Scheduling Technicians Based On Distance To Customer

I need to dispatch 10 technicians across the US starting each Monday. They go to 10 different customers for the whole week. I know the distance between each technician and each customer. What I would like to do is assign each technician to a customer so that the total distance traveled for all the technicians is minimized. I know that if it was only 3 techs and 3 customers (as an example), I could build a table of all the possible combinations (3 factorial or 6 permutations), determine the distance for each permutation and select the minimum. I'm not sure that doing this method with 10 techs is feasible as the number of permutations is 10 factorial or over 3 million possibilities. Anyone see a workable solution?

I've include a spreadsheet with customers, technicians and the distances between them!