Bicycle-sharing programs have expanded rapidly in cities around the world over the past decade. Users can rent a bicycle from one docking station and return it to another, paying a small fee through a smartphone application. City officials promote these programs because they reduce traffic congestion and provide an affordable transportation option for short trips. However, operators face several practical difficulties. Bicycles tend to accumulate at stations located in lower areas of a city, because riders prefer traveling downhill. As a result, companies must hire trucks to redistribute bicycles to emptier stations, which increases operating costs. Some cities have introduced discounts for users who return bicycles to less crowded stations, encouraging riders themselves to keep the network balanced.