This research investigates the problem of resupplying points of dispensing (PODs), which will dispense medications to millions of people in case of a bioterrorist attack such as anthrax. After receiving an initial but limited supply of medication, the PODs will operate continuously. Vehicles will resupply the PODs continuously from a central depot that has a stockpile of medication. Each vehicle will repeatedly follow the same route and will deliver at each POD enough medication to replace what was consumed since the last visit. Because the number of drivers and trucks may be limited during an emergency, we wish to minimize the number of vehicles used to resupply the PODs. This thesis presents heuristics and a branch-and-bound approach for solving this NP-hard problem and evaluates their performance. We also analyze a special case in which all of the PODs have the same demand.