrent version of the LKH heuristic using SPC3 in the literature. We illustrate our approach with an application in the design of order picking warehouses.