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This paper presents a biased random-key genetic algorithm designed to solve the open vehicle routing problem with capacity and distance constraints. Consider a depot from which vehicles depart to deliver goods demanded by clients. Every client is served by one vehicle that is part of a homogeneous fleet. The vehicles initiate their routes at the depot and finish them after servicing the last client without returning to the depot. The problem’s objective function is to minimize the total distance traveled by the vehicles while respecting the capacity and maximum distance constraints. The potential applications in real life scenarios make this problem relevant among other vehicle routing problems. Three sets of benchmark problems from the literature are used to test the proposed algorithm. The obtained results show the algorithm’s good performance since the best-known solutions for 16 of the 30 instances were improved.