Residential buildings are large consumers of energy. They contribute significantly to the demand placed on the grid, particularly during hours of peak demand. Demand-side management is crucial to reducing this demand placed on the grid and increasing renewable utilisation. This research study presents a multi-objective tunable deep reinforcement learning algorithm for demand-side management of household appliances. The proposed tunable Deep Q-Network (DQN) algorithm learns a single policy that accounts for different preferences for multiple objectives present when scheduling appliances. These include electricity cost, peak demand, and punctuality. The tunable Deep Q-Network algorithm is compared to two rule-based approaches for appliance scheduling. When comparing the 1-month simulation results for the tunable DQN with an electricity cost rule-based benchmark method, the tunable DQN agent provides a statistically significant improvement of 30%, 18.2%, and 37.3% for the cost, peak power, and punctuality objectives. Moreover, the tunable Deep Q-Network can produce a range of appliance scheduling policies for different objective preferences without requiring any computationally intensive retraining. This is the key advantage of the proposed tunable Deep Q-Network algorithm for appliance scheduling.