The Continuous Replenishment Inventory Routing Problem (CRIRP) is a special type of inventory routing problem (IRP) in which vehicle operations occur around the clock. The problem requires determining how many vehicles are needed to resupply the sites, which sites each vehicle should resupply, and the route that each vehicle should take. The objective is to minimize the number of vehicles. This technical report describes a special case of the CRIRP that is equivalent to the bin-packing problem. For the general problem, this report presents necessary and sufficient conditions for feasibility, a lower bound on the number of vehicles needed, and procedures for finding feasible solutions. These include solution construction heuristics and a genetic algorithm. We discuss the results of computational tests used to test the quality and computational effort of the heuristics. These results show that the route-building heuristic performs better than the other heuristics and the genetic algorithm.